Measure voltage, current, power and power factor in a R-L series circuit. (Feee)

 AIM: Measurement of Voltage, Current, Power, and Power Factor in a Series R-L Circuit

Objective

To measure the voltage, current, power, and power factor in a series R-L circuit.

Apparatus Required

1. AC Power Supply (Single-phase, 230V, 50Hz)
2. Resistor (Known value, R)
3. Inductor (Known value, L)
4. Voltmeter (Range: 0-300V, AC)
5. Ammeter (Range: 0-10A, AC)
6. Wattmeter (Range: 0-2kW)
7. Power Factor Meter (Optional)
8. Connecting Wires
9. Oscilloscope (Optional, for waveform visualization)

Circuit Diagram

The circuit should include:

• Resistor (R) and Inductor (L) connected in series to the AC power supply.
• Ammeter in series to measure current.
• Voltmeter across the circuit to measure voltage.
• Wattmeter to measure power.
• (Optional) Oscilloscope to observe phase difference between voltage and current.

Theory

1. In a series R-L circuit:

• A series R-L circuit consists of a resistor (R) and an inductor (L) connected in series with each other. When an alternating current (AC) voltage is applied to the circuit, the resistor and inductor each have their own effects on the current and voltage.

• Voltage (ε) is the total voltage across the resistor and inductor.
• Current (“I”) flows through the circuit, lagging behind the voltage by an angle (φ) due to the inductive reactance.
• Power (“P”) is the real power consumed, calculated as: $$P = V \times I \times \cos(\phi)$$
• Apparent Power (“S”): $$S = V \times I$$
• Power Factor (“pf”): $$pf=\cos (\varphi )=\frac{P}{S}$$

1. The phase angle (φ) is determined by:

   $$\phi = \tan^{-1}\left(\frac{\omega L}{R}\right)$$

   where $\omega = 2\pi f$ is the angular frequency.

Procedure

1. Setup:

   • Connect the resistor (R) and inductor (L) in series as per the circuit diagram.
   • Connect the ammeter in series to measure current.
   • Connect the voltmeter across the circuit.
   • Connect the wattmeter to measure power.

2. Measurement:

   • Turn on the AC power supply.
   • Record the voltage across the circuit using the voltmeter.
   • Record the current through the circuit using the ammeter.
   • Record the power consumption from the wattmeter.
   • If using a power factor meter, note the direct reading of the power factor.

3. Calculations:

   • Compute the apparent power: $$S = V \times I$$
   • Calculate the power factor: $$pf = \frac{P}{S}$$
   • Verify the power factor using the phase angle (φ): $$pf = \cos(\phi)$$

4. Optional:

   • Use an oscilloscope to observe and measure the phase difference between the voltage and current waveforms.

Observation Table

 

Sample Calculation

Suppose the following measurements are made:

• Voltage (“V”) = 230V
• Current (“I”) = 5A
• Real Power (“P”) = 920W

Apparent Power:

$$S = V \times I = 230 \times 5 = 1150 \text{ VA}$$

Power Factor:

$$pf = \frac{P}{S} = \frac{920}{1150} = 0.8$$

Phase Angle:

$$\phi = \cos^{-1}(pf) = \cos^{-1}(0.8) \approx 36.87^°$$

Result

The measured values of voltage, current, power, and power factor for the series R-L circuit are as follows:

• Voltage: ______ V
• Current: ______ A
• Real Power: ______ W
• Apparent Power: ______ VA
• Power Factor: ______
• Phase Angle: ______

Precautions

1. Ensure proper insulation of all connections to avoid electrical hazards.
2. Verify the calibration of measuring instruments.
3. Avoid loose connections to prevent sparking or incorrect readings.
4. Ensure the wattmeter connections are correct to avoid errors in power measurement.

Conclusion

The voltage, current, power, and power factor in the series R-L circuit were successfully measured. The observed phase difference and power factor matched theoretical predictions based on the circuit parameters.