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 . 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 = \sqrt{R^2 + (X_L - X_C)^2}
and the power factor is:
\text{PF} = \cos\phi = \frac{R}{Z}
When the inductive reactance is partially or fully neutralized by the capacitive reactance , the phase angle decreases and the PF increases.
Apparatus
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AC supply (220 V, 50 Hz)
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2-pin plug
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Switch and connection wires
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Bulb (100 W, 220 V)
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Inductor ballast (0.43 A, 220 V, 50 W)
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Capacitor (3.5 µF, 400 V AC)
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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
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Before correction (RL circuit): Connect the bulb and inductor in series across the AC supply.
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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 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) 151.8 V Voltage across inductor 173 V Voltage across capacitor 248.4 V Supply voltage 232.5 V
Calculations
- Impedance of circuit (after correction):
Z = \frac{V}{I} = \frac{232.5}{0.36} = 646.0, \Omega
- Resistance (bulb):
R = \frac{P}{I^2} = \frac{66}{0.36^2} = 509.3, \Omega
- Net reactance:
X = \sqrt{Z^2 - R^2} = \sqrt{646.0^2 - 509.3^2} = 389.6, \Omega
- Power Factor:
\text{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\pi f C} = \frac{1}{2\pi(50)(3.5 \times 10^{-6})} = 910.0, \Omega
Vector Diagram
(Insert two phasor diagrams)
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RL circuit: Current lags voltage by large .
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RLC circuit: After adding C, current lag decreases, giving 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.
References
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J. D. Irwin, Basic Engineering Circuit Analysis, Wiley.
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B. L. Theraja, Electrical Technology.
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Department Lab Manual, ECE, KUET.
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Energy Pack brand datasheet (Inductor/Capacitor specifications).
To be filled with missing data:
RL-only readings (V, I, W, PF).
Actual measured frequency if not exactly 50 Hz.
Photos of setup and instruments (optional for report completeness).
End of Report