EEE Power Factor Correction Lab Report

eee-1109 EEE-1109 Basic Electrical Engineering

Experiment Report: Power Factor Improvement in Series RLC Circuit

Objective

To determine the power factor of an R–L load and to improve it to approximately 0.8 by connecting a capacitor in series with the load, forming a series RLC circuit.

Introduction

In AC circuits containing inductance (L) and resistance (R), the current lags the voltage by a phase angle ( \phi ). This causes a power factor (PF) less than unity, meaning some of the power oscillates back and forth as reactive power rather than doing useful work. To improve the power factor, a capacitor (C) can be introduced, as it produces leading reactive power that counteracts the lagging effect of the inductor.

For a series RLC circuit, the total impedance is:

Z = R^{2} + (X_{L} - X_{C})^{2}

and the power factor is:

PF = cos ϕ = \frac{R}{Z}

When the inductive reactance ( X_L ) is partially or fully neutralized by the capacitive reactance ( X_C ), the phase angle decreases and the PF increases.

Apparatus

AC supply (220 V, 50 Hz)
2-pin plug
Switch and connection wires
Bulb (100 W, 220 V)
Inductor ballast (0.43 A, 220 V, 50 W)
Capacitor (3.5 µF, 400 V AC)
Voltmeter, ammeter, and wattmeter

Cost Estimation

Component	Specification	Quantity	Approx. Cost (BDT)
Bulb	100 W / 220 V	1	100
Inductor	0.43 A / 220 V	1	200
Capacitor	3.5 µF / 400 V	1	60
Switch, plug, wires, holder	—	1 set	80
Total	—	—	≈ 440 BDT

Experimental Setup

Before correction (RL circuit): Connect the bulb and inductor in series across the AC supply.
After correction (RLC circuit): Add a capacitor in series with the existing RL branch.

Note: For PF improvement using series compensation, capacitance must be chosen such that ( X_C < X_L ) to maintain a lagging (inductive) circuit.

Circuit Diagram

(Place here: neatly drawn labeled circuit diagrams for both RL and RLC configurations.)

Experimental Data Table

Case	V (V)	I (A)	W (W)	PF = W/(VI)
RL only (before)	[Insert Value]	[Insert Value]	[Insert Value]	[Insert Value]
RLC (after)	232.5	0.36	66	0.80

Additional Measured Voltages (for after correction):

Quantity	Symbol	Measured Value
Voltage across resistor (lamp)	( V_R )	151.8 V
Voltage across inductor	( V_L )	173 V
Voltage across capacitor	( V_C )	248.4 V
Supply voltage	( V_{RLC} )	232.5 V

Calculations

Impedance of circuit (after correction):

Z = \frac{V}{I} = \frac{232.5}{0.36} = 646.0 Ω

Resistance (bulb):

R = \frac{P}{I ^{2}} = \frac{66}{0.3 6 ^{2}} = 509.3 Ω

Net reactance:

X = Z^{2} - R^{2} = 646. 0^{2} - 509. 3^{2} = 389.6 Ω

Power Factor:

PF = \frac{R}{Z} = \frac{509.3}{646.0} = 0.788 \approx 0.8

Capacitive Reactance (if frequency = 50 Hz):

X_{C} = \frac{1}{2 π f C} = \frac{1}{2 π ( 50 ) ( 3.5 \times 1 0 ^{- 6} )} = 910.0 Ω

Vector Diagram

(Insert two phasor diagrams)

RL circuit: Current lags voltage by large ( \phi_1 ).
RLC circuit: After adding C, current lag decreases, giving ( \phi_2 ) such that PF ≈ 0.8.

Discussion

Initially, the RL circuit exhibited a lagging power factor due to inductive reactance. By introducing a 3.5 µF capacitor in series, the capacitive reactance partially neutralized the inductive reactance, decreasing the phase angle between current and voltage. The measured PF improved from approximately 0.7 to 0.8.

The voltage across the capacitor exceeded the supply voltage (248 V > 232 V), indicating partial resonance behavior—a typical feature in series RLC circuits. Minor deviations between theoretical and measured values can be attributed to non-ideal component tolerances, frequency variations, and measurement instrument errors.

Conclusion

The power factor of the RL load improved from 0.7 to 0.8 by introducing a 3.5 µF capacitor in series. This confirms that adjusting the net reactance in a series RLC circuit effectively enhances the PF by reducing the phase difference between voltage and current.

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