Measurement of DC Voltage on One Analog Input

1. Aim

To measure a DC voltage using one selected analog input of SEELab3/ExpEYES (A1, A2, or A3) with respect to GND.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Connecting wires
• A DC source (single cell, battery pack, PV1/PV2, or lab supply)
• A PC, Laptop, or Android Phone with SEELab3 software

3. Theory & Principle

The analog inputs of SEELab3 act as digital voltmeters (12 bit resolution).

Use only one input at a time for now:

• A1 or A2: wider range, typically about $\pm16V$, but can also measure smaller signals down to $\pm250mV$ using the built-in amplifier.
• A3: higher input impedance and better low-voltage use. Fixed range of $\pm3.3V$

Always measure voltage with respect to GND: \(V_{\text{measured}} = V(\text{Input}) - V(\text{GND})\)

4. Circuit Diagram / Setup

1. Select one channel: A1 (or A2 or A3).
2. Connect source negative to GND.
3. Connect source positive to the selected input.
4. Open the voltage-measurement tool in software.

5. Procedure

1. Start with a small DC source (for example, a 1.5V cell).
2. Note the reading on the selected input.
3. Reverse leads once to observe sign change (+V becomes -V).
4. For batteries in series:
   • Measure one cell.
   • Then measure two cells in series.
   • Then measure three cells in series (if expected value is within channel limit).
5. In the mobile app, you can select the voltage range by clicking on the range button at the top right corner of the graph.
6. Record all readings and compare with expected sums.

6. Observation Table

7. Error Analysis

Possible causes of small mismatch:

• Source internal resistance: meter loading can reduce measured voltage if it’s a very weak source.
• Input impedance effect: A1/A2 (about $1M\Omega$) load more than A3 (about $10M\Omega$).
• ADC resolution and offset: small quantization and zero-offset errors are normal.

8. Results and Discussion

• DC voltage was measured correctly on one selected input.
• Series battery voltages approximately added: \(V_{\text{series}} \approx V_1 + V_2 (+V_3)\)
• A3 generally shows less loading error for high-resistance sources.

9. Precautions

1. Voltage limits are critical:
   • A1, A2: keep within about $\pm16V$
   • A3: keep within about $\pm3.3V$
2. Battery checks:
   • 1 cell (AA): ~1.2 to 1.6V
   • 2 cells in series: ~2.4 to 3.2V (safe on A3, near upper side for fresh cells)
   • 3 cells in series: ~3.6 to 4.8V (do not use A3, use A1/A2)
3. Use common GND.
4. Do not leave input floating during observation .

10. Troubleshooting

Measuring Resistance

1. Aim

To measure an unknown resistance connected between SEN and GND using SEELab/ExpEYES.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Resistors (typical range: 100 ohm to 100 kohm)
• Connecting wires
• PC/Laptop/Android phone with SEELab software

3. Theory & Principle

Inside ExpEYES, SEN is connected to 3.3V through an internal 5.1 kohm resistor. When an unknown resistor R is connected from SEN to GND, a voltage divider is formed.

Hence, \(R=5100\cdot\frac{V_{SEN}}{3.3-V_{SEN}}\)

Best accuracy is obtained when R is of the same order as 5.1 kohm.

4. Circuit Diagram / Setup

1. Connect one terminal of unknown resistor to SEN.
2. Connect other terminal to GND.
3. Open “Measure Resistance” in software/app.

5. Procedure

1. Start with a known resistor (for example 1 kohm) for verification.
2. Note displayed resistance.
3. Repeat for 470 ohm, 2.2 kohm, 10 kohm, 47 kohm.
4. Compare measured and nominal values.
5. For unknown resistor, repeat measurement 3 times and average.

6. Observation Table

7. Series and Parallel Combinations

Use two known resistors (example: R1 = 1 kohm, R2 = 2.2 kohm) and verify equivalent resistance.

For series: \(R_{series}=R_1+R_2\)

For parallel: \(R_{parallel}=\frac{R_1R_2}{R_1+R_2}\)

Procedure:

1. Measure R1 and R2 individually.
2. Connect R1 and R2 in series between SEN and GND, then measure.
3. Connect R1 and R2 in parallel between SEN and GND, then measure.
4. Compare measured equivalents with calculated values.

8. Advanced: Manual Calculation from SEN Voltage

If software shows V_SEN, calculate R manually using: \(R=5100\cdot\frac{V_{SEN}}{3.3-V_{SEN}}\)

Example: if V_SEN = 1.65V, \(R=5100\cdot\frac{1.65}{1.65}=5100\ \Omega\)

9. Error Analysis

• Measurement is less accurate at very low (<<100 ohm) or very high (>>100 kohm) resistance.
• Lead/contact resistance affects low-value measurements.
• Internal resistor tolerance and ADC resolution introduce small errors.

10. Precautions

1. Keep resistor leads firm and clean.
2. Do not apply external voltage directly to SEN in this experiment.
3. Use dry fingers / insulated clips; finger touch may alter high values.

11. Troubleshooting

Measuring Capacitance

1. Aim

To measure capacitance connected between IN1 and GND, and study how geometry affects capacitance.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Capacitors of known values
• Connecting wires / crocodile clips
• Two foil plates + paper/plastic sheet (for homemade capacitor)
• PC/Laptop/Android phone with SEELab software

3. Theory & Principle

Capacitance is defined as: \(C=\frac{Q}{V}\)

SEElab measures small capacitances (pF and nF ranges) by charging with a constant current source and measuring the voltage rise produced. Q is the product of C and V, and Q can be calculated as a product of this constant current and the time spent charging. For a parallel-plate capacitor: \(C\propto\frac{A}{d}\) More explicitly (same dielectric): \(C = \epsilon \frac{A}{d}\) where A is plate overlap area and d is separation.

For larger values, it charges the capacitor via a built-in 10K resistor whilst simultaneously capturing the capacitor voltage using the oscilloscope. All this magic happens internally, and the capacitance value is extracted after fitting the charging curve to an appropriate function to extract the time constant.

Mobile App

Photo with ExpEYES17

4. Circuit Diagram / Setup

1. Connect capacitor between IN1 and GND.
2. Open the “Measure Capacitance” tool and trigger measurement.
3. Repeat with different capacitors.

5. Procedure

1. Measure known capacitors and record values.
2. Build a parallel-plate capacitor using foil-paper-foil.
3. Measure capacitance for full overlap.
4. Reduce overlap area gradually and re-measure.
5. Compare trends in measured values.

6. Observation Table

7. Advanced: Area Dependence Check

For same dielectric and separation: \(\frac{C_2}{C_1} \approx \frac{A_2}{A_1}\)

Example: if overlap area is reduced to half, measured capacitance should be approximately half.

8. Error Analysis

• Stray capacitance of wires and surroundings affects small-capacitance readings.
• Touching plates with fingers adds parallel leakage paths and body capacitance.
• Poor clip contacts and unstable setup can cause fluctuations.

9. Precautions

1. Do not touch capacitor plates during measurement.
2. Keep leads short for pF-range measurements.
3. Ensure capacitor is discharged before reconnecting.
4. Use firm clips and avoid movement while reading.

10. Troubleshooting

Measurement of DC Voltages on A1, A2, and A3

1. Aim

To measure and display DC voltages applied to the analog input terminals (A1, A2, and A3) of the SEELab3/ExpEYES device and to observe voltage variations over time.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Connecting wires
• A regulated DC power source (e.g., PV1, PV2, or a battery/cell)
• A PC, Laptop, or Android Phone with SEELab3 software

3. Theory & Principle

The analog inputs A1, A2, and A3 on the SEELab3 function as digital voltmeters.

• A1 and A2: Designed for general purpose use with a wider input range (typically $\pm 16V$).
• A3: Optimized for high sensitivity with a smaller range (typically $\pm 3.3V$).

The device utilizes an Analog-to-Digital Converter (ADC) to translate continuous voltage levels into digital values. In “Multimeter” mode, the software displays instantaneous values. In “Oscilloscope” or “Plot” mode, it tracks these values over time ($t$), allowing you to visualize the stability of a DC source.

4. Circuit Diagram / Setup

1. Connect the Ground (GND) terminal of the SEELab3 to the negative terminal of the voltage source.
2. Connect the positive terminal of the voltage source to the A1, A2, or A3 input.
3. Self-Test: You can connect PV1 to A1 to measure the voltage generated by the SEELab3 device itself.

5. Procedure

1. Open the SEELab3 software and select the “Measure Voltages” or “Multimeter” experiment.
2. Instantaneous View: Observe the live digital display for each channel. If using PV1 as a source, adjust the slider and watch the reading on A1 change accordingly.
3. Time-Domain View: Switch to the “Plot” or “Oscilloscope” mode.
4. Observe the horizontal trace. A steady DC voltage should appear as a perfectly flat line.
5. Sensitivity Check: Connect a small 1.5V cell to A3 and then to A1 to compare the precision of the readings.

6. Observation Table

7. Error Analysis

While digital voltmeters are highly accurate, small discrepancies can occur due to:

• Resolution Limits: The ADC has a finite number of bits. On a $16V$ range, a 12-bit ADC has a resolution of roughly $16/4096 \approx 4\text{ mV}$. Changes smaller than this cannot be detected.
• Input Impedance: A1 and A2 typically have an input impedance of $1\text{ M}\Omega$. If measuring a source with very high internal resistance, the voltmeter itself might “load” the circuit, causing a lower voltage reading.
• Zero Offset: Even with no input, the software might show a few millivolts (e.g., $0.003V$). This is a common calibration offset.

8. Results and Discussion

• The DC voltages applied to inputs A1, A2, and A3 were measured accurately.
• The software plotting feature allowed for the observation of voltage stability over the measured time interval.
• It was observed that A3 provides higher precision for low-voltage signals compared to A1.

9. Precautions

1. Voltage Limits: Do not exceed $\pm 16V$ on A1/A2. Exceeding $\pm 3.3V$ on A3 may clip the signal or trigger protection circuits.
2. Common Ground: The measurement is always relative to GND. Ensure the ground is common between the source and the SEELab.
3. Input Floating: If nothing is connected to an input, it may “float” and show random, rapidly changing values due to electromagnetic interference.

10. Troubleshooting

Study of Light Dependent Resistor (LDR)

1. Aim

To study variation of LDR resistance with light intensity using SEN and GND.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• LDR
• Connecting wires
• Light source (phone torch / LED lamp)
• PC/Laptop/Android phone with SEELab software

3. Theory & Principle

LDR resistance decreases when light intensity increases.

In this experiment, LDR is connected between SEN and GND. Internally, SEN is connected to 3.3V through 5.1 kohm. From measured V_SEN, LDR resistance is: \(R_{LDR}=5100\cdot\frac{V_{SEN}}{3.3-V_{SEN}}\)

Lower light -> higher R_LDR -> higher V_SEN trend depends on divider orientation; verify experimentally.

4. Circuit Diagram / Setup

1. Connect LDR between SEN and GND.
2. Open resistance/LDR measurement screen in software.
3. Ensure ambient light condition is stable before taking readings.

5. Procedure

1. Record reading in room light.
2. Increase light on LDR (torch close to LDR) and record reading.
3. Reduce light (cover partly or move source away) and record reading.
4. Repeat for multiple light levels.
5. Plot R_LDR vs relative light level (low/medium/high) or lux (if lux meter is available).

6. Observation Table

7. Advanced: Sensitivity Estimation

Estimate change ratio: \(\text{Sensitivity ratio}=\frac{R_{\text{dark}}}{R_{\text{bright}}}\)

Larger ratio indicates better light sensitivity.

If multiple points are taken, a log plot (\log R vs \log L) can be used to estimate empirical exponent: \(R\propto L^{-k}\)

8. Error Analysis

• Ambient light fluctuations cause drift.
• Sensor heating or light-source flicker changes reading.
• Shadows and angle of incidence affect effective illumination.

9. Precautions

1. Keep light source distance fixed for repeated trials.
2. Avoid hand shadow while recording.
3. Wait 1-2 seconds after changing light before reading.
4. Do not apply external voltage directly to SEN.

10. Troubleshooting

Lemon Cell Experiment

1. Aim

To construct a lemon cell and measure the EMF produced by different metal electrode pairs using one SEELab input channel.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Connecting wires / crocodile clips
• 1-2 lemons (or any acidic fruit)
• Common metal electrodes (for example: Zinc nail, Copper strip/coin, Iron nail, Aluminium strip)
• A PC, Laptop, or Android Phone with SEELab3 software

3. Theory & Principle

A lemon acts as an electrolyte. Two dissimilar metals inserted into the lemon form a galvanic cell.
The open-circuit voltage (EMF) depends on the electrode pair and electrolyte condition.

For this experiment, use one channel (A1 or A3) and measure with respect to GND.

Expected EMF trend follows metal reactivity difference:

• larger reactivity difference -> higher EMF
• copper is commonly used as the positive electrode in these pairs

Always measure voltage with respect to GND: \(V_{\text{measured}} = V(\text{Input}) - V(\text{GND})\)

4. Circuit Diagram / Setup

1. Select one input channel (A1 recommended; A3 is also fine here).
2. Insert two different metal electrodes into the lemon, separated by ~2-3 cm.
3. Connect the electrode expected to be negative (e.g., zinc) to GND.
4. Connect the other electrode (e.g., copper) to the selected input.
5. Open DC voltage measurement in the SEELab software/app.

5. Procedure

1. Start with the Zn-Cu pair and note the voltage.
2. Swap leads once and confirm sign reversal.
3. Repeat with other pairs (Fe-Cu, Al-Cu, Zn-Fe, etc.).
4. For each pair, wait 5-10 seconds for reading to stabilize and record value.
5. Optional: connect two lemon cells in series and verify voltage addition.

Mobile App

Desktop App

6. Observation Table

7. Reference EMF Values (Common Metals)

Approximate standard electrode potentials (vs SHE, at 25 C):

Approximate ideal EMF for common pairs (difference of $E^\circ$):

In real lemon cells, measured values are usually lower due to internal resistance, polarization, oxide layers, and non-standard ion concentrations.

8. Advanced: Estimating Internal Resistance of Lemon Cell

Model the lemon cell as an ideal source $E$ in series with internal resistance $r$.

When connected to a voltmeter of input resistance $R_{in}$, measured terminal voltage is: \(V = E\cdot\frac{R_{in}}{r+R_{in}}\)

For this experiment:

• A1 input resistance $R_{A1}\approx1M\Omega$
• A3 input resistance $R_{A3}\approx10M\Omega$

Steps

1. Build one lemon cell (for example Zn-Cu).
2. Measure open terminal voltage with A1: call it $V_{A1}$.
3. Measure same cell with A3: call it $V_{A3}$.
4. Use the formula below to estimate $r$.

From two readings: \(r=\frac{R_{A1}R_{A3}(V_{A3}-V_{A1})}{V_{A1}R_{A3}-V_{A3}R_{A1}}\)

Then estimate EMF: \(E=V_{A1}\left(1+\frac{r}{R_{A1}}\right)\)

Worked Example

Suppose measured values are:

• $V_{A1}=0.60V$
• $V_{A3}=0.90V$

Using $R_{A1}=1M\Omega$, $R_{A3}=10M\Omega$: \(r=\frac{(1)(10)(0.90-0.60)}{(0.60)(10)-(0.90)(1)}M\Omega =\frac{3}{5.1}M\Omega\approx0.588M\Omega\)

So internal resistance is about: \(r\approx5.9\times10^5\Omega\)

Now EMF: \(E\approx0.60\left(1+\frac{0.588}{1}\right)\approx0.95V\)

9. Error Analysis

Possible causes of small mismatch:

• Electrode surface condition: rust/oxide layer reduces effective EMF.
• Electrolyte variability: acidity differs from lemon to lemon.
• Internal resistance: lemon cell has high internal resistance, especially under load.
• Input loading: A3 (about $10M\Omega$) disturbs weak sources less than A1/A2 (about $1M\Omega$).

10. Results and Discussion

• Different metal pairs produced different EMF values.
• Pairs with larger reactivity difference generally gave higher voltage (e.g., Zn-Cu > Zn-Fe).
• For two lemon cells in series, total voltage approximately added: \(V_{\text{total}} \approx V_1 + V_2\)

11. Precautions

1. Keep electrode tips clean for repeatable readings.
2. Do not let electrodes touch each other inside the lemon.
3. Use common GND reference and firm connections.

12. Troubleshooting

Measurement of AC Resistance / Impedance of the Human Body

1. Aim

To estimate the human body’s AC impedance using SEELab3 with an AC source (WG) and the built-in high input impedance at A2.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Connecting wires and two metal electrodes (coins/plates/strips)
• PC / Laptop / Android with SEELab3 software

3. Theory & Principle

This is a measurement using a voltage divider model:

• The human body behaves like an impedance $Z_{body}$.
• The SEELab3 input at A2 has a known input impedance $R_{in}$, typically about $1\text{ M}\Omega$.

Let:

• $V_{A1}$ = RMS voltage at A1 (across the whole divider)
• $V_{A2}$ = RMS voltage at A2 (across $R_{in}$)

Current through the series path is: \(I=\frac{V_{A2}}{R_{in}}\)

Voltage across the body is: \(V_{body}=V_{A1}-V_{A2}\)

So the estimated impedance is: \(Z_{body}=\frac{V_{body}}{I}=(V_{A1}-V_{A2})\cdot\frac{R_{in}}{V_{A2}}\)

For comparison/learning (at moderate frequency like 1000 Hz), $Z_{body}$ can be reported in kilo-ohms.

4. Circuit Diagram / Setup

1. Connect the AC source WG (sine wave) to one electrode and also to A1 for monitoring.
2. Connect the other electrode to A2.
3. Ensure SEELab3 GND reference is correctly wired (as per your hardware).
4. Keep electrode contact area similar between trials.

5. Procedure

1. Launch the SEELab3 app and open the AC resistance / impedance measurement screen (or oscilloscope/plot mode with $V_{rms}$ readouts).
2. Set:
   • WG frequency = 1000 Hz
   • WG amplitude = start with a moderate value so RMS voltages stay within A1/A2 range.
3. Enable analysis/readout for:
   • A1 (input RMS)
   • A2 (output RMS)
4. Touch the electrodes with intact skin and hold contact stable for 3–5 seconds.
5. Record:
   • $V_{A1,\text{rms}}$
   • $V_{A2,\text{rms}}$
6. Calculate $Z_{body}$ using $R_{in}=1\text{ M}\Omega$: \(Z_{body}=(V_{A1}-V_{A2})\cdot\frac{10^6}{V_{A2}}\)
7. Repeat for different contact conditions (dry, wet, increased contact area).

6. Observation Table

Reference: $R_{in} = 1.0\text{ M}\Omega$

7. Precautions

1. Use only the low voltage AC output from SEELab3 (WG). Never connect to AC mains.
2. Do not touch with cut/bruised skin or if you have any wound.
3. Keep contact stable to avoid large fluctuations.

8. Error Analysis

• At AC frequencies, the body impedance includes non-resistive components (skin capacitance), so $Z_{body}$ is an approximation.
• Contact pressure and contact area change $Z_{body}$ during measurement.
• Noise/trigger settings can affect RMS estimation.

9. Troubleshooting

Measurement of DC Resistance of the Human Body

1. Aim

To measure the electrical resistance offered by the human body to a DC voltage using the SEELab3/ExpEYES toolkit and to observe how physical conditions like moisture and contact area affect this value.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 Test & Measurement Tool
• Set of connecting wires
• A PC, Laptop, or Android Phone with SEELab3 software installed
• Metal coins (optional, to test the effect of surface area)

3. Theory & Principle

The human body acts as a conductor, though it offers significant resistance primarily due to the dry outer layer of the skin (stratum corneum). In this experiment, the body is treated as a component in a Potential Divider Network.

The SEELab3 device has a known internal input impedance ($R_{in}$) at the A2 terminal, typically $1\text{ M}\Omega$. When you connect your body between the voltage source (PV1) and the input terminal (A2), the voltage measured at A2 ($V_{A2}$) is determined by:

By measuring the voltage drop, the software calculates $R_{body}$ using Ohm’s Law. For example, if your body offers exactly $1\text{ M}\Omega$ of resistance, the voltage at A2 will be exactly half of the voltage supplied by PV1.

4. Circuit Diagram / Setup

1. Connect a wire from PV1 to A1 to monitor the source voltage.
2. Connect a second wire to PV1 and hold its metal tip firmly with your left hand.
3. Connect a third wire to A2 and hold it with your right hand.
4. The circuit is completed through your chest and arms, flowing from PV1 to A2.

5. Procedure

1. Launch the SEELab3 software and navigate to the “DC Resistance of Human Body” experiment.
2. Hold the bare end of the PV1 wire in one hand and the A2 wire in the other.
3. Observe the resistance value displayed on the software interface.
4. Test for Surface Area: Place a metal coin between your fingers and the wire tips to increase the contact area and note the change.
5. Test for Moisture: Dampen your fingertips slightly with water and repeat the measurement.

6. Observation Table

Reference Impedance ($R_{in}$): $1.0\text{ M}\Omega$

7. Error Analysis

• Contact Pressure: Variable pressure on the wire tips changes the effective contact area, leading to fluctuating resistance values.
• Internal Impedance Tolerance: The $1\text{ M}\Omega$ internal resistance of A2 may have a $\pm 1\%$ tolerance, which directly affects the calculated $R_{body}$.
• Sweat and Electrolytes: Natural salts on the skin can create a parallel conductive path, making the “dry” reading vary significantly between different individuals.

8. Results and Discussion

• The DC resistance of the human body was found to be approximately ____ $M\Omega$ under normal dry conditions.
• Observation on Area: Increasing the contact area using coins decreased the measured resistance. This follows the formula $R = \rho L/A$.
• Observation on Moisture: Wetting the hands decreased the resistance significantly, as water provides a much better conductive path through the skin’s surface.

9. Precautions

1. Consistent Contact: Ensure the wires make firm contact with the skin; loose contact will lead to erratic resistance calculations.
2. Voltage Safety: Use only the low-voltage DC outputs (PV1) provided by the SEELab3. Never connect the inputs to AC mains.
3. Software Selection: Ensure the correct hardware model is selected in the software settings so the internal $1\text{ M}\Omega$ impedance is correctly factored.

10. Troubleshooting

Capturing AC Pickup from Domestic Wiring

1. Aim

To demonstrate the presence of electromagnetic fields around domestic electrical wiring and to observe the induced AC signal using a long wire as an antenna.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• A long flexible wire (approx. 1–2 meters)
• PC, Laptop, or Smartphone with SEELab3 software

3. Theory & Principle

All current-carrying conductors in our domestic wiring (carrying 230V, 50Hz AC) create a weak, oscillating electromagnetic field in their surroundings. This field is a form of “Electromagnetic Interference” (EMI).

When a long wire is connected to a high-impedance input like A1, it acts as a Receiving Antenna. The changing magnetic and electric fields from the room’s wiring induce a tiny alternating voltage in this wire.

The human body also acts as a large conductor. When you touch the tip of the wire, your body effectively increases the “antenna surface area,” significantly increasing the magnitude of the induced 50Hz signal (or 60Hz depending on your region).

4. Circuit Diagram / Setup

1. Connect one end of a long wire to the A1 input.
2. Leave the other end of the wire free (ensure it is not touching GND or any other terminal).
3. Ensure the SEELab3 is connected to your computer or phone and the software is running.

5. Procedure

1. Open the SEELab3 software and select the “Oscilloscope” tool.
2. Enable the trace for A1 and set the “Timebase” to 10 ms/div or 20 ms/div.
3. Observe the waveform on the screen. Even with the wire hanging freely, you may see a small 50Hz sine wave.
4. Increase Pickup: Touch the bare metal tip of the long wire with your finger. Observe the immediate increase in the amplitude of the sine wave.
5. Frequency Check: Use the software’s “Measure” or “Frequency” tool to verify that the captured signal is exactly 50 Hz (or 60 Hz).
6. Power Source Test: Observe the difference in amplitude when your laptop is running on battery versus when it is plugged into the wall charger.

Fig A: Pickup from a long wire(Desktop App)

Fig B: Pickup increased by touching the tip

6. Observation Table

7. Results and Discussion

• The presence of a 50Hz sine wave on the screen confirms that the wire is picking up electromagnetic radiation from the environment.
• Touching the wire increased the induced voltage to ____ V.
• The amount of induced voltage is typically higher when using a Desktop or Laptop because they are often connected to the mains earth, which provides a larger return path for the common-mode noise.

8. Precautions

1. Safety First: Do NOT insert the wire into a wall power socket. This experiment only captures the field near the wiring.
2. Input Range: The pickup signal is usually within a few volts. However, if the signal looks “flat” at the top and bottom, it has exceeded the input range of A1.
3. Isolation: For a cleaner signal, move away from large electric motors or heavy machinery that might add noise to the 50Hz sine wave.

9. Troubleshooting

Principles of an AC Generator

1. Aim

To demonstrate the conversion of mechanical energy into electrical energy and to study the characteristics of the Alternating Current (AC) produced by a rotating magnetic field.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Solenoid coil (3000 turns)
• Strong Neodymium magnet (Cuboidal or Cylindrical)
• A motor or manual spinning mechanism (to rotate the magnet)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

An AC Generator works on the principle of Faraday’s Law of Electromagnetic Induction. When a magnet rotates near a stationary coil, the magnetic flux ($\Phi_B$) passing through the coil changes continuously. This change in flux induces an Electromotive Force (EMF) in the coil.

The induced EMF ($\varepsilon$) follows a sine wave pattern because the rate of change of flux varies sinusoidally with the angle of rotation ($\theta$): \(\varepsilon(t) = \varepsilon_0 \sin(\omega t)\)

Where:

• $\varepsilon_0$ is the peak voltage.
• $\omega$ is the angular frequency ($2\pi f$).
• $t$ is the time.

The peak voltage $\varepsilon_0$ depends on the number of turns in the coil, the strength of the magnet, and the speed of rotation. Faster rotation leads to a higher frequency and a higher peak voltage.

4. Circuit Diagram / Setup

1. Coil Connection: Connect the two terminals of the solenoid coil to A1 and GND.
2. Magnet Orientation: * Cuboidal Magnet: The poles are on the long faces. Attach it vertically to the motor’s pulley.
   • Cylindrical Magnet: Lay it flat so the poles rotate past the coil face.
3. Position the magnet such that it can rotate freely very close to one face of the coil.
4. If using a DC motor, connect it to a separate power source or PV1 (ensure current < 30mA).

5. Procedure

1. Open the SEELab3 software and select the “AC Generator” or “Oscilloscope” tool.
2. Set the software to display the signal from A1.
3. Start rotating the magnet at a constant speed.
4. Observe the induced AC waveform on the screen.
5. Effect of Speed: Increase the speed of rotation and observe how both the amplitude (height) and frequency (closeness of peaks) of the sine wave change.
6. Distance: Move the coil further away from the rotating magnet and observe the drop in induced voltage.

6. Observation Table

7. Error Analysis

• Magnetic Alignment: If the axis of rotation is not perfectly aligned with the center of the coil, the sine wave may appear distorted or asymmetrical.
• Mechanical Loading: The “Cogging” effect (magnetic attraction between the magnet and the coil’s core, if any) can cause non-uniform rotation speeds at low RPM.
• Ambient Noise: Long unshielded wires between the coil and SEELab can pick up $50\text{ Hz}$ mains hum, which overlays on the generator signal.

8. Results and Discussion

• The rotating magnet induces an alternating voltage in the coil, as evidenced by the sinusoidal waveform.
• As the speed of rotation increases, the peak voltage increases linearly with frequency ($V_p \propto f$).
• This experiment confirms that mechanical energy is converted into electrical energy.

9. Precautions

1. Mechanical Stability: Ensure the rotating magnet is securely balanced to prevent vibrations.
2. Proximity: Keep the coil as close to the magnet as possible without physical contact to maximize the induced EMF.
3. Input Limits: Do not use high-power industrial generators with the A1 input.

10. Troubleshooting

3 Phase AC Generator

A 3D Printable 3 Phase AC Generator Demo

Distinction Between AC and DC

1. Aim

To study the fundamental differences between Direct Current (DC) and Alternating Current (AC) by observing their waveforms and behavior over time.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Capacitor ($C = 0.1\text{ }\mu F$)
• Connecting wires
• PC or Smartphone with SEELab3 software
• A small battery (optional, for external DC testing)

3. Theory & Principle

Direct Current (DC): In a DC circuit, electrons flow in only one direction. The voltage remains constant (steady DC) or may vary in magnitude but never changes its polarity. Batteries and regulated power supplies (like PV1) provide DC. \(V_{DC} = \text{Constant}\)

Alternating Current (AC): In an AC circuit, the direction of electron flow reverses periodically. The voltage varies sinusoidally with time, crossing the zero-axis and reaching positive and negative peaks. \(V_{AC}(t) = V_p \sin(2\pi ft)\) Where $V_p$ is the peak voltage and $f$ is the frequency (measured in Hertz, Hz).

Capacitive Blocking: A capacitor acts as an open circuit to DC (after a brief charging period) but allows AC to pass through. By connecting a signal through a capacitor, we can “filter out” the DC component and observe only the alternating part.

4. Circuit Diagram / Setup

1. AC Setup: Connect WG (Waveform Generator) to A1.
2. DC Setup: Connect PV2 (Programmable Voltage) to A3.
3. Mixed/Blocked Setup: Connect SQ1 (0-5V Square Wave) to one end of a $0.1\text{ }\mu F$ capacitor. Connect the other end of the capacitor to A2.

5. Procedure

1. Open the SEELab3 software and select the “AC/DC Difference” or “Oscilloscope” tool.
2. Observe DC: Set PV2 to $+3V$. Observe the trace on channel A3. It should be a steady horizontal line. Change PV2 to $-1V$ and notice the line moves below the zero-axis.
3. Observe AC: Set WG to a frequency of $50\text{ Hz}$ and an amplitude of $3V$. Observe the trace on channel A1. Adjust the “Timebase” (ms/div) to see multiple cycles.
4. Observe SQ1 Blocking: Observe the signal on A2. Note how the $0-5V$ square wave (which is DC-offset) becomes centered around $0V$ after passing through the capacitor.
5. Compare the traces simultaneously on the screen to visualize the differences in stability and polarity.

6. Observation Table

7. Error Analysis

The primary sources of error in visualizing these waveforms include:

• Quantization Error: The resolution of the Analog-to-Digital Converter (ADC) can cause small “steps” in the DC line if the vertical scale is too large.
• Offset Error: Small calibration offsets in the SEELab inputs may show $0V$ slightly above or below the actual axis.
• Capacitor Leakage: For very low-frequency AC, the $0.1\text{ }\mu F$ capacitor may not block DC perfectly if it has high internal leakage.

8. Results and Discussion

• The DC signal appears as a straight line, indicating the voltage is constant over time.
• The AC signal appears as a sine wave, indicating that the voltage changes magnitude and direction periodically.
• The capacitor effectively blocked the DC component of the SQ1 signal, shifting the waveform to be symmetrical around the zero-axis.

9. Troubleshooting

Phase Relationship in AC Capacitive Circuits

1. Aim

To study the phase relationship between voltage and current in an AC circuit containing a capacitor and a resistor, and to verify that current leads voltage in a capacitive circuit.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 1000\text{ }\Omega$)
• One Capacitor ($C \approx 1\text{ }\mu F$ or similar)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

A capacitor opposes changes in voltage by storing energy in an electric field. In a purely capacitive circuit, the current leads the voltage by $90^\circ$ ($\pi/2$ radians). This means the current reaches its peak when the voltage across the capacitor is zero.

The Capacitive Reactance ($X_C$) is given by: \(X_C = \frac{V_C}{I_C} = \frac{1}{2\pi f C}\)

From this, the capacitance can be calculated as: \(C = \frac{I_C}{V_C \cdot 2\pi f}\)

Current Measurement:

We measure the voltage across a series resistor ($R$) to represent the current waveform ($I = V_R / R$). Since $V_{total}$ is measured at A1 and $V_R$ is measured at A2, the voltage across the capacitor is calculated as the difference: $V_C = A1 - A2$. Since both are simultaneously measured, and instantaneous values for both are available as a function of time, direct subtraction is possible.

4. Circuit Diagram / Setup

1. Connect the Capacitor ($C$) and Resistor ($R$) in series between WG and GND.
2. Connect A1 to WG (measures total voltage $V_{total}$).
3. Connect A2 to the junction between the Capacitor and the Resistor (measures $V_R$).
4. The voltage across the Capacitor is obtained mathematically as $A1 - A2$.

5. Procedure

1. Launch the SEELab3 software and select the “AC through Capacitor” experiment.
2. Set WG to a sine wave (e.g., $150\text{ Hz}$).
3. Enable traces for A1 and A2.
4. Select a region of the graph to display calculated values. The software extracts amplitudes and phases by fitting the data to $V = V_0 \sin(\omega t + \theta) + C$.
5. Observe that the current (A2) is at its peak when the voltage across the capacitor ($A1-A2$) is at zero, confirming the $90^\circ$ phase shift.
6. Compare the calculated $C$ with the value obtained by measuring the capacitor directly using the IN1 terminal.

6. Observation Table

7. Error Analysis

The measurement of capacitance is influenced by the precision of the series resistor $R$ and the sampling resolution of the device.

The percentage error in $C$ can be estimated by: \(\frac{\Delta C}{C} \approx \frac{\Delta I_C}{I_C} + \frac{\Delta V_C}{V_C} + \frac{\Delta f}{f}\)

Key Factors Affecting Accuracy:

• ESR (Equivalent Series Resistance): Real capacitors have a small internal resistance. For large electrolytic capacitors, this ESR can shift the phase slightly away from the ideal $90^\circ$.
• Input Impedance: The $1\text{ M}\Omega$ input impedance of A2 is in parallel with the resistor $R$. Using a $1\text{ k}\Omega$ resistor keeps this error at $0.1\%$, which is negligible.
• Frequency Effect: If the frequency is too high, stray inductance in the leads might interfere; if too low, the capacitive reactance $X_C$ might become large enough to reduce the signal-to-noise ratio.

8. Results and Discussion

• The current waveform reaches its maximum value before the voltage across the capacitor.
• The results confirm the theory within experimental error, as shown by the agreement between calculated and measured capacitance values.
• The phase difference $(\theta_1 - \theta_2)$ extracted from the curve fitting represents the shift between voltage and current.

9. Python Programming & Data

The capture2(samples, gap) function returns voltage vectors which are fitted to determine Amplitudes and Phases. The ratio of Amplitudes gives the Capacitive Reactance.

• Download Python Program for Experiment
• Download Sample Data
• Download Analysis Script

10. Troubleshooting

Phase Relationship in AC Inductive Circuits

1. Aim

To study the phase relationship between voltage and current in an AC circuit containing an inductor and a resistor, and to verify that voltage leads current in an inductive circuit.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 100\text{ }\Omega$ or $1000\text{ }\Omega$)
• One Inductor (e.g., 10mH provided in the kit)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

An inductor opposes changes in current by storing energy in a magnetic field. This property, known as self-inductance ($L$), causes the current to “lag” behind the applied voltage.

In a purely inductive circuit, the voltage leads the current by exactly $90^\circ$ ($\pi/2$ radians). In a series RL circuit, the phase angle $\phi$ is between $0^\circ$ and $90^\circ$, determined by the resistance ($R$) and the inductive reactance ($X_L$): \(X_L = 2\pi f L\) \(\phi = \tan^{-1}\left(\frac{X_L}{R}\right)\)

Current Measurement:

We measure the voltage across a series resistor ($R$) to represent the current waveform ($I = V_R / R$). Since $V_{total}$ is measured at A1 and $V_R$ is measured at A2, the voltage across the inductor is calculated mathematically as $V_L = A1 - A2$.

4. Circuit Diagram / Setup

1. Connect the Inductor ($L$) and Resistor ($R$) in series between WG and GND.
2. Connect A1 to WG (measures total voltage $V_{total}$).
3. Connect A2 to the junction between the Inductor and the Resistor.
4. In this configuration, A2 measures the voltage across the Resistor ($V_R$), which is in phase with the current ($I$).
5. The voltage across the Inductor ($V_L$) is obtained as A1 - A2.

5. Procedure

1. Launch the SEELab3 software and select the “AC through Inductor” experiment.
2. Set WG to a sine wave (e.g., $4000\text{ Hz}$ or $5000\text{ Hz}$ to get significant reactance).
3. Enable traces for A1 and A2.
4. Select a region of the graph. The software will extract the amplitudes and phases using mathematical curve fitting.
5. Observe that the peak of the voltage across the inductor ($A1-A2$) occurs before the peak of the current (A2). This confirms that voltage leads the current.
6. Note the phase difference $\phi$ and calculate the inductance $L$ using the formula $L = X_L / (2\pi f)$.

6. Observation Table

7. Error Analysis

The measurement of inductance $L$ is subject to errors from the reference resistor $R$ and the inductor’s own internal DC resistance ($R_L$).

The percentage error in $L$ can be estimated as: \(\frac{\Delta L}{L} \approx \frac{\Delta R}{R} + \frac{\Delta f}{f} + \frac{\Delta \phi}{\sin \phi \cos \phi}\)

Key Factors Affecting Accuracy:

• Inductor Resistance: Real inductors have a finite resistance $R_L$. If $R_L$ is not accounted for, the phase shift will be less than the theoretical $90^\circ$ even if the series resistor $R$ is small.
• Frequency Selection: At low frequencies, $X_L$ is small compared to $R_L + R$, making the phase shift difficult to measure accurately. Always use higher frequencies ($>2\text{ kHz}$) for small inductors.

8. Results and Discussion

• The voltage waveform across the inductor reaches its maximum value before the current waveform.
• The measured phase shift $\phi$ was approximately ____ degrees.
• As the frequency increases, the inductive reactance $X_L$ increases, which ____ (increases/decreases) the phase shift towards $90^\circ$.

9. Python Programming & Data

The SEELab3 software uses the capture2 function to retrieve the waveforms. The phase difference between the fitted sine waves $(\theta_1 - \theta_2)$ and the ratio of amplitudes allow for the calculation of Inductive Reactance ($X_L$) and Inductance ($L$).

• Download Python Program for Experiment
• Download Sample Data
• Download Analysis Script

10. Troubleshooting

Phase and Resonance in Series RLC Circuits

1. Aim

To study the phase relationships between voltage and current in a series RLC circuit and to observe the phenomenon of series resonance using a Capacitor-Inductor-Resistor (C-L-R) configuration.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 1000\text{ }\Omega$)
• One Inductor ($L \approx 10\text{ mH}$ to $100\text{ mH}$, typical winding resistance $\approx 20\text{ }\Omega$)
• One Capacitor ($C \approx 0.1\text{ }\mu F$ to $1\text{ }\mu F$)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

A series RLC circuit is governed by Kirchhoff’s Voltage Law (KVL), which states that the sum of voltages across the inductor ($L$), resistor ($R$), and capacitor ($C$) must equal the applied source voltage ($v$):

The total opposition to the current is the Impedance ($Z$): \(Z = \sqrt{R^2 + (X_L - X_C)^2}\)

Resonance

At the Resonant Frequency ($f_r$), the inductive reactance ($X_L$) and capacitive reactance ($X_C$) cancel each other out ($X_L - X_C = 0$): \(f_r = \frac{1}{2\pi\sqrt{LC}}\)

At resonance, the circuit becomes purely resistive. The voltages across $L$ and $C$ are equal in magnitude but $180^\circ$ out of phase. In this C-L-R sequence, we monitor the intermediate nodes to visualize these individual components.

4. Circuit Diagram / Setup

1. Series Connection: Connect WG $\rightarrow$ Capacitor ($C$) $\rightarrow$ Inductor ($L$) $\rightarrow$ Resistor ($R$) $\rightarrow$ GND.
2. A1 Connection: Connect A1 to WG (measures total voltage $V_{total}$ across the whole string).
3. A3 Connection: Connect A3 to the junction (midpoint) between C and L.
4. A2 Connection: Connect A2 to the junction (midpoint) between L and R.

Voltage measurements derived by the software:

• $V_C$ (Voltage across Capacitor): Calculated as $A1 - A3$.
• $V_L$ (Voltage across Inductor): Calculated as $A3 - A2$.
• $V_R$ (Voltage across Resistor): Measured directly at A2 (represents current $I$).
• $V_{LC}$ (Combined Reactance): Calculated as $A1 - A2$.

5. Procedure

1. Launch the SEELab3 software and select the “AC Through RLC” experiment.
2. Set WG to a sine wave. Start near the expected resonance (e.g., $1600\text{ Hz}$).
3. Enable traces for A1, A2, and A3.
4. Fine-tune the frequency to minimize the voltage across the L-C combination ($V_{A1} - V_{A2}$).
5. Observe that at resonance, the current ($V_{A2}$) is at its maximum and is in phase with the input voltage ($V_{A1}$).

6. Observation Table

7. Error Analysis

• Inductor Resistance: The voltage $V_{A3}-V_{A2}$ at resonance will not be purely reactive due to the $20\text{ }\Omega$ internal resistance. This causes a small residual voltage that is in phase with the current.
• Phase Extraction: Error in $\phi$ increases if the signal-to-noise ratio is low. Ensure the WG amplitude is at least $3\text{ V}$.
• Stray Capacitance: At very high frequencies, the breadboard or wires may introduce stray capacitance, shifting the observed $f_r$ slightly.

8. Results and Discussion

• At $f < f_r$, the voltage across the capacitor ($A1-A3$) is larger than the voltage across the inductor.
• At $f > f_r$, the voltage across the inductor ($A3-A2$) dominates.
• At resonance, $V_C$ and $V_L$ are nearly equal, and their vector sum is minimized.

Sample Data (500 Hz vs 3000 Hz)

At 500 Hz (below resonance), the circuit is capacitive. At 3000 Hz (above resonance), it is inductive.

Fig A: 500 Hz (Capacitive)

Fig B: 3000 Hz (Inductive)

9. Python Programming & Data

• Download Python Program for RLC Experiment
• Download RLC Analysis Script

10. Troubleshooting

Phase and Amplitude in AC Resistive Circuits

1. Aim

To explore the relationship between voltage and current in an AC circuit containing only resistors, and to verify that they are in phase.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Two resistors ($R_1 = 1000\text{ }\Omega$ and $R_2 = 560\text{ }\Omega$ or similar)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

In a purely resistive AC circuit, the current ($I$) at any instant is directly proportional to the instantaneous voltage ($V$) across the resistor, according to Ohm’s Law: \(I(t) = \frac{V(t)}{R}\)

If the applied voltage is sinusoidal, $V(t) = V_p \sin(\omega t)$, then the current is: \(I(t) = \frac{V_p}{R} \sin(\omega t)\)

This shows that in a resistor, the voltage and current waveforms reach their peaks and zero-crossings at the exact same time. We say that the voltage and current are in phase, meaning the phase difference ($\phi$) is $0^\circ$.

Current Measurement Method: Since SEELab3 measures voltage, we measure the current indirectly. By placing a known resistor ($R_1$) in series, the voltage measured across it ($V_{R1}$) is a direct representation of the current flowing through the circuit ($I = V_{R1} / R_1$).

4. Circuit Diagram / Setup

1. Connect $R_2$ and $R_1$ in series between WG (Waveform Generator) and GND.
2. Connect A1 to WG (to measure the total applied voltage).
3. Connect A2 to the junction between $R_1$ and $R_2$ (to measure the voltage across $R_1$, which represents the current).
4. The voltage across $R_2$ is calculated by the software as $V_{A1} - V_{A2}$.

5. Procedure

1. Open the SEELab3 app and select the “AC through Resistor” experiment.
2. Observe the two sine waves on the screen. Note that they cross the zero-axis and reach their maxima simultaneously.
3. Use the “Measure” or “Analyze” tool to obtain the peak voltages ($V_p$) and phase difference ($\phi$). You can tap on the A1 or A2 icons in the app to select the parameter to be viewed.
4. Calculate the RMS values: $V_{RMS} = V_p / \sqrt{2}$.

6. Observation Table

Reference Resistor ($R_1$): ____ $\Omega$

7. Error Analysis

• Input Loading: The $1\text{ M}\Omega$ input impedance of A2 is in parallel with $R_1$. For a $1\text{ k}\Omega$ resistor, this introduces an error of only $0.1\%$.
• Tolerance: Most standard resistors have a $\pm 5\%$ tolerance. Measure the resistors with the SEELab ohmmeter first to improve the accuracy of your $R_2$ calculation.
• Thermal Noise: At very low signal amplitudes, electronic noise may make the zero-crossing point appear to jitter, leading to small errors in the measured phase angle.

8. Results and Discussion

• The voltage and current waveforms are in phase, as they reach their peaks at the same time.
• The calculated value of $R_2$ is ____ $\Omega$, which matches the labeled value within experimental error.
• For a purely resistive load, the phase angle $\phi$ is approximately 0 degrees.

9. Precautions

1. Impedance: Ensure the resistors used are much smaller than the $1\text{ M}\Omega$ input impedance of the SEELab terminals.
2. Connections: Ensure the series junction is tight to avoid noisy readings at A2.
3. Frequency: Avoid extremely high frequencies where stray capacitance of the breadboard might begin to affect the phase.

10. Troubleshooting

Driven Pendulum and Resonance

1. Aim

To study the behavior of a driven pendulum, determine its natural frequency, and demonstrate the phenomenon of resonance using a periodic magnetic force.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Solenoid coil (approx. 3000 turns)
• Two small button-shaped magnets
• A strip of paper and adhesive tape (to construct the pendulum)
• Rigid support/stand
• Connecting wires

3. Theory & Principle

A simple pendulum undergoes periodic motion, transferring energy between kinetic and potential modes. Its natural frequency ($f_0$) is determined by its length ($L$) from the pivot to the center of mass, and the acceleration due to gravity ($g$):

In a driven oscillation, an external periodic force is applied to the system. If the frequency of this external force ($f_{drive}$) matches the natural frequency of the pendulum ($f_0$), the system absorbs energy most efficiently, and the amplitude of oscillation increases significantly. This condition is known as Resonance.

4. Setup & Circuit (Common for both Apps)

1. Pendulum Construction: Tape two button magnets to the bottom of a 5–10 cm paper strip. Suspend the strip from a rigid support so it can swing freely.
2. Driving Mechanism: Place the solenoid coil directly below the equilibrium position of the magnets. Align it so the magnetic field acts vertically on the magnets.
3. Connections: Connect the solenoid coil between the signal output (SQ1 or PV1) and GND.

Mobile App Setup (Using SQ1)

5. Procedure (Mobile App with SQ1)

In this setup, the solenoid coil acts as an electromagnet. When connected to the SQ1 (Square Wave) output, it creates a periodic magnetic pulse that exerts a force on the magnets.

1. Measure the length ($L$) of your pendulum in meters.
2. Calculate the theoretical natural frequency: $f_0 = \frac{1}{2\pi}\sqrt{\frac{9.8}{L}}$.
3. Open the SEELab3 mobile app and select the “Driven Pendulum” tool.
4. Set SQ1 to a frequency well below your calculated $f_0$.
5. Slowly increase the frequency in small steps (e.g., $0.1\text{ Hz}$) and observe the amplitude of the pendulum’s swing.
6. Identify the frequency at which the amplitude is maximum. This is the Resonant Frequency.

Desktop App Setup (Using PV1)

6. Procedure (Desktop App with PV1)

In the desktop version, the software can oscillate the PV1 (+/-5V DC) output back and forth in a smooth sine wave motion to drive the pendulum more gently.

1. Open the SEELab3 desktop software and select the “Driven Pendulum Resonance” experiment under the Mechanics section.
2. Follow the same steps as the mobile procedure, using the frequency slider for PV1.
3. Observe the “Phase” of the oscillation—notice how the pendulum’s timing relative to the drive changes as you pass through resonance.

7. Observation Table

Pendulum Length ($L$): ____ cm
Theoretical Frequency ($f_0$): ____ Hz

8. Error Analysis

• Damping Effects: Air resistance and friction at the pivot point “damp” the oscillation, which slightly lowers the resonant frequency and limits the maximum amplitude.
• Effective Length: The formula assumes all mass is at a single point. If the paper strip is heavy relative to the magnets, the “center of oscillation” shifts, affecting $f_0$.
• Coil Position: If the coil is not perfectly centered, the driving force will have a horizontal component, causing the pendulum to wobble or “precess” rather than swing in a straight line.

9. Results and Discussion

• The natural frequency was found to be ____ Hz experimentally.
• Resonance occurred when the frequency of the drive was equal to the natural frequency.
• At resonance, the transfer of energy from the magnetic field to the pendulum was maximum.

10. Precautions

1. Alignment: Ensure the coil is close enough to influence the magnets but not so close that the pendulum hits the coil.
2. Damping: Perform the experiment in a draft-free area to minimize air resistance.
3. Current: Avoid running high currents through the coil for long durations to prevent overheating.

11. Troubleshooting

Study of an Electromagnet

1. Aim

To demonstrate that a current-carrying conductor produces a magnetic field and to study the properties of an electromagnet using a solenoid coil and a permanent magnet.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Solenoid coil (e.g., 3000 turns of SWG44 wire included in the kit)
• Small permanent bar magnet or a Compass
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

When an electric current ($I$) flows through a conductor, it creates a magnetic field around it (Oersted’s discovery). A Solenoid is a long coil of wire consisting of many loops. When current passes through it, the magnetic fields of the individual loops add together to create a strong, uniform magnetic field inside the coil, behaving like a bar magnet.

The magnetic field strength ($B$) at the center of a long solenoid is given by: \(B = \mu_0 \cdot n \cdot I\)

Where:

• $B$ is the magnetic flux density in Tesla ($T$).
• $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$).
• $n$ is the number of turns per unit length ($N/L$).
• $I$ is the current in Amperes ($A$).

Current Limitation: The Programmable Voltage source (PV1) on SEELab3/ExpEYES has a maximum current limit of 30mA.

• The standard coil provided (3000 turns) has a resistance ($R$) of approximately $500\text{ }\Omega$.
• At $5V$, the current drawn is $I = V/R = 5/500 = 10\text{ mA}$, which is well within the limit.

4. Circuit Diagram / Setup

1. Connect one end of the solenoid coil to PV1 and the other end to GND.
2. Connect PV1 to A1 using a wire to monitor the actual voltage applied across the coil.
3. Place a small permanent magnet or a compass needle near one end of the coil, aligned with its axis.

5. Procedure

1. Open the SEELab3 software and select the “Electromagnet” or “Power Supply” tool.
2. Set the voltage at PV1 to $0V$.
3. Slowly increase the voltage to $+5V$ and observe the movement of the magnet (Attraction or Repulsion).
4. Change the voltage to $-5V$ (reverse polarity) and observe how the magnetic poles of the coil flip, causing the opposite force on the permanent magnet.
5. AC Study: Set the Waveform Generator (WG) to a low frequency (e.g., $5\text{ Hz}$) and connect it to the coil to see the magnet vibrate as the poles oscillate.

6. Observation Table

Coil Resistance ($R$): ____ $\Omega$

7. Error Analysis

• Voltage Drop: If the measured voltage at A1 is lower than the set PV1 value, it indicates that the coil resistance is too low, hitting the $30\text{ mA}$ safety limit of the device.
• Ambient Fields: Nearby electronic devices or large metal objects can distort the magnetic field, affecting the compass needle or magnet movement.
• Thermal Drift: As the coil carries current, it heats up, which slightly increases its resistance ($R = R_0[1 + \alpha\Delta T]$), thereby decreasing the current and the magnetic field strength over time. Although this effect will not present itself for such low currents.

8. Results and Discussion

• The coil behaves as a magnet when current flows through it, confirming the magnetic effect of electric current.
• Reversing the direction of the current reverses the polarity of the electromagnet.
• The strength of the electromagnet is directly proportional to the magnitude of the current flowing through it.

9. Precautions

1. Current Limit: Do not use coils with resistance less than $170\text{ }\Omega$ at $5V$ to avoid overloading the source.
2. Heat: Do not leave the current running through the coil for extended periods.
3. Interference: Keep sensitive electronic devices away from the strong magnetic field.

10. Troubleshooting

Faraday’s Law of Electromagnetic Induction

1. Aim

To study the generation of an Electromotive Force (EMF) in a coil by a changing magnetic field and to verify Faraday’s Law of Induction.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Solenoid coil (e.g., 3000 turns)
• Strong cylindrical Neodymium magnet
• A non-magnetic tube (paper or plastic) to guide the magnet
• Connecting wires (Jumper wires with alligator clips)
• PC or Smartphone with SEELab3 software

3. Theory & Principle

Faraday’s Law of Induction states that the magnitude of the induced EMF ($\varepsilon$) in a circuit is proportional to the rate of change of magnetic flux ($\Phi_B$) through the circuit:

Where $N$ is the number of turns in the coil. The negative sign represents Lenz’s Law, indicating that the induced current creates a magnetic field that opposes the change in flux.

As a magnet falls through a stationary coil, the magnetic flux increases as the magnet approaches and decreases as it leaves. This results in a characteristic “double-peak” waveform. The second peak is typically larger because the magnet is accelerating due to gravity, meaning the rate of change of flux ($d\Phi_B/dt$) is higher as it exits the coil.

4. Circuit Diagram / Setup

1. Connect the solenoid coil between A1 and GND using alligator clips.
2. Ensure the non-magnetic guide tube is inserted through the center of the coil and held vertically.
3. Position the coil towards the bottom of the tube so the magnet reaches a high velocity before entering.

5. Procedure

1. Open the SEELab3 software and select the “Electromagnetic Induction” experiment.
2. Click on “Capture Signal” or “Start” to wait for a trigger.
3. Hold the magnet at the top of the tube and drop it so it passes through the center of the coil.
4. The software will automatically capture and display the induced voltage waveform when the voltage exceeds the trigger threshold.
5. Observe the two peaks of opposite polarity.
6. Repeat: Drop the magnet from different heights and observe how the peak voltage changes with velocity.

6. Observation Table

7. Error Analysis

The primary sources of error in this induction experiment include:

• Air Resistance: Drag on the falling magnet can cause it to fall slower than $g = 9.8\text{ m/s}^2$, affecting the predicted velocity.
• Magnetic Alignment: If the magnet is not perfectly centered in the tube, the flux distribution may be asymmetrical, leading to uneven peaks.
• Sampling Rate: If the magnet moves extremely fast, a low sampling rate might “miss” the exact peak voltage, resulting in lower measured values.

8. Results and Discussion

• The induced EMF shows two peaks because the flux increases as the magnet enters and decreases as it leaves.
• The second peak is larger than the first because the magnet is moving faster due to gravitational acceleration ($v = \sqrt{2gh}$).
• The area under the voltage-time curve ($\int V dt$) represents the total change in magnetic flux.

9. Precautions

1. Alignment: Ensure the magnet falls straight through the center of the coil without hitting the sides for a clean waveform.
2. Triggering: If the software fails to capture, check the trigger level settings; it should be set slightly above the noise floor.
3. Coil Orientation: The polarity of the peaks (which one is positive/negative) depends on which pole of the magnet enters first.

10. Troubleshooting

Mutual Induction and Transformer Action

1. Aim

To demonstrate the phenomenon of mutual induction between two coils and to understand the basic working principle of an AC transformer.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Two Solenoid Coils (e.g., 3000 turns each)
• One Ferrite or Iron core (an iron nail or bolt will also work)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

Mutual induction is the process by which a changing current in one coil (the Primary) induces an Electromotive Force (EMF) in a nearby second coil (the Secondary).

This experiment combines two previously studied phenomena:

1. Oersted’s Discovery: A current-carrying conductor creates a magnetic field.
2. Faraday’s Law: A changing magnetic field induces a voltage across a conductor.

When an AC voltage is applied to the primary coil, it produces a continuously changing magnetic field. This field lines pass through the secondary coil, inducing an AC voltage across it. The efficiency of this energy transfer depends on the coupling between the coils.

The induced EMF ($\varepsilon_s$) in the secondary coil is given by: \(\varepsilon_s = -M \frac{dI_p}{dt}\) Where $M$ is the Mutual Inductance between the two coils.

4. Circuit Diagram / Setup

1. Primary Circuit: Connect one coil between WG and GND.
2. Monitoring Primary: Connect A1 to WG to observe the input AC waveform.
3. Secondary Circuit: Connect the second coil between A2 and GND.
4. Physical Alignment: Place the two coils close to each other, coaxially.

5. Procedure

1. Open the SEELab3 software and select the “Mutual Induction” or “Oscilloscope” tool.
2. Set WG to a sine wave (e.g., $1000\text{ Hz}$ or $2000\text{ Hz}$).
3. Observe the waveforms on A1 (Input) and A2 (Induced Output).
4. Distance Test: Slowly move the coils further apart and observe the decrease in the amplitude of A2.
5. Core Test: Insert a piece of magnetic material (like an iron bolt or ferrite rod) through the center of both coils.
6. Observe the significant increase in the induced voltage at A2 due to improved magnetic coupling.

Mutual Inductance

6. Observation Table

7. Error Analysis

• Magnetic Leakage: In the air-core setup, most magnetic field lines do not pass through the secondary coil, leading to poor efficiency.
• Eddy Currents: If a solid iron core is used instead of a laminated core, heat losses due to eddy currents can reduce the output voltage at higher frequencies.
• Orientation: If the coils are placed at $90^\circ$ to each other, the induced EMF will drop to nearly zero because no flux lines from the primary will thread the secondary.

8. Results and Discussion

• The presence of an AC signal in the secondary coil without any direct electrical connection confirms the principle of Mutual Induction.
• Using an iron core increases the induced voltage because it has high permeability, which channels the magnetic flux more effectively from the primary to the secondary.
• This experiment demonstrates that an AC transformer requires proper geometry and core materials to be efficient.

9. Precautions

1. GND Connection: Ensure both coils share a common GND terminal on the SEELab3 for stable oscilloscope readings.
2. Frequency: If the frequency is too low, the rate of change of flux ($d\Phi/dt$) will be low, resulting in a very weak secondary signal.
3. Core Material: Use only magnetic materials (Iron, Steel, Ferrite) for the core; materials like Aluminum or Brass will not increase the induction.

10. Troubleshooting

Basic Principle of Optical Communication

1. Aim

To demonstrate the conversion of electrical signals into light signals for transmission and their subsequent conversion back into electrical signals using an LED and an LDR.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One High-Brightness LED (White or Red) / Diode Laser
• One Light Dependent Resistor (LDR)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

Optical communication involves transmitting information using light as the carrier. In this simplified demonstration:

1. Transmitter: An LED acts as the source. When a pulsing electrical signal (SQ1) is applied, the LED converts these electrical pulses into flashes of light.
2. Channel: The light travels through the air (or an optical fiber in practical systems).
3. Receiver: An LDR acts as the detector. The resistance of the LDR decreases when light falls on it. By connecting the LDR between SEN and GND , the light pulses are converted back into a pulsing voltage signal.

While this setup uses low-frequency visible light, modern high-speed internet uses infrared lasers and fiber optic cables to transmit data over thousands of kilometers.

4. Circuit Diagram / Setup

1. Transmitter: Connect the LED between SQ1 and GND. (Ensure correct polarity).
2. Receiver: Connect the LDR/Phototransistor between SEN and GND.
3. Alignment: Place the LED directly facing the LDR at a distance of $2\text{ cm} - 5\text{ cm}$.

5. Procedure

1. Open the SEELab3 software and select the “Optical Communication” or “Oscilloscope” tool.
2. Set SQ1 to a frequency of 20 Hz and a duty cycle of 50%. The LED should start blinking rapidly.
3. Observe the waveform on the screen. You should see a square-like wave representing the light pulses detected by the LDR.
4. Analysis: Tap on the SEN icon. The software will display the frequency and duty cycle of the received signal. Verify that it matches the SQ1 settings.
5. Interference Test: Block the light path with a piece of paper and observe the signal disappear.
6. Ambient Light: Observe how the “DC offset” of the signal changes if you perform the experiment in a dark room versus under bright tube lights.

6. Observation Table

7. Results and Discussion

• The electrical pulses from SQ1 were successfully transmitted as light pulses and recovered as electrical signals.
• The received frequency matched the transmitted frequency, demonstrating a basic communication link.
• It was observed that the “sharpness” of the received pulses decreases at higher frequencies. This is due to the slow response time (latency) of the LDR compared to the LED.

8. Precautions

1. Alignment: The LED must be pointed directly at the sensitive surface of the LDR for a strong signal.
2. External Light: Avoid direct sunlight on the LDR, as it can saturate the sensor and mask the LED pulses.
3. Current Limit: Do not connect the LED directly to a high-voltage source; SQ1 provides a safe current for standard LEDs.

9. Troubleshooting

Distance Measurement and Free Fall using Ultrasound

1. Aim

To measure the distance of an object using an HC-SR04 ultrasonic sensor and to study the motion of a freely falling body to determine the acceleration due to gravity ($g$).

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• HC-SR04 Ultrasonic Sensor module
• A flat reflecting surface (for distance) and a flat plate (for free fall)
• Jumper wires (Female-to-Male)
• PC or Smartphone with SEELab3 software

3. Theory & Principle

The HC-SR04 sensor uses Time of Flight (ToF) of sound waves to measure distance. It contains two piezoelectric discs: one transmits a $40\text{ kHz}$ ultrasonic pulse, and the other receives the reflected echo.

The distance ($S$) is calculated as: \(S = \frac{v \times t}{2}\) Where $v$ is the speed of sound ($\approx 340\text{ m/s}$) and $t$ is the time interval between trigger and echo.

Free Fall: For a body falling from rest, the distance traveled follows the equation: \(S = \frac{1}{2}gt^2\) By plotting $S$ against $t$, we can observe a parabolic trajectory and calculate $g$ from the curve fit.

4. Circuit Diagram / Setup

1. Vcc: Connect to the 5V terminal of SEELab3.
2. Trig: Connect to the SQ2 output.
3. Echo: Connect to the IN2 input.
4. GND: Connect to any GND terminal.
5. For Free Fall: Mount the sensor facing downwards on a stand at a height of $\approx 1.5\text{m}$.

5. Procedure

Part A: Distance Measurement

1. Open the SEELab3 software and select the “Ultrasonic Distance” tool.
2. Hold a flat object in front of the sensor.
3. Observe the live distance reading and the real-time plot.
4. Verify the accuracy using a standard ruler.

Part B: Measurement on a Freely Falling Body

1. Execute the Python program for distance measurement.
2. Hold a flat plate just below the sensor facing downwards.
3. release the plate.
4. The Python script will plot the distance as a function of time.

Fig A: Falling body setup

Fig B: Free fall parabolic data

6. Observation Table

7. Results and Discussion

• The distance measurement confirmed the “Time of Flight” principle using ultrasound.
• The free-fall data followed a parabolic path, verifying the equation $S = \frac{1}{2}gt^2$.
• The value of $g$ was calculated as ____ $\text{m/s}^2$. Discrepancies may arise from air resistance on the falling plate.

8. Python Programming & Data

• Download Python Program for Distance Measurement
• Download Python Program for Falling Body Analysis
• Download Sample Data

9. Troubleshooting

Stroboscopic Effect and Rotational Speed

1. Aim

To demonstrate the stroboscopic effect and use a pulsed light source (LED) to “freeze” the motion of a rotating motor, thereby measuring its frequency of rotation.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Small DC Motor with a pulley (having a distinct dot or pattern)
• One High-Brightness White LED
• One $100\text{ }\Omega$ current-limiting resistor
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

The Stroboscopic Effect is a visual phenomenon caused by aliasing that occurs when continuous motion is represented by a series of short samples (light pulses).

Imagine a disc rotating at 50 revolutions per second ($50\text{ Hz}$). One full rotation takes $20\text{ ms}$. If we look at the disc under continuous light, a dot on its edge appears as a blurred circular ring due to the Persistence of Vision of the human eye (which lasts about $1/16$th of a second).

However, if we illuminate the disc with a light that flashes exactly once every $20\text{ ms}$, the dot is only visible when it is at one specific angular position. To our eyes, the rotating dot will appear perfectly stationary.

Key Relationships:

• If $f_{light} = f_{motor}$, the object appears stationary.
• If $f_{light}$ is slightly less than $f_{motor}$, the object appears to rotate slowly forward.
• If $f_{light}$ is slightly more than $f_{motor}$, the object appears to rotate slowly backward.

4. Circuit Diagram / Setup

1. Motor Connection: Connect the DC motor between PV1 and GND.
2. LED Connection: Connect the White LED in series with a $100\text{ }\Omega$ resistor between SQ1 and GND. (Ensure correct polarity: long lead of LED to SQ1). The resistor is optional only because SQ1 is internally current limited.
3. Positioning: Aim the LED so it directly illuminates the pulley of the motor. Ensure the motor pulley has a clear white dot or a black-and-white pattern.

5. Procedure

1. Open the SEELab3 software and select the “Stroboscope” experiment or “Oscilloscope” where you have access to SQ! frequency and duty cycle controls.
2. Start the Motor: Set PV1 to approximately $1.0V$. The motor will begin to spin rapidly, and any pattern on the pulley will become a blur.
3. Pulsed Light: Enable SQ1 and set the initial frequency to $10\text{ Hz}$. Adjust the “Duty Cycle” of SQ1 to a low value (e.g., $5\% - 10\%$). A short duty cycle creates sharper “flashes.”
4. Find Resonance: Slowly increase the frequency of SQ1. Watch the pattern on the pulley.
5. As you approach the actual frequency of the motor, the blurred pattern will begin to resolve into distinct dots.
6. Fine-tune the frequency until the dots appear perfectly stationary. Record this frequency as the motor’s rotational speed in Hz.

6. Observation Table

7. Results and Discussion

• At a specific frequency of SQ1, the rotating motor pulley appeared stationary, confirming the stroboscopic effect.
• When the strobe frequency was slightly higher than the motor frequency, the pulley appeared to rotate backward.
• The rotational speed of the motor at $1.0V$ was found to be ____ Hz, which corresponds to ____ RPM.

8. Precautions

1. Duty Cycle: If the duty cycle is too high (e.g., $50\%$), the LED stays on too long per pulse, and the “frozen” image will look blurred. Keep it below $10\%$.
2. Ambient Light: This experiment works best in a darkened room so that the pulsed LED light is the primary source of illumination.
3. Motor Load: Do not touch the spinning pulley during measurement, as friction will change the rotational speed.

9. Troubleshooting

Measurement of the Resistance of Water

1. Aim

To measure the electrical resistance of a water column and understand why an AC voltage source is required for stable measurements in liquids.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Known resistor ($R_1 \approx 10\text{ k}\Omega$)
• A plastic cup or tube to hold the water sample
• Two metal electrodes (probes)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

The resistivity of water is a direct indicator of its purity; dissolved salts provide ions that reduce resistivity. If you attempt to measure the resistance of water using a standard DC multimeter, the reading will not stabilize. This is due to electrolysis and chemical reactions at the electrodes, which create a back-EMF and change the ion concentration near the probes.

To obtain a stable reading, we use an AC voltage from the Waveform Generator (WG). This prevents the build-up of ions at the electrodes.

The water column is connected in series with a known resistor ($R_1$). By measuring the AC voltages across the combination and the junction, we can determine the current and the resistance of the water.

Where $I_{R1}$ is the current flowing through the series circuit, calculated using the voltage across the known resistor ($I_{R1} = (V_{A1} - V_{A2}) / R_1$).

4. Circuit Diagram / Setup

1. Connect a $10\text{ k}\Omega$ resistor ($R_1$) between WG and a junction point.
2. Connect the water column (via electrodes) between that junction point and GND.
3. Connect A1 to WG to monitor the input AC voltage.
4. Connect A2 to the junction between $R_1$ and the water column.

Fig A: 1000 Hz

Fig B: 100 Hz

5. Procedure

1. Open the SEELab3 software and select the experiment for measuring water resistance.
2. Fill the container with the water sample and insert the electrodes.
3. Set WG to a sine wave (e.g., $1000\text{ Hz}$).
4. If the voltage ratio between A1 and A2 is extremely high, change $R_1$ to a value more comparable to the water’s resistance.
5. Tap on the displayed resistor value in the app to enter the actual value of $R_1$ used.
6. Select a region on the graph to analyze the waveforms. The software will display the RMS voltages and the calculated current.

6. Observation Table

Reference Resistor ($R_1$): ____ $\Omega$

Example Calculation: If $V_{A2} = 1.438\text{ V}$ and $I = 0.000077\text{ A}$: $R_{water} = 1.438 / 0.000077 = 18,675\text{ }\Omega$

7. Error Analysis

In this experiment, the measurement of $R_w$ depends on the accuracy of the reference resistor $R_1$ and the voltage measurements at A1 and A2.

The percentage error in water resistance ($\frac{\Delta R_w}{R_w}$) can be estimated using: \(\frac{\Delta R_w}{R_w} \approx \frac{\Delta R_1}{R_1} + \frac{\Delta V_{A1} + \Delta V_{A2}}{V_{A1} - V_{A2}} + \frac{\Delta V_{A2}}{V_{A2}}\)

Key Factors Affecting Accuracy:

• Impedance Loading: A2 has an input impedance of $1\text{ M}\Omega$. If $R_w$ is very high (e.g., $>100\text{ k}\Omega$), A2 will act as a parallel path, leading to a lower measured resistance than actual.
• Fringing Effects: The electric field lines between probes are not perfectly straight. Using a narrow, long tube for the water column reduces this geometric error.
• Temperature Sensitivity: Water’s resistance changes by roughly 2% per degree Celsius. Ensure the water temperature is stable during measurements.

8. Results and Discussion

• The resistance of the tap water sample was found to be ____ $\Omega$.
• Using AC voltage provided a stable reading compared to a DC measurement.
• To find the specific resistance (resistivity), the dimensions of the water column (length $L$ and cross-section area $A$) must be known, using the formula $\rho = R \cdot A / L$.

9. Precautions

1. Resistor Matching: For maximum accuracy, $R_1$ should be of the same order of magnitude as the water column’s resistance.
2. Electrode Distance: Ensure the distance between electrodes remains constant during comparative tests.
3. No DC: Do not use PV1 or PV2 for this experiment, as the DC component will cause bubble formation and steadily climbing readings.

10. Troubleshooting

Transduction of Sound Waves

1. Aim

To study the conversion of electrical energy into sound energy using a piezoelectric buzzer and the conversion of sound energy back into electrical energy using a condenser microphone.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Piezoelectric Buzzer
• One Electret Condenser Microphone
• Connecting wires
• A whistle or tuning fork (optional)
• PC or Smartphone with SEELab3 software

3. Theory & Principle

Sound is a mechanical wave that requires a medium to travel. The devices that convert energy from one form to another (like electrical to mechanical) are called Transducers.

• Piezoelectric Buzzer (Output Transducer): Works on the Inverse Piezoelectric Effect. When an AC voltage is applied to a piezoelectric material, it deforms mechanically, vibrating the air and creating sound waves at the same frequency as the electrical input.
• Condenser Microphone (Input Transducer): Contains a thin diaphragm that acts as one plate of a capacitor. Sound waves cause the diaphragm to vibrate, changing the capacitance and generating a small varying electrical signal that mimics the sound wave’s pressure variations.

4. Circuit Diagram / Setup

1. Microphone: Connect the electret condenser microphone between the MIC terminal and GND. (Note: The MIC terminal provides the necessary DC bias for the microphone).
2. Buzzer: Connect the piezoelectric buzzer between WG and GND.
3. Placement: Align the microphone and buzzer so they face each other at a distance of about $5\text{ cm} - 10\text{ cm}$.

5. Procedure

1. Open the SEELab3 software and select the “Oscilloscope” or “Sound” tool.
2. Testing the Microphone: Enable the trace for the MIC channel. Speak into the microphone or whistle near it. Observe the complex electrical waveforms generated by your voice.
3. Generating Sound: Set WG to a sine wave. Adjust the frequency to find the buzzer’s resonant point (usually around $3000\text{ Hz} - 4000\text{ Hz}$). At this frequency, the sound will be loudest and the trace on the oscilloscope will be most stable.
4. Signal Capture: Observe the waveform on the MIC channel while the buzzer is sounding. Compare its frequency with the WG frequency.
5. Distance Study: Move the buzzer further away and observe the decrease in the amplitude of the captured electrical signal.

6. Observation Table

7. Results and Discussion

• The piezoelectric buzzer successfully converted the AC electrical signal from WG into an audible sound wave.
• The condenser microphone converted the sound waves back into electrical signals, which were visualized on the oscilloscope.
• It was observed that the amplitude of the captured signal is highly dependent on the frequency and the distance between the source and the receiver.

8. Precautions

1. Microphone Polarity: Electret microphones have polarity. Ensure the terminal connected to the casing is grounded.
2. Avoid Clipping: If you shout too loudly into the microphone, the signal may “clip” (flatten at the top), leading to distortion.
3. Buzzer Resonance: Piezo buzzers are very quiet outside their resonant frequency. Always check the datasheet or sweep the frequency to find the peak performance point.

9. Troubleshooting

Separating AC and DC Components

1. Aim

To demonstrate how a composite signal (containing both AC and DC) can be separated into its individual components using a capacitor and a resistor.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Capacitor ($C = 1\text{ }\mu F$ or $0.1\text{ }\mu F$)
• One Resistor ($R = 100\text{ k}\Omega$)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

A $0$ to $5V$ square wave (like the one from SQ1) is mathematically a combination of:

1. A DC component of $+2.5V$ (the average value).
2. An AC component (a square wave oscillating between $-2.5V$ and $+2.5V$).

Capacitive Blocking: A capacitor has a very high reactance ($X_C = 1/2\pi fC$) at low frequencies and acts as an open circuit to DC ($0\text{ Hz}$). However, it allows AC signals to pass through. By placing a capacitor in series with the signal and a resistor to ground, we create a High Pass Filter that “blocks” the steady DC voltage and “passes” only the alternating part.

4. Circuit Diagram / Setup

1. Reference Signal: Connect SQ1 directly to A1 to monitor the original $0-5V$ signal.
2. AC Separation: Connect SQ1 to one end of the $1\text{ }\mu F$ capacitor.
3. Measurement: Connect the other end of the capacitor to A2.
4. Load Resistor: Connect a $100\text{ k}\Omega$ resistor from A2 to GND. This provides a reference path for the AC signal.

5. Procedure

1. Open the SEELab3 software and select the “AC/DC Separation” or “Oscilloscope” tool.
2. Set SQ1 to a frequency of $500\text{ Hz}$.
3. Observe the trace on A1. It should be a square wave jumping between $0V$ and $5V$. Note that its average value is $+2.5V$.
4. Observe the trace on A2. Note that the signal is now a square wave centered around the zero-axis, oscillating between $-2.5V$ and $+2.5V$.
5. Verification: Check the “Mean” or “Average” value displayed for both channels. A1 should show $\approx 2.5V$, while A2 should show $\approx 0V$.

6. Observation Table

7. Results and Discussion

• The signal at A1 is a combination of AC and DC because its average value is non-zero.
• The signal at A2 is pure AC because its average value is zero.
• The capacitor successfully blocked the $+2.5V$ DC offset while allowing the $500\text{ Hz}$ frequency component to pass.
• This technique is commonly used in audio amplifiers to pass the sound signal (AC) between stages while blocking the supply voltages (DC).

8. Precautions

1. Resistor Importance: Always use the $100\text{ k}\Omega$ resistor to ground at A2. Without it, the capacitor has no discharge path, and the input may “float” or take a long time to stabilize at $0V$.
2. Frequency: If the frequency is very low (e.g., $1\text{ Hz}$), the capacitor might start blocking the AC component as well, causing the square wave to “droop” or look like spikes.
3. Polarity: If using an electrolytic capacitor, ensure the positive lead is connected to the signal source (SQ1).

9. Troubleshooting

Verification of Ohm’s Law Using an AC Source

1. Aim

To verify Ohm’s Law for resistors under an applied AC (sinusoidal) voltage by measuring the peak voltages across two series resistors, calculating the peak current, and confirming that the voltage and current remain in phase for a purely resistive circuit.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Resistor $R_1 = 1\text{ k}\Omega$
• Resistor $R_2 = 560\text{ }\Omega$
• Connecting wires
• PC or Smartphone with SEELab3 / ExpEYES software

3. Theory & Principle

3.1 Ohm’s Law under AC

Ohm’s Law states that for a linear resistor, the voltage across it is directly proportional to the current through it at every instant:

For a sinusoidal source $v(t) = V_0 \sin(\omega t)$, the instantaneous current is:

This shows that for a resistor, voltage and current are always in phase — there is no phase difference between them, regardless of frequency. This is what distinguishes a resistor from a capacitor or inductor.

3.2 Series Resistor Circuit

When two resistors $R_1$ and $R_2$ are connected in series, the same current flows through both (neglecting the $1\text{ M}\Omega$ input impedance of the measurement channels, which is much larger than the circuit resistances). The peak current can therefore be determined from either resistor:

Rearranging to find the unknown resistance $R_2$:

This gives a purely experimental determination of $R_2$ from voltage measurements alone — no separate current meter is required.

3.3 RMS Voltage

For a sinusoidal waveform, the RMS (Root Mean Square) voltage is related to the peak voltage by:

The SEELab3 software computes RMS from instantaneous sampled values over a full cycle:

This general formula works correctly for any waveform shape, not just sinusoids.

3.4 Worked Example

From the experiment on the ExpEYES website:

• Peak voltage across $R_1$: $V_{R_1} = 2.01\text{ V}$
• Peak current: $I_0 = \dfrac{2.01}{1000} = 2.01\text{ mA}$
• Peak voltage across $R_2$: $V_{R_2} = 1.13\text{ V}$
• Calculated $R_2 = \dfrac{1.13}{2.01 \times 10^{-3}} = 562\text{ }\Omega$

This agrees with the marked value of $560\text{ }\Omega$ within experimental tolerance — verifying Ohm’s Law under AC.

4. Circuit Diagram / Setup

1. Connect $R_1$ ($1\text{ k}\Omega$) and $R_2$ ($560\text{ }\Omega$) in series.
2. Connect the free end of $R_1$ to WG (the AC sinusoidal source).
3. Connect the free end of $R_2$ to GND.
4. Connect the WG end (top of $R_1$) to A1 — this monitors the total applied voltage $V_{WG}$.
5. Connect the junction between $R_1$ and $R_2$ to A2 — this monitors $V_{R_2}$ directly.
6. The voltage across $R_1$ is then $V_{R_1} = V_{A1} - V_{A2}$.

5. Procedure

1. Open the SEELab3 / ExpEYES app and select the “Ohm’s Law (AC)” experiment.
2. Set the WG to a suitable frequency — $500\text{ Hz}$ is a good starting point — with a moderate amplitude.
3. Click “Start”. Two traces will appear:
   • A1 — the total applied voltage (also the voltage across both $R_1 + R_2$)
   • A2 — the voltage across $R_2$
4. Select a region of the graph (a clean sinusoidal section). The software will analyse it and display:
   • Peak voltage of each trace
   • Frequency
   • Phase difference between A1 and A2
5. Record the peak voltages from the display. Note that the phase difference between A1 and A2 should be $0°$, confirming that both traces are in phase (as expected for a resistive circuit).
6. Observe the RMS values displayed on the channel icons. Verify that $V_{rms} \approx V_{peak}/\sqrt{2}$.
7. Calculate $I_0$ from $V_{R_1,\text{peak}} / R_1$ and then compute $R_2 = V_{R_2,\text{peak}} / I_0$.
8. Compare the calculated $R_2$ with its marked value.
9. Optional: Repeat at different frequencies (e.g., 100 Hz, 1000 Hz, 2000 Hz) to confirm that the result is frequency-independent — a key property of resistors.

Steady State Response (Phone App)

Steady State Setup For ExpEYES17

6. Observation Table

6a. Voltage and Phase Measurements

6b. Ohm’s Law Verification (at $f = 500\text{ Hz}$)

6c. RMS Verification

7. Results and Discussion

• The peak voltage across $R_1$ was found to be ____ V, giving a peak current of ____ mA.
• The peak voltage across $R_2$ was ____ V, yielding a calculated resistance of ____ $\Omega$, which agrees with the marked value of $560\text{ }\Omega$ within ____ %.
• The phase difference between the two voltage traces was measured to be ____ °, confirming that voltage and current are in phase for a resistive element under AC, as predicted by Ohm’s Law.
• The RMS voltages displayed by the software agreed with $V_{peak}/\sqrt{2}$ to within experimental error, verifying the sinusoidal nature of the waveform.
• The calculated value of $R_2$ remained consistent across all tested frequencies, confirming that resistance is frequency-independent — a fundamental property that distinguishes resistors from reactive components.

8. Precautions

1. Input Impedance Effect: The $1\text{ M}\Omega$ input impedance of channels A1 and A2 is in parallel with the circuit elements they monitor. For the resistor values used here ($R_1 = 1\text{ k}\Omega$, $R_2 = 560\text{ }\Omega$), this loading effect is negligible (less than $0.1\%$). For very high circuit resistances (e.g., $> 100\text{ k}\Omega$), this error becomes significant and must be corrected.
2. Clean Region Selection: When the software analyses the selected region of the graph to extract peak voltage and phase, select a portion with at least 2–3 complete, undistorted sinusoidal cycles. Avoid the transient start-up region.
3. Resistor Tolerance: Standard resistors have $\pm 5\%$ tolerance (gold band) or $\pm 1\%$ (brown band). A discrepancy of a few percent between the calculated and marked value is expected and acceptable.

9. Troubleshooting

Pulse Width and Duty Cycle Measurement

1. Aim

To measure the frequency and duty cycle of a square wave signal using the digital frequency counter input (IN2) and to observe the effect of pulse-width modulation.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

A square wave is characterized by its Frequency (how many cycles per second) and its Duty Cycle (the percentage of time the signal remains in the “High” state).

The Duty Cycle ($D$) is calculated as: \(D = \frac{T_{on}}{T_{total}} \times 100\%\)

Where:

• $T_{on}$ is the time the signal is at high level (Pulse Width).
• $T_{total}$ is the total time for one full cycle ($T_{on} + T_{off}$).

The IN2 terminal on the SEELab3 acts as a high-speed digital timer. It measures the time interval between a rising edge and a falling edge ($T_{on}$) and between two consecutive rising edges ($T_{total}$) to calculate the duty cycle accurately.

4. Circuit Diagram / Setup

1. Signal Source: Connect SQ1 to IN2.
2. Monitoring: Connect SQ1 to A1 so you can visually confirm the waveform on the oscilloscope.
3. Note: The digital inputs (IN2, SEN) expect a “Logic Level” signal. The Low level should be $0V$, and the High level should be between $3V$ and $5V$.

5. Procedure

1. Open the SEELab3 software and select the “Duty Cycle” or “Frequency Counter” tool.
2. Set the Source: In the Waveform Generator panel, set SQ1 to a frequency (e.g., $1000\text{ Hz}$) and an initial duty cycle of 50%.
3. Measure: Tap or click on the IN2 icon in the software interface. The device will perform the timing measurement and display the Frequency and Duty Cycle.
4. Vary the Width: Change the duty cycle of SQ1 to 20% and then 80%. Re-measure using the IN2 icon and observe how the $T_{on}$ width changes on the A1 trace.
5. Timeout Check: Disconnect the wire from IN2 and try to measure again. The software will report a “Timeout” because it cannot find the signal edges.

6. Observation Table

7. Results and Discussion

• The frequency and duty cycle of the signal from SQ1 were accurately measured by the IN2 terminal.
• It was observed that the $1000\text{ Hz}$ frequency remained constant while the pulse width varied according to the duty cycle setting.
• The “Timeout” error confirms that the digital timer requires a continuous series of pulses (edges) to perform a calculation.

8. Precautions

1. Voltage Levels: Do not apply more than $5V$ to the IN2 or SEN terminals, as these are digital logic inputs.
2. Grounding: Ensure a clean common ground to avoid “triggering” on electrical noise, which could lead to incorrect frequency readings.
3. Frequency Limits: For very high frequencies, the precision of the duty cycle measurement may decrease due to the internal clock resolution of the microcontroller.

9. Troubleshooting

Study of Active Filter Circuits

1. Aim

To study the frequency and phase response of an active band-pass filter built around an operational amplifier, to measure the voltage gain as a function of frequency, to identify the resonant (centre) frequency, and to automate the frequency sweep using a Python program.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Resistors: $R_1 = 10\text{ k}\Omega$, $R_2 = 1\text{ k}\Omega$, $R_3 = 100\text{ k}\Omega$
• Capacitors: $C_1 = 0.1\text{ }\mu F$, $C_2 = 0.01\text{ }\mu F$
• Operational Amplifier: OP07 (or equivalent precision op-amp) with $\pm 6\text{ V}$ supply
• Breadboard and connecting wires
• PC with Python 3 (libraries: expeyes, numpy, scipy, matplotlib)

3. Theory & Principle

3.1 Filters

A filter is a circuit whose gain depends on the frequency of the input signal. The four basic types are:

• Low-pass filter (LPF): passes frequencies below a cut-off frequency $f_c$; attenuates higher frequencies.
• High-pass filter (HPF): passes frequencies above $f_c$; attenuates lower frequencies.
• Band-pass filter (BPF): passes a band of frequencies centred on a resonant frequency $f_0$; attenuates both below and above.
• Band-stop (Notch) filter: attenuates a specific narrow band of frequencies.

3.2 Active vs Passive Filters

A passive filter uses only R, L, C components. An active filter incorporates an operational amplifier, which provides gain, impedance buffering, and eliminates the loading effect between stages — allowing sharper and more controllable roll-off without the use of bulky inductors.

3.3 Voltage Gain and the Bode Plot

The voltage gain at each frequency is defined as:

Expressed in decibels (dB):

A plot of gain (dB) versus frequency on a logarithmic frequency axis is called a Bode plot. The frequency at which the gain drops to $\frac{1}{\sqrt{2}}$ of its peak value (i.e., $-3\text{ dB}$ below the peak) defines the bandwidth edges $f_1$ and $f_2$. The SEELab app plots the amplitude ratio of output and input signals vs frequency.

3.4 The Designed Circuit

The active band-pass filter in this experiment uses an OP07 op-amp with the following component values:

The circuit was designed using the Okawa Online Filter Design Tool. The theoretical resonant frequency is:

Design constraint: Choose component values such that the peak gain $A_v < 1$ (i.e., $< 0\text{ dB}$) to prevent output clipping. The WG frequency range of SEELab3/ExpEYES-17 is 5 Hz to 5000 Hz — all measurements must lie within this range.

3.5 Phase Response

In addition to amplitude, the output signal is phase-shifted relative to the input by an angle $\phi(f)$ that varies with frequency. At the resonant frequency of a band-pass filter, the phase shift is $0°$. Below $f_0$ the output leads the input; above $f_0$ it lags. Extracting phase requires fitting the time-domain waveforms to a sinusoidal model.

4. Circuit Diagram / Setup

1. Assemble the active band-pass filter on a breadboard using the component values listed above. Refer to the schematic displayed in the SEELab3 app.
2. Power the op-amp from the $\pm 12\text{ V}$ supply rails (or the available dual supply). Connect GND of the supply to the SEELab3 GND.
3. WG → Filter input: Connect the Wave Generator output (WG) to both the filter input and channel A2 (to monitor $V_{in}$).
4. Filter output → A2: Connect the op-amp output to channel A1 (to monitor $V_{out}$).

Steady State Response (Phone App)

Steady State Setup For ExpEYES17

5. Procedure

5a. Manual / App-Based Measurement

1. Open the SEELab3 app and select the “Filter” experiment.
2. Screen 1 — Waveform View: Set an initial frequency of $\approx 100\text{ Hz}$. The display shows $V_{in}$ (A1) and $V_{out}$ (A2) simultaneously. Slide vertically on the WG icon to change the frequency.
3. Sweep the frequency from $\approx 100\text{ Hz}$ to $5000\text{ Hz}$ and observe how the output amplitude changes. Note the frequency at which $V_{out}$ is maximum — this is close to $f_0$.
4. If output amplitude clips anywhere within the range, reduce input signal to 1V amplitude.
5. Screen 2 — Record Data: Enter the start frequency, stop frequency, and step size. Click “Record”. The software automatically sweeps through all frequencies and plots:
   • Gain plot: $A_v$ (or dB) vs $f$
   • Phase plot: $\phi$ vs $f$
6. Read off the peak frequency ($f_0$), the $-3\text{ dB}$ bandwidth edges ($f_1$, $f_2$), and the peak gain from the plot.

5b. Python Automation

The Python program replicates the manual sweep programmatically:

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# filter-resp.py
# Measures voltage gain vs frequency and saves to CSV

import expeyes.eyesj as eyes
import numpy as np
import time

p = eyes.open()          # connect to SEELab3 / ExpEYES

start_freq  = 100        # Hz
stop_freq   = 5000       # Hz
step_freq   = 50         # Hz
amplitude   = 80         # WG amplitude (0–100 %)

results = []             # list to collect [freq, Vin, Vout, gain]

freq = start_freq
while freq <= stop_freq:
    p.set_sine(freq, amplitude)          # set WG frequency
    time.sleep(0.1)                      # allow signal to settle
    Vin  = p.get_voltage('A1')           # measure input amplitude
    Vout = p.get_voltage('A2')           # measure output amplitude
    gain = Vout / Vin if Vin != 0 else 0
    results.append([freq, Vin, Vout, gain])
    print(f"f={freq:5d} Hz  Vin={Vin:.3f}  Vout={Vout:.3f}  Gain={gain:.4f}")
    freq += step_freq

# Save data to CSV
with open('filter-resp.csv', 'w') as f:
    f.write('frequency,Vin,Vout,gain\n')
    for row in results:
        f.write(','.join(f'{v:.6f}' for v in row) + '\n')

print("Data saved to filter-resp.csv")
p.close()

The analysis program reads the saved CSV and fits a Gaussian curve to the gain-frequency data to extract $f_0$ and bandwidth:

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# filter-resp-analyse.py
# Reads CSV, plots frequency response, fits Gaussian to gain peak

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

data = np.loadtxt('filter-resp.csv', delimiter=',', skiprows=1)
freq = data[:, 0]
gain = data[:, 3]

# Gaussian model: A * exp( -(f - f0)^2 / (2*sigma^2) )
def gaussian(f, A, f0, sigma):
    return A * np.exp(-0.5 * ((f - f0) / sigma) ** 2)

# Initial guesses
p0 = [max(gain), freq[np.argmax(gain)], 200]
popt, _ = curve_fit(gaussian, freq, gain, p0=p0)
A_fit, f0_fit, sigma_fit = popt

# -3 dB bandwidth: for Gaussian, BW ≈ 2 * sqrt(2*ln2) * sigma
bw = 2 * np.sqrt(2 * np.log(2)) * abs(sigma_fit)

print(f"Peak gain  : {A_fit:.4f}")
print(f"Centre freq: {f0_fit:.1f} Hz")
print(f"Bandwidth  : {bw:.1f} Hz")
print(f"Q factor   : {f0_fit / bw:.2f}")

plt.figure(figsize=(8, 4))
plt.plot(freq, gain, 'o', markersize=4, label='Measured')
plt.plot(freq, gaussian(freq, *popt), '-', label=f'Gaussian fit  $f_0$={f0_fit:.1f} Hz')
plt.axhline(A_fit / np.sqrt(2), color='gray', linestyle='--', label='-3 dB level')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Voltage Gain $A_v$')
plt.title('Active Band-Pass Filter — Frequency Response')
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('freq-resp.png', dpi=150)
plt.show()

6. Observation Table

6a. Manual Frequency Sweep

6b. Bandwidth and Quality Factor

7. Results and Discussion

• The filter exhibited a band-pass characteristic with maximum gain at $f_0 =$ ____ Hz, against a theoretical value of $527.8\text{ Hz}$.
• The peak voltage gain was $A_{v,\text{max}} =$ ____ (____ dB), which is less than unity as designed.
• The $-3\text{ dB}$ bandwidth was found to be $\Delta f =$ ____ Hz, giving a quality factor $Q =$ ____.
• The Gaussian fit to the Python-acquired data gave $f_0 =$ ____ Hz and $Q =$ ____, in close agreement with the app-based measurement.
• The phase response crossed $0°$ at the resonant frequency, confirming band-pass behavior.
• If the 100K is replaced with 20K ohms, the filter exhibited a band-pass characteristic with maximum gain at $f_0 =$ ____ Hz, against a theoretical value of $____\text{ Hz}$.

8. Precautions

1. Gain less than unity: Design the filter so the peak gain $A_v < 1$. A gain $> 1$ will cause the op-amp output to clip against the supply rails, distorting the waveform and making amplitude measurements unreliable.
2. Frequency range: The WG of SEELab3/ExpEYES-17 operates only between 5 Hz and 5000 Hz. Design $f_0$ well within this range; a value near $500\text{ Hz}$ is ideal to allow observation of both roll-off slopes.
3. Op-amp supply: Ensure the OP07 is powered from a stable dual supply ($\pm 12\text{ V}$ or $\pm 9\text{ V}$) with the supply GND tied to the SEELab3 GND. A floating supply ground will corrupt all measurements.
4. Settle time in Python sweep: Insert a short delay (time.sleep) after changing the WG frequency before measuring amplitudes, so the circuit reaches steady state. Too short a delay at low frequencies introduces significant error.
5. Step size selection: Use a fine step size (e.g., $20$–$50\text{ Hz}$) near the resonant frequency to capture the peak accurately; a coarser step is sufficient at the extremes of the sweep.

9. Troubleshooting

Output Impedance of a Voltage Source

1. Aim

To demonstrate the concept of output impedance of a practical voltage source using the programmable DC source PV1 of SEELab3, and to determine the voltage at which the actual output begins to deviate from the set-point due to the finite output impedance of the source.

2. Apparatus / Components Required

• SEELab3 unit
• Resistor $R_L = 100\text{ }\Omega$ (load resistor)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

3.1 Ideal vs Practical Voltage Source

An ideal voltage source maintains a perfectly constant terminal voltage regardless of the current drawn from it. Its output impedance is zero.

A practical voltage source, however, has a finite internal (output) impedance $Z_{out}$ in series with the ideal source. This can be modelled as:

where $V_{set}$ is the no-load (open-circuit) set-point voltage, $I$ is the load current, and $Z_{out}$ is the output impedance. The terminal voltage $V_{terminal}$ is what actually appears at the output terminals and is always less than $V_{set}$ whenever current is drawn.

3.2 Voltage Divider Effect

When a load resistor $R_L$ is connected, the circuit forms a voltage divider between $Z_{out}$ and $R_L$:

The fractional voltage drop across $Z_{out}$ is:

For $Z_{out} \ll R_L$ this drop is negligible and the source behaves nearly ideally. As $V_{set}$ is increased, the current $I = V_{terminal}/R_L$ increases, and the drop $I \cdot Z_{out}$ grows until the source can no longer sustain the set-point — the terminal voltage saturates.

3.3 Determining $Z_{out}$

By measuring the open-circuit voltage $V_{OC}$ (no load, $R_L = \infty$) and the loaded terminal voltage $V_L$ with a known load $R_L$, the output impedance can be calculated as:

Alternatively, from the slope of the $V_{terminal}$ vs $I$ graph:

A steeper slope indicates a higher output impedance (a “weaker” source).

3.4 Current Limit and Saturation

Every practical source has a maximum current it can deliver, set by either the output impedance or an internal current-limiting circuit. Beyond the saturation point, increasing $V_{set}$ no longer raises the terminal voltage proportionally — the $V_{terminal}$ vs $V_{set}$ curve bends away from the ideal $45°$ line.

4. Circuit Diagram / Setup

1. Connect one end of the load resistor $R_L$ ($100\text{ }\Omega$) to PV1 (Programmable Voltage output).
2. Connect the other end of $R_L$ to GND.
3. Connect PV1 also to A1 to monitor the actual terminal voltage of the source.

The measured voltage at A1 is the true terminal voltage — it includes the effect of output impedance. The set-point is what you program in the software. Comparing the two reveals the voltage drop across $Z_{out}$.

5. Procedure

1. Open the SEELab3 app and navigate to the “Output Impedance” experiment (or use the PV1 control panel directly).
2. No-load measurement: Before connecting $R_L$, set PV1 to several voltages and record $V_{A1}$ each time. This establishes the open-circuit ($V_{OC}$) baseline — any deviation here is due to the input impedance of A1 ($1\text{ M}\Omega$), which is negligible.
3. Connect $R_L$: Connect the $100\text{ }\Omega$ load from PV1 to GND with A1 still monitoring PV1.
4. Sweep the set-point: Increase $V_{set}$ in steps from $0\text{ V}$ upward. At each step, record:
   • The programmed set-point voltage $V_{set}$
   • The actual terminal voltage $V_{terminal}$ read from A1
5. Continue until the terminal voltage clearly stops tracking the set-point (saturation / current limit is reached).
6. Plot $V_{terminal}$ vs $V_{set}$. The ideal curve is the $45°$ line $V_{terminal} = V_{set}$. Deviation from this line marks the onset of current limiting.
7. Calculate $Z_{out}$ in the linear region using the formula in §3.3 at a chosen operating point.

6. Observation Table

Load Resistor $R_L$: ____ $\Omega$

6a. No-Load ($R_L$ disconnected)

6b. Loaded ($R_L = 100\text{ }\Omega$ connected)

7. Results and Discussion

• In the no-load condition, $V_{terminal} \approx V_{set}$ across the full range, confirming that the input impedance of A1 has negligible loading effect.
• With $R_L = 100\text{ }\Omega$ connected, the terminal voltage tracked the set-point closely at low voltages but began to deviate at $V_{set} \approx$ ____ V, indicating the onset of current saturation.
• The output impedance $Z_{out}$ was estimated to be approximately ____ $\Omega$ from the loaded measurements in the linear region.
• The maximum current deliverable by PV1 before saturation was approximately $I_{max} = V_{terminal,\text{sat}} / R_L =$ ____ mA.
• The results demonstrate that a practical source behaves ideally only when the load current is well below its current limit, i.e., when $R_L \gg Z_{out}$.

8. Precautions

1. Do not short-circuit PV1: Never connect PV1 directly to GND without a load resistor. With $Z_{out}$ being small, even a short circuit draws a very large current that may damage the output stage. Always keep $R_L \geq 100\text{ }\Omega$.
2. Monitor A1, not the software set-point: The set-point displayed in the software is what the firmware requests; the actual output depends on the load. Always use the A1 reading as the true terminal voltage.
3. Allow settling time: After changing $V_{set}$, wait briefly for the output to settle before recording the A1 value, especially at higher currents where the internal regulator may take a moment to stabilize.
4. Component power rating: At $5\text{ V}$ across $100\text{ }\Omega$, the power dissipated is $P = V^2/R_L = 250\text{ mW}$. Ensure the resistor is rated for at least $0.5\text{ W}$ to avoid overheating.

9. Troubleshooting

Steady-State Response of a Series RC Circuit

1. Aim

To study the behavior of a series RC circuit under a sinusoidal (AC) voltage, and to measure the voltage amplitudes across each element and the phase difference between the applied voltage and the current.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 1\text{ k}\Omega$)
• One Capacitor ($C = 1\text{ }\mu F$)
• Connecting wires
• PC or Smartphone with SEELab3 / ExpEYES software

3. Theory & Principle

When a sinusoidal voltage $V(t) = V_0 \sin(\omega t)$ is applied to a series RC circuit, the capacitor offers a frequency-dependent opposition called Capacitive Reactance, given by:

The total impedance of the series RC circuit is:

The current in the circuit leads the voltage across the capacitor by $90°$ (i.e., $\frac{\pi}{2}$ radians). The phase angle between the applied voltage and the current (which is in phase with $V_R$) is:

Since the voltages across $R$ and $C$ are $90°$ out of phase with each other, the total applied voltage is obtained by vector addition:

Note: For $R = 1\text{ k}\Omega$, $C = 1\text{ }\mu F$, and $f = 150\text{ Hz}$, the calculated phase angle is $\phi = 46.79°$, and the voltages across $R$ and $C$ are nearly equal, making this an ideal configuration to visualize the phase relationships.

4. Circuit Diagram / Setup

1. Series Connection: Connect the Capacitor ($C$) and Resistor ($R$) in series.
2. AC Source: Connect the free end of the capacitor to WG (Wave Generator output of SEELab3/ExpEYES-17).
3. Ground: Connect the free end of the resistor to GND.
4. Measurement (Applied Voltage): Connect the WG end also to A1 to monitor the applied sinusoidal voltage.
5. Measurement (Resistor Voltage): Connect the junction between $C$ and $R$ to A2 to monitor $V_R$ (which is in phase with the current).
6. Measurement (Capacitor Voltage): $V_C$ can be derived as $V_{applied} - V_R$.

5. Procedure

1. Open the SEELab3 / ExpEYES app and select the “RC Steady State” experiment.
2. Set the wave generator (WG) to output a sinusoidal signal at $f = 150\text{ Hz}$.
3. Click “Start” to begin data acquisition. The oscilloscope screen will display three traces:
   • The applied voltage (from WG / A1)
   • The voltage across R ($V_R$, in phase with the current)
   • The voltage across C ($V_C$, lagging behind the current by $90°$)
4. Note the peak amplitudes of each trace from the display.
5. Observe the phase difference ($\phi$) between the applied voltage and $V_R$ as reported by the software.
6. Vary the frequency (e.g., 50 Hz, 100 Hz, 200 Hz, 500 Hz) and repeat Steps 3–5 to study how $Z_C$ and $\phi$ change with frequency.
7. Compare the measured phase angle and voltages with theoretically calculated values.

Steady State Response (Phone App)

Steady State Response (Desktop)

6. Observation Table

7. Results and Discussion

• The voltage across the capacitor was observed to lag behind the current (and $V_R$) by approximately $90°$.
• At $f = 150\text{ Hz}$, the measured phase angle was found to be ____ °, against a theoretical value of $46.79°$.
• The vector sum $\sqrt{V_R^2 + V_C^2}$ was found to be ____ V, which agrees closely with the directly measured applied voltage of ____ V, verifying Kirchhoff’s Voltage Law in phasor form.
• As frequency increases, $Z_C$ decreases, causing the phase angle $\phi$ to decrease and $V_R$ to dominate over $V_C$.

8. Precautions

1. Frequency Selection: Choose a frequency where $Z_C \approx R$ (i.e., $f \approx \frac{1}{2\pi RC}$) to get a clear, observable phase difference and roughly equal voltage division. For $R = 1\text{ k}\Omega$, $C = 1\text{ }\mu F$, this is approximately $159\text{ Hz}$.
2. Component Tolerance: Resistors and capacitors have manufacturing tolerances ($\pm 5\%$ to $\pm 20\%$). The measured phase angle may differ slightly from the theoretical value; this is expected.
3. Input Impedance Loading: The $1\text{ M}\Omega$ input impedance of the measurement channels is much larger than the circuit impedances used here and can generally be ignored. However, for very high $R$ values, this loading effect must be considered.
4. Stable Waveform: Allow the waveform display to stabilize for a few seconds before recording amplitudes and phase differences.

9. Troubleshooting

Transient Response of an RC Circuit

1. Aim

To study the charging and discharging behavior of a capacitor in a series RC circuit and to determine the Time Constant ($\tau$) by fitting the experimental data.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 1\text{ k}\Omega$ )
• One Capacitor ($C = 1\text{ }\mu F$ )
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

When a voltage step ($V_0$) is applied to an empty capacitor through a resistor, the voltage across the capacitor ($V_C$) does not jump instantly. It increases exponentially according to: \(V_C(t) = V_0(1 - e^{-t/RC})\)

Similarly, when a charged capacitor is allowed to discharge through a resistor, the voltage decays as: \(V_C(t) = V_0 e^{-t/RC}\)

The product $RC$ is called the Time Constant ($\tau$). It represents the time required for the capacitor to charge to approximately $63.2\%$ of the applied voltage or discharge to $36.8\%$ of its initial value.

4. Circuit Diagram / Setup

1. Series Connection: Connect the Resistor ($R$) and Capacitor ($C$) in series.
2. Input Source: Connect the free end of the resistor to OD1 (Digital Output used for the voltage step).
3. Ground: Connect the free end of the capacitor to GND.
4. Measurement: Connect the junction between the resistor and capacitor to A1 to monitor $V_C$.

5. Procedure

1. Open the SEELab3 app and select the “RC Transient” experiment.
2. The software is programmed to toggle OD1 from $0V$ to $5V$ and simultaneously start high-speed data acquisition on A1.
3. Click on “Charge” (or Start). The software will apply the step and display the rising exponential curve.
4. Click on “Discharge”. The software will set OD1 to $0V$ and capture the falling exponential curve.
5. Data Fitting: Select a region of the captured curve. Use the “Fit” tool to apply an exponential fit. The software will display the value of the time constant ($RC$).
6. Compare the experimental $RC$ value with the theoretical value calculated from the component markings ($R \times C$).

6. Observation Table

7. Results and Discussion

• The voltage across the capacitor followed an exponential path during both charging and discharging phases.
• The measured time constant was found to be ____ ms.
• The results verify that it takes approximately $5\tau$ for the capacitor to reach its steady-state (fully charged or discharged) condition.

8. Precautions

1. Selection of RC: Choose $R$ and $C$ values such that the time constant is between $1\text{ ms}$ and $100\text{ ms}$. If $\tau$ is too small, the software may not have enough sampling resolution to capture the curve accurately.
2. Input Impedance: The $1\text{ M}\Omega$ input impedance of A1 is in parallel with the capacitor during discharge. For very high $R$ values (e.g., $1\text{ M}\Omega$), this will introduce significant error.
3. Residual Charge: Ensure the capacitor is fully discharged before starting a new “Charge” cycle for a clean plot starting from $0V$.

9. Troubleshooting

Steady-State Response and Series Resonance of a Series RLC Circuit

1. Aim

To study the behavior of a series RLC circuit under a sinusoidal (AC) voltage, to measure the voltage amplitudes across each element and their phase relationships, and to observe the condition of series resonance — where the net reactive voltage across the LC combination drops to zero.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 1\text{ k}\Omega$)
• One Capacitor ($C = 1\text{ }\mu F$)
• One Inductor ($L = 10\text{ mH}$, with internal DC resistance $r \approx 20\text{ }\Omega$)
• Connecting wires
• PC or Smartphone with SEELab3 / ExpEYES software

3. Theory & Principle

When a sinusoidal voltage is applied to a series RLC circuit, the inductor and capacitor each present a frequency-dependent reactance:

where $R_{eff} = R + r$ accounts for the winding resistance $r$ of the inductor.

The phase angle between the applied voltage and the current is:

Series Resonance

A special condition arises when $Z_L = Z_C$, i.e., when:

Solving for the resonant frequency $f_0$:

At resonance:

• The net reactive impedance $(Z_L - Z_C) = 0$, so the total impedance reduces to $Z = R_{eff}$ — its minimum value.
• The current in the circuit reaches its maximum value.
• The entire applied voltage appears across $R$ — none appears across the LC combination.
• $V_L$ and $V_C$ are individually non-zero and equal in magnitude, but cancel each other exactly because they are $180°$ out of phase.
• The phase angle $\phi = 0°$ — current and applied voltage are in phase.

Note: For $L = 10\text{ mH}$ and $C = 1\text{ }\mu F$, the theoretical resonant frequency is: \(f_0 = \frac{1}{2\pi\sqrt{0.01 \times 10^{-6}}} = \frac{1}{2\pi \times 10^{-4}} \approx 1592\text{ Hz}\) The experiment starts at $1600\text{ Hz}$ and is fine-tuned to find the exact resonance point.

4. Circuit Diagram / Setup

1. Series Connection: Connect $C$, $L$, and $R$ in series in that order.
2. AC Source: Connect the free end of the capacitor to WG (Wave Generator).
3. Ground: Connect the free end of the resistor to GND.
4. A1 (Applied Voltage): Connect the WG end to A1.
5. A3 (Voltage after C): Connect the junction between $C$ and $L$ to A3, so the software can display the voltage across the C (A1-A3) and across L(A3-A2) and detect the zero-phase condition at resonance.
6. A2 (Resistor Voltage): Connect the junction between $R$ and $L$ to A2 to monitor $V_R$ directly (in phase with current).

5. Procedure

1. Open the SEELab3 / ExpEYES app and select the “RLC Steady State” experiment.
2. Set the wave generator (WG) to output a sinusoidal signal starting at $f = 1600\text{ Hz}$.
3. The screen will show many traces: applied voltage, $V_R$, $V_LC$, $V_L$, $V_C$.
4. Finding Resonance: Slowly vary the frequency up and down around $1600\text{ Hz}$ while watching the phase difference between A1 (applied voltage) and A2 (V_R). Resonance is reached when:
   • The LC voltage trace collapses to near zero, and
   • The phase difference between applied voltage and $V_R$ becomes $0°$.
5. Record the resonant frequency $f_0$ from the software display.
6. At resonance, note the individual amplitudes of $V_R$, $V_L$, and $V_C$ and verify that $V_L \approx V_C$ while $V_{LC} \approx 0$.
7. Off-resonance sweep: Record voltages and phase angles at several frequencies below and above $f_0$ to map out the full impedance–frequency behavior.

Steady State Response (Phone App)

Steady State Setup For ExpEYES17

6. Observation Table

6a. Frequency Sweep

6b. At Resonance ($f = f_0$)

7. Results and Discussion

• Series resonance was observed at $f_0 =$ ____ Hz, against a theoretical value of $\approx 1592\text{ Hz}$.
• At resonance, the net voltage across the LC combination fell to approximately ____ V (ideally $0\text{ V}$), confirming that $V_L$ and $V_C$ cancel each other out.
• The individual voltages at resonance were $V_L =$ ____ V and $V_C =$ ____ V, which are nearly equal, verifying $Z_L = Z_C$ at $f_0$.
• Below resonance, the circuit was capacitive ($Z_C > Z_L$, $\phi < 0°$, current leads voltage).
• Above resonance, the circuit was inductive ($Z_L > Z_C$, $\phi > 0°$, current lags voltage).
• The phasor sum $\sqrt{V_R^2 + (V_L - V_C)^2}$ agreed closely with the directly measured applied voltage at all frequencies, verifying Kirchhoff’s Voltage Law in phasor form.

8. Precautions

1. Include Winding Resistance: Always measure the DC resistance $r$ of the inductor with a multimeter and use $R_{eff} = R + r$ in all theoretical calculations to avoid a systematic error in the phase angle.
2. Fine-tune for Resonance: The resonant frequency is sharp. Adjust the WG frequency in small steps (e.g., $10\text{ Hz}$ at a time) near the theoretical $f_0$ and watch for the simultaneous collapse of $V_{LC}$ and the zeroing of the phase angle.
3. Component Tolerance: Capacitors and inductors may deviate from marked values by $\pm 10\%$ to $\pm 20\%$. The measured $f_0$ may differ from the theoretical value; use the measured component values if an LCR meter is available.
4. Avoid Core Saturation: Do not use excessively large WG amplitudes with iron-core inductors, as nonlinearity distorts the waveforms.
5. Stable Readings: Allow the waveform display to stabilize at each frequency before recording amplitudes and phase values.

9. Troubleshooting

Transient Response of an RLC Circuit

1. Aim

To study the evolution of voltage across a capacitor in a series LCR circuit in response to a voltage step and to analyze the resulting damped oscillations.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• Resistor ($R = 100\text{ }\Omega$)
• Inductor ($L = 10\text{ mH}$)
• Capacitor ($C = 0.1\text{ }\mu F$)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

A series LCR circuit is a second-order system. When a voltage step ($v_s$) is applied, the relationship between the components is governed by Kirchhoff’s Voltage Law (KVL):

Substituting $i = C\frac{dv_c}{dt}$, we get the second-order differential equation:

The behavior of the system depends on the roots of the characteristic equation: \(\alpha^2 + \frac{R}{L}\alpha + \frac{1}{LC} = 0\)

Depending on the values of $L$, $C$, and $R$, the response can be:

1. Underdamped: $(R/2L)^2 < 1/LC$ (Oscillations that decay over time).
2. Critically Damped: $(R/2L)^2 = 1/LC$ (Fastest return to steady state without oscillation).
3. Overdamped: $(R/2L)^2 > 1/LC$ (Slow return to steady state without oscillation).

For the underdamped case (using the provided components), the solution is a damped sinusoid: \(v(t) = e^{\beta t} [K \sin(\gamma t + \theta)]\) Where $\beta = -R/2L$ is the damping factor and $\gamma = \sqrt{\frac{1}{LC} - (\frac{R}{2L})^2}$ is the angular frequency of oscillation.

4. Circuit Diagram / Setup

1. Connect the Resistor ($R$), Inductor ($L$), and Capacitor ($C$) in series.
2. Connect the free end of the Resistor to OD1 (Digital Output).
3. Connect the free end of the Capacitor to GND.
4. Connect A1 to the junction between the inductor and the Capacitor to measure $v_c(t)$.

5. Procedure

1. Open the SEELab3 software and select the “LCR Transient” experiment.
2. Click on “Step OD1 0-5V”. The software applies a $5V$ step and captures the high-speed voltage variation at A1.
3. Observe the oscillating waveform. Note how the amplitude of the sine wave decreases over time.
4. Analysis: Select the oscillating region on the graph.
5. Use the “Damped Sine Fit” tool. The software will extract the frequency and the damping factor ($\beta$).
6. Export: Save the data as a CSV file for further analysis in Python.
7. Click on “Step OD1 5-0V”. The software applies a $5-0V$ step and captures the high-speed voltage variation at A1. Repeat steps 3 through 6 .

Transient Response (Phone App)

Charging and Discharge Curves

6. Observation Table

Components: $L = 10\text{ mH}$, $C = 0.1\text{ }\mu F$, $R = 100\text{ }\Omega$

7. Results and Discussion

• The circuit exhibited _____________, as expected from the selected component values.
• The frequency of oscillation was found to be ____ Hz.
• Increasing the resistance $R$ _____ (increases/decreases) the damping, causing the oscillations to die out______ (faster/slower).

8. Python Programming & Data

• Download Python Program for LCR Transient
• Download Analysis Script (Rename exported file to lcr.csv)
• Download Sample Data

9. Troubleshooting

Steady-State Response of a Series RL Circuit

1. Aim

To study the behavior of a series RL circuit under a sinusoidal (AC) voltage, and to measure the voltage amplitudes across each element and the phase difference between the applied voltage and the current.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Inductor ($L = 10\text{ mH}$, with internal DC resistance $r \approx 20\text{ }\Omega$)
• One Resistor ($R = 1\text{ k}\Omega$)
• Connecting wires
• PC or Smartphone with SEELab3 / ExpEYES software

3. Theory & Principle

When a sinusoidal voltage $V(t) = V_0 \sin(\omega t)$ is applied to a series RL circuit, the inductor offers a frequency-dependent opposition called Inductive Reactance, given by:

Unlike a resistor, an ideal inductor does not dissipate energy — it stores energy in its magnetic field. However, a real inductor also has a small DC winding resistance $r$ that must be included. The effective series resistance is therefore $R_{eff} = R + r$.

The total impedance of the series RL circuit is:

The voltage across the inductor leads the current by $90°$ (i.e., $\frac{\pi}{2}$ radians). The phase angle between the applied voltage and the current (which is in phase with $V_R$) is:

Since the voltages across $R$ and $L$ are $90°$ out of phase, the total applied voltage is obtained by phasor (vector) addition:

Note: For $R = 1\text{ k}\Omega$ (+ $20\text{ }\Omega$ winding resistance), $L = 10\text{ mH}$, and $f = 5000\text{ Hz}$, the inductive reactance $Z_L = 2\pi \times 5000 \times 0.01 \approx 314\text{ }\Omega$. The calculated phase angle is $\phi = 17.12°$ and the measured value is approximately $18°$. The small discrepancy is due to component tolerances and the winding resistance of the inductor.

4. Circuit Diagram / Setup

1. Series Connection: Connect the Resistor ($R$) and Inductor ($L$) in series.
2. AC Source: Connect the free end of the inductor to WG (Wave Generator output of SEELab3/ExpEYES-17).
3. Ground: Connect the free end of the resistor to GND.
4. Measurement (Applied Voltage): Connect the WG end also to A1 to monitor the applied sinusoidal voltage.
5. Measurement (Resistor Voltage): Connect the junction between $L$ and $R$ to A2 to monitor $V_R$ (which is in phase with the current).

5. Procedure

1. Open the SEELab3 / ExpEYES app and select the “RL Steady State” experiment.
2. Set the wave generator (WG) to output a sinusoidal signal at $f = 5000\text{ Hz}$.
3. The oscilloscope screen will display three traces:
   • The applied voltage (from WG / A1)
   • The voltage across R ($V_R$, in phase with the current. A2.)
   • The voltage across L ($V_L$, leading the current by $90°$ . calculated as A1-A2 )
4. Note the peak amplitudes of each trace from the display.
5. Observe the phase difference ($\phi$) between the applied voltage and $V_R$ as reported by the software.
6. Vary the frequency (e.g., 1000 Hz, 2000 Hz, 5000 Hz, 10000 Hz) and repeat Steps 3–5 to study how $Z_L$ and $\phi$ change with frequency.
7. Compare the measured phase angle and voltages with theoretically calculated values, remembering to include the winding resistance $r$ of the inductor.

Steady State Response (Phone App)

Steady State Setup For ExpEYES17

6. Observation Table

Effective Resistance $R_{eff} = R + r$: ____ $\Omega$

7. Results and Discussion

• The voltage across the inductor was observed to lead the current (and $V_R$) by approximately $90°$, which is opposite in sense to the RC circuit where $V_C$ lags.
• At $f = 5000\text{ Hz}$, the measured phase angle was found to be ____ °, against a theoretical value of $17.12°$.
• The vector sum $\sqrt{V_R^2 + V_L^2}$ was found to be ____ V, agreeing closely with the directly measured applied voltage of ____ V, verifying Kirchhoff’s Voltage Law in phasor form.
• As frequency increases, $Z_L$ increases, causing the phase angle $\phi$ to increase and $V_L$ to dominate over $V_R$. This is the dual behavior of an RC circuit, where $Z_C$ decreases with frequency.

8. Precautions

1. Include Winding Resistance: A real inductor has a DC resistance $r$ in its winding. Always measure this with a multimeter and add it to $R$ when calculating the theoretical phase angle; ignoring it leads to a systematic error.
2. Frequency Selection: Choose a frequency where $Z_L$ is comparable to $R_{eff}$ to get a clearly observable phase difference. For $L = 10\text{ mH}$ and $R = 1\text{ k}\Omega$, this is around $f \approx \frac{R}{2\pi L} \approx 15.9\text{ kHz}$. Lower frequencies like $5000\text{ Hz}$ give a small but measurable phase angle.
3. Core Saturation: Do not use very large signal amplitudes with iron-core inductors, as the core may saturate, making the inductance non-linear and waveforms distorted.
4. Stable Waveform: Allow the waveform display to stabilize for a few seconds before recording amplitudes and phase differences.

9. Troubleshooting

Transient Response of an RL Circuit

1. Aim

To study the transient behavior of an Inductor-Resistor (RL) circuit, observe the growth and decay of current, and determine the Inductance ($L$) by fitting the experimental data.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One Resistor ($R = 100\text{ }\Omega$ or $1000\text{ }\Omega$)
• One Inductor (e.g., 3000-turn coil provided in the kit)
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

Unlike a capacitor which opposes changes in voltage, an Inductor ($L$) opposes changes in current ($I$). When a voltage step ($V_0$) is applied to a series RL circuit, the current does not reach its maximum value ($V_0/R$) instantaneously due to the induced back-EMF.

The current growth is described by: \(I(t) = \frac{V_0}{R} (1 - e^{-t/\tau})\)

The voltage across the inductor ($V_L$) during this growth is: \(V_L(t) = V_0 e^{-t/\tau}\)

The Time Constant ($\tau$) is defined as: \(\tau = \frac{L}{R_{total}}\) Where $R_{total}$ is the sum of the external resistor and the internal DC resistance of the inductor coil.

4. Circuit Diagram / Setup

1. Series Connection: Connect the Resistor ($R$) and Inductor ($L$) in series.
2. Input Source: Connect one end of the Resistor to OD1 (Digital Output used for the voltage step).
3. Ground: Connect one end of the Inductor to GND.
4. Measurement: Connect the junction between the Resistor and Inductor to A1.
5. Note: In this configuration, A1 measures the voltage across the Inductor ($V_R$).

5. Procedure

1. Open the SEELab3 software and select the “RL Transient” experiment.
2. The software toggles OD1 from $0V$ to $5V$ while capturing high-speed data at A1.
3. Click “Capture”. You will see the current ($V_R$) rising exponentially toward a steady-state value.
4. Data Analysis: Select the rising portion of the curve.
5. Use the “Exponential Fit” tool. The software will calculate the time constant $\tau$.
6. Measure the DC resistance of your coil ($R_L$) using the SEELab ohmmeter.
7. Calculate Inductance: $L = \tau \times (R + R_L)$.

Schematic Diagram (A2 Optional)

Charging and Discharge Curves

6. Observation Table

7. Results and Discussion

• The current in the RL circuit increased exponentially, confirming the presence of a back-EMF in the inductor.
• The measured inductance was found to be ____ mH.
• If a different resistor ($R$) is used, the time constant $\tau$ ____ (increases/decreases), but the calculated $L$ should remain constant.

8. Python Programming & Data

This experiment utilizes high-speed triggering to capture the sub-millisecond transition of the inductor.

• Download Python Program for RL Transient
• Download Analysis Script
• Download Sample Data

9. Troubleshooting

XY Plots and Lissajous Figures

1. Aim

To study the relationship between two independent electrical signals by plotting them against each other in XY mode and to observe Lissajous figures generated by different frequency ratios.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• One LC Low Pass Filter (Inductor coil and 0.1uF Capacitor)
• Jumper wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

In standard oscilloscope mode, we plot Voltage (Y) vs. Time (X). In XY Mode, the software plots the instantaneous voltage of one channel (A1) on the X-axis and another channel (A2) on the Y-axis.

Lissajous Figures: When two sine waves are plotted against each other, the resulting pattern is called a Lissajous figure. These patterns are determined by:

1. The ratio of their frequencies ($f_1 / f_2$).
2. The phase difference between them ($\phi$).

If $f_x = f_y$ and they are in phase, the plot is a diagonal line. If they are $90^\circ$ out of phase, it is a circle. For more complex ratios like $1:2$, the figure resembles a figure-eight.

4. Circuit Diagram / Setup

1. Direct XY: Connect WG to A1 and SQ1 to A2.
2. Filter Setup (for complex curves): * Connect SQ1 ($1000\text{ Hz}$) to the input of an LC low-pass filter.
   • Connect the output of the filter to A2. (This converts the square wave into a near-sine wave).
   • Connect WG ($500\text{ Hz}$ sine wave) directly to A1.

5. Procedure

1. Open the SEELab3 app and select the “XY Plot” experiment.
2. Set WG to a $500\text{ Hz}$ Sine Wave.
3. Set SQ1 to a $1000\text{ Hz}$ Square Wave.
4. Observe the standard time-domain traces first to ensure both signals are stable.
5. Switch the display mode to “XY Mode”.
6. Adjust the frequencies slightly to “freeze” the pattern. If the frequencies are exactly $1:2$, the figure-eight pattern will remain stationary. If they are slightly off, the pattern will appear to rotate as the phase drifts.

6. Observation Table

7. Results and Discussion

• The XY plot successfully visualized the phase and frequency relationship between two independent sources.
• Plotting a $500\text{ Hz}$ sine wave against a $1000\text{ Hz}$ filtered square wave produced a classic 1:2 Lissajous figure.
• It was observed that the stability of the figure depends on the precise synchronization of the two frequencies.

8. Precautions

1. Filtering: Using a raw square wave on the Y-axis results in “jumping” dots rather than smooth curves. Passing the square wave through an LC filter smooths the transitions.
2. Scaling: Ensure the Volt/Div settings for both A1 and A2 are similar so the figure is not squashed or stretched.
3. Frequency Limits: Keep frequencies within the range where the software can maintain a high enough sampling rate for a smooth plot.

9. Troubleshooting

Astable Multivibrator Using IC 555

1. Aim

To wire the IC 555 timer in astable (free-running) mode, to measure the output frequency and duty cycle, and to verify the theoretical values predicted by the RC component values using SEELab3.

2. Apparatus / Components Required

• SEELab3 or ExpEYES-17 unit
• IC 555 timer
• Resistors: $R_1 = 2.2\text{ k}\Omega$, $R_2 = 1\text{ k}\Omega$
• Capacitor $C = 1\text{ }\mu F$ (timing), $C_{bypass} = 0.01\text{ }\mu F$ (pin 5 to GND, noise suppression)
• DC supply: $5\text{ V}$ (or $V_{CC}$ from SEELab3)
• Breadboard and connecting wires
• PC or Smartphone with SEELab3 / ExpEYES software

3. Theory & Principle

3.1 The 555 in Astable Mode

In astable mode the 555 has no stable state — its output continuously oscillates between HIGH ($\approx V_{CC}$) and LOW ($\approx 0\text{ V}$) without any external trigger. The timing is set entirely by $R_1$, $R_2$, and $C$.

Internally, the 555 contains a voltage divider that sets two thresholds: the upper threshold at $\frac{2}{3}V_{CC}$ and the lower threshold at $\frac{1}{3}V_{CC}$. The capacitor $C$ charges through $R_1 + R_2$ and discharges through $R_2$ alone, cycling between these two thresholds indefinitely.

3.2 Timing Equations

The charge time (output HIGH) while $C$ charges from $\frac{1}{3}V_{CC}$ to $\frac{2}{3}V_{CC}$ through $R_1 + R_2$:

The discharge time (output LOW) while $C$ discharges from $\frac{2}{3}V_{CC}$ to $\frac{1}{3}V_{CC}$ through $R_2$:

The total period and frequency:

The duty cycle (fraction of period the output is HIGH):

Worked example (ExpEYES-17 values): $R_1 = 2.2\text{ k}\Omega$, $R_2 = 1\text{ k}\Omega$, $C = 1\text{ }\mu F$: \(f = \frac{1.443}{(2200 + 2000) \times 10^{-6}} = 343.6\text{ Hz}, \quad D = \frac{3200}{4200} = 76.2\%\)

Because the capacitor charges through $R_1 + R_2$ but discharges through $R_2$ only, $t_{HIGH} > t_{LOW}$ always — the duty cycle is always above 50% in the standard astable configuration.

3.3 Pin Functions (IC 555)

4. Circuit Diagram / Setup

1. Wire the IC 555 on the breadboard following the schematic in §3.
2. Connect $R_1$ between $V_{CC}$ and pin 7 (discharge).
3. Connect $R_2$ between pin 7 and pin 6/2 (threshold/trigger, tied together).
4. Connect $C$ between pin 6/2 and GND.
5. Connect $C_{bypass}$ ($0.01\text{ }\mu F$) between pin 5 and GND.
6. Tie pin 4 (reset) to $V_{CC}$.
7. A1 monitors pin 3 (output square wave). Also connect pin 3 to IN2 for frequency and duty cycle measurement.
8. A2 monitors pin 6 (capacitor voltage — the sawtooth charging waveform).

5. Procedure

1. Open the SEELab3 / ExpEYES app and navigate to the “IC 555 Astable” experiment or use the oscilloscope directly.
2. Power the 555 from $V_{CC}$ ($5\text{ V}$). The output on A1 should immediately begin toggling — no trigger is needed.
3. Observe A1 (square wave) and A2 (capacitor sawtooth) simultaneously. Confirm:
   • A1 switches between $\approx 0\text{ V}$ and $\approx V_{CC}$.
   • A2 oscillates between $\frac{1}{3}V_{CC}$ and $\frac{2}{3}V_{CC}$.
   • A1 goes HIGH when A2 reaches $\frac{1}{3}V_{CC}$, and LOW when A2 reaches $\frac{2}{3}V_{CC}$.
4. Read the frequency and duty cycle from the IN2 measurement display.
5. Compare with the theoretical values calculated from the formulae in §3.2.
6. Component variation: Swap $R_1$, $R_2$, or $C$ for different values and record how frequency and duty cycle change. Use the online 555 calculator to predict values before measuring.

Mobile App

Desktop App

6. Observation Table

6a. Verification with Standard Values ($R_1 = 2.2\text{ k}\Omega$, $R_2 = 1\text{ k}\Omega$, $C = 1\text{ }\mu F$)

6b. Component Variation

7. Results and Discussion

• The 555 produced a continuous square wave without any external trigger, confirming astable operation.
• At $R_1 = 2.2\text{ k}\Omega$, $R_2 = 1\text{ k}\Omega$, $C = 1\text{ }\mu F$, the measured frequency was ____ Hz against a theoretical value of $343.6\text{ Hz}$ — a discrepancy of ____ %, consistent with the $\pm 5\%$ tolerance of the resistors and $\pm 20\%$ of the capacitor.
• The capacitor voltage at A2 oscillated between ____ V and ____ V, in close agreement with $\frac{1}{3}V_{CC}$ and $\frac{2}{3}V_{CC}$.
• The duty cycle was always above 50%, as expected, because $R_1 > 0$ always makes $t_{HIGH} > t_{LOW}$.
• Increasing $C$ by 10× reduced the frequency by approximately 10×, confirming the inverse proportionality $f \propto 1/C$.

8. Precautions

1. Pin 4 must be HIGH: Pin 4 (Reset) is active-LOW. If left floating it may pick up noise and reset the oscillator unpredictably. Always tie it firmly to $V_{CC}$.
2. Pin 5 bypass capacitor: The $0.01\text{ }\mu F$ from pin 5 to GND suppresses power-supply noise on the internal voltage divider. Omitting it can cause jitter in the output frequency, especially at high frequencies or on a noisy supply.
3. Supply voltage: The 555 operates from $5\text{ V}$ to $15\text{ V}$. The output HIGH level is approximately $V_{CC} - 1.5\text{ V}$. At $5\text{ V}$ supply the output swings $0$–$3.5\text{ V}$, which is within the safe input range of A1.
4. Component tolerance: Standard resistors ($\pm 5\%$) and electrolytic capacitors ($\pm 20\%$) will cause measured frequency to differ from theoretical by up to $\sim 25\%$ in the worst case. Use $1\%$ metal-film resistors and a measured capacitor value for closer agreement.
5. Duty cycle cannot reach 50% with the standard astable configuration because $R_1$ is always in the charge path. To achieve 50% duty cycle, place a diode in parallel with $R_2$ so the capacitor charges only through $R_1$.

9. Troubleshooting

Clamping Circuit Using a PN Junction Diode

1. Aim

To study the action of a diode clamping circuit — a circuit that shifts the entire AC waveform up or down by adding a DC offset — and to observe how the clamped output level is controlled by the DC bias applied through PV1.

2. Apparatus / Components Required

• SEELab3 unit
• PN junction diode (1N4148)
• Capacitor $C = 1\text{ }\mu F$
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

3.1 Clipper vs Clamper — the key distinction

A clipper (previous experiment) cuts away part of the waveform — the shape of the surviving portion is unchanged but some of it is removed. A clamper shifts the entire waveform up or down without altering its shape — the peak-to-peak amplitude is preserved, only the DC level changes.

Mobile App

Desktop App

3.2 How the clamper works

The circuit consists of a series capacitor $C$ between WG and the output node, with a diode connecting the output node to PV1.

On the first negative peak of the input, the output node is pulled low and the diode becomes forward biased, clamping the output node to:

The capacitor charges rapidly to the difference $V_{in,\text{neg_peak}} - V_{clamp}$ and holds this charge. On subsequent cycles the capacitor’s stored voltage acts as a DC offset, shifting the entire waveform upward so that the negative peaks sit at $V_{clamp}$.

For a $3\text{ V}$ peak sinusoid and $V_{PV1} = 1\text{ V}$:

The entire waveform is lifted so its lowest point sits at $\approx +0.3\text{ V}$, and the positive peak rises to $\approx 0.3 + 6 = 6.3\text{ V}$ (peak-to-peak preserved at $6\text{ V}$).

Important: The output peak-to-peak voltage equals the input peak-to-peak — the clamper adds DC offset only. This is what distinguishes it from a clipper, which reduces peak-to-peak.

3.3 Reverse clamping

Reversing the diode flips the action — the diode now clamps the positive peaks instead of the negative ones, shifting the entire waveform downward. Applying a negative voltage to PV1 with the reversed diode clamps the positive peaks below zero.

4. Circuit Diagram / Setup

1. Connect WG to one plate of capacitor $C$ ($1\text{ }\mu F$). Connect A1 to WG to monitor the input.
2. Connect the other plate of $C$ to the anode of the diode. This is the output node — connect it to A2.
3. Connect the cathode of the diode to PV1.

For reverse clamping: swap the diode (cathode to output node, anode to PV1) and apply negative voltages on PV1.

5. Procedure

Part A — Positive (upward) clamping

1. Open the SEELab3 app. Set WG to a sinusoidal output at $f = 1000\text{ Hz}$, amplitude $\approx 3\text{ V}$ peak.
2. Set PV1 = 1 V. Click “Start” and observe A1 and A2.
   • A1 shows the original symmetric sinusoid centred on $0\text{ V}$.
   • A2 should show the same waveform shifted upward — negative peaks lifted to $\approx V_{PV1} - 0.6\text{ V}$.
3. Confirm the peak-to-peak amplitude of A2 equals that of A1.
4. Vary PV1: 0 V, 0.5 V, 1.0 V, 1.5 V, 2.0 V. Record the clamped negative-peak level each time.

Part B — Reverse (downward) clamping

1. Reverse the diode and set PV1 to negative values: 0 V, −0.5 V, −1.0 V, −1.5 V.
2. Observe that the positive peaks are now clamped and the waveform shifts downward.
3. Record the clamped positive-peak level at each PV1 setting.

6. Observation Table

6a. Part A — Positive Clamping

6b. Part B — Reverse Clamping (diode reversed)

7. Results and Discussion

• With PV1 = 1 V, the negative peaks of the output were clamped to ____ V, against a theoretical value of $1.0 - 0.6 = 0.4\text{ V}$.
• The peak-to-peak amplitude at A2 was ____ V, equal to the input peak-to-peak of ____ V, confirming that the clamper preserves waveform shape and only shifts the DC level.
• As PV1 was increased, the clamped level rose proportionally — each $1\text{ V}$ increase in PV1 raised the output by $1\text{ V}$, verifying $V_{clamp} = V_{PV1} - V_f$.
• With the diode reversed and PV1 negative, the waveform shifted downward symmetrically, confirming that the clamping direction is controlled entirely by diode orientation and PV1 polarity.

8. Precautions

1. Capacitor value: The capacitor must fully charge within the first few cycles for steady-state clamping to be established. For $f = 1000\text{ Hz}$, $C = 1\text{ }\mu F$ with the $1\text{ M}\Omega$ input impedance of A2 gives $\tau = RC = 1\text{ s}$ — very long. In practice the diode provides a fast charge path on the clamping half-cycle; however, the discharge through $1\text{ M}\Omega$ is slow, which is what holds the DC shift. Do not add a low-value load resistor across the output — it will discharge the capacitor too quickly and degrade the clamping action.
2. A2 input impedance dependence: The clamped DC level depends on the $1\text{ M}\Omega$ input impedance of A2 holding the capacitor charge between cycles. With a real load (e.g., $10\text{ k}\Omega$) the clamping will degrade — the practical clamper needs a buffer amplifier for low-impedance loads.
3. Allow settling: The output takes a few cycles to settle to steady-state after changing PV1. Wait briefly before recording measurements.
4. Capacitor polarity: If an electrolytic capacitor is used, it must be oriented correctly. Preferred: use a non-polarised film or ceramic capacitor for this experiment.

9. Troubleshooting

Clipping Circuit Using a PN Junction Diode

1. Aim

To study the action of a diode clipping circuit — a circuit that removes (clips) the portion of an AC waveform that exceeds a set voltage level — and to observe how the clipping level shifts when the DC bias on the diode is varied using the programmable source PV1.

2. Apparatus / Components Required

• SEELab3 unit
• PN junction diode (1N4148)
• Resistor $R = 1\text{ k}\Omega$
• Connecting wires
• PC or Smartphone with SEELab3 software

3. Theory & Principle

3.1 Clipping Action

A clipper (or limiter) circuit passes the input signal unchanged as long as it stays within a defined voltage window, and flattens (clips) it to a fixed level once it crosses that threshold.

In the circuit here, $R$ and the diode form a series path from WG to PV1. Channel A2 monitors the voltage at the junction between $R$ and the diode anode — i.e., the output node.

When the input swings positive and the output node voltage tries to rise above $V_{clip}$, the diode becomes forward biased and clamps the output to:

Excess current is diverted through the diode into PV1 rather than appearing across the output. Below $V_{clip}$ the diode is reverse biased and the output follows the input (reduced slightly by the $R$–load divider).

Setting PV1 = 0 V gives $V_{clip} \approx +0.6\text{ V}$ (one diode drop above ground).

Raising PV1 raises the clipping level proportionally — the diode does not conduct until the output reaches $V_{PV1} + V_f$.

3.2 Negative Clipping

Reversing the diode direction flips the circuit so the diode conducts on the negative half-cycle instead. The clipping level becomes:

Applying a negative voltage to PV1 with the reversed diode clips the negative half at a programmable level below zero.

4. Circuit Diagram / Setup

1. Connect WG to one end of $R$ ($1\text{ k}\Omega$).
2. Connect the other end of $R$ to the anode of the diode. This junction is the output node — connect it to A2.
3. Connect the cathode of the diode to PV1.
4. Connect WG also to A1 to monitor the input.

For negative clipping: reverse the diode (cathode to $R$, anode to PV1) and set PV1 to a negative value.

5. Procedure

Part A — Positive clipping, variable level

1. Open the SEELab3 app. Set WG to a sinusoidal signal at $f = 1000\text{ Hz}$, amplitude $\approx 3\text{ V}$ peak.
2. Set PV1 = 0 V. Click “Start” and observe A1 (input) and A2 (output).
   • The positive peaks of A2 should be clipped flat at $\approx +0.6\text{ V}$; the negative half should follow the input.
3. Increase PV1 in steps: 0.5 V, 1.0 V, 1.5 V, 2.0 V. At each step note the clipping level on A2 and confirm it tracks $V_{PV1} + 0.6\text{ V}$.
4. Set PV1 high enough (e.g., $> 3\text{ V}$) that clipping disappears entirely — the output should now follow the full input waveform.

Part B — Negative clipping

1. Reverse the diode in the breadboard (cathode to $R$, anode to PV1).
2. Set PV1 to 0 V and observe — the negative peaks are now clipped at $\approx -0.6\text{ V}$.
3. Set PV1 to −0.5 V, −1.0 V, −1.5 V (negative values) and record the clipping level each time.

Mobile App

Desktop App

6. Observation Table

6a. Part A — Positive Clipping

6b. Part B — Negative Clipping (diode reversed)

7. Results and Discussion

• With PV1 = 0 V and the diode in the forward orientation, the positive peaks were clipped at ____ V, agreeing with the expected $V_f \approx 0.6\text{ V}$.
• As PV1 was increased, the clipping level rose by the same amount, confirming $V_{clip} = V_{PV1} + V_f$.
• With the diode reversed and PV1 set to negative values, the negative half was clipped at programmable levels below zero, verifying $V_{clip} = V_{PV1} - V_f$.
• The unclipped half of the waveform reproduced the input faithfully, confirming that the diode is fully off (reverse biased) during that half-cycle.

8. Troubleshooting