Visualize phase difference between voltage and current in series R-L and R-C circuits with the help of oscilloscope and plot the phasor diagram. (Feee)

 AIM: Visualize phase difference between voltage and current in series R-L and R-C circuits with the help of oscilloscope and plot the phasor diagram.

Objective

To observe and analyze the phase difference between voltage and current in series R-L and R-C circuits using an oscilloscope, and to plot the corresponding phasor diagrams.

Apparatus Required

1. AC Power Supply (Single-phase, 230V, 50Hz)
2. Resistor (Known value, for R-L and R-C circuits)
3. Inductor (Known value, for R-L circuit)
4. Capacitor (Known value, for R-C circuit)
5. Oscilloscope (Dual-channel)
6. Probes (For oscilloscope)
7. Connecting Wires

Circuit Diagrams

1. Series R-L Circuit

   • Resistor (R) and Inductor (L) connected in series to the AC power supply.
   • Voltage across the circuit and current through the circuit measured using the oscilloscope.

2. Series R-C Circuit

   • Resistor (R) and Capacitor (C) connected in series to the AC power supply.
   • Voltage across the circuit and current through the circuit measured using the oscilloscope.

Theory

1. R-L Circuit:

   • In a series R-L circuit, the current lags the voltage by a phase angle (φ) that depends on the inductive reactance (ωL) and resistance (R).
   • The phase angle is given by: $$\phi = \tan^{-1}\left(\frac{\omega L}{R}\right)$$

2. R-C Circuit:

   • In a series R-C circuit, the current leads the voltage by a phase angle (φ) that depends on the capacitive reactance (1/ωC) and resistance (R).
   • The phase angle is given by: $$\phi = \tan^{-1}\left(\frac{1}{\omega C R}\right)$$

3. Oscilloscope Observations:

   • The oscilloscope will display two waveforms: one representing the voltage and the other the current.
   • The horizontal shift between these waveforms corresponds to the phase difference.

4. Phasor Diagram:

   • The voltage and current phasors are represented with the phase angle derived from the oscilloscope.
   • For an R-L circuit, current lags voltage.
   • For an R-C circuit, current leads voltage.

Procedure

1. Setup:

   • Connect the R-L circuit as shown in the diagram.
   • Connect Channel 1 of the oscilloscope across the circuit to measure voltage.
   • Connect Channel 2 in series to measure current using a suitable current sensing resistor (if required).

2. Measurement:

   • Switch on the AC power supply.
   • Observe the waveforms on the oscilloscope.
   • Measure the phase difference (φ) between the voltage and current waveforms.

3. Repeat for R-C Circuit:

   • Replace the inductor with the capacitor in the circuit.
   • Repeat the measurement process.

4. Phasor Diagram:

   • Using the measured phase difference, plot the phasor diagrams for both R-L and R-C circuits.
   • Ensure the relative positions of voltage and current phasors reflect the observed phase relationships.

Observation Table

Sample Calculation

Suppose the following measurements are made:

• R-L Circuit:

  • Resistance (R) = 10 Ω
  • Inductance (L) = 0.1 H
  • Voltage = 230V
  • Current = 5A
  • Phase angle: $$\phi = \tan^{-1}\left(\frac{\omega L}{R}\right) = \tan^{-1}\left(\frac{2\pi \times 50 \times 0.1}{10}\right) \approx 26.6°$$

• R-C Circuit:

  • Resistance (R) = 10 Ω
  • Capacitance (C) = 100 μF
  • Voltage = 230V
  • Current = 5A
  • Phase angle: $$\phi = \tan^{-1}\left(\frac{1}{\omega C R}\right) = \tan^{-1}\left(\frac{1}{2\pi \times 50 \times 100 \times 10^{-6} \times 10}\right) \approx 63.4°$$

Result

The phase differences between voltage and current in the R-L and R-C circuits were successfully observed and analyzed. The phasor diagrams were plotted based on the measured phase angles.

Precautions

1. Ensure proper grounding of the oscilloscope to avoid noise or incorrect readings.
2. Use appropriate ranges on the oscilloscope for accurate measurements.
3. Avoid loose connections to prevent sparking or incorrect results.
4. Verify all components and connections before powering the circuit.

Conclusion

The experiment demonstrated the phase relationship between voltage and current in series R-L and R-C circuits. The oscilloscope provided a clear visualization of the phase difference, and the phasor diagrams accurately represented the observed relationships.