Introduction:

In AC circuits, power calculation is different from DC circuits due to the phase difference between voltage and current. The power factor plays a crucial role in determining the efficiency of the circuit. Understanding real power, apparent power, and reactive power is essential in analyzing AC circuits used in electrical systems.



Power in AC Circuits:

AC circuits involve alternating current and voltage, which may or may not be in phase. The power delivered depends on the phase angle (φ) between them. The three types of power in AC circuits are:

- Real Power (P): Actual power consumed (measured in watts, W)

- Apparent Power (S): Total power supplied (measured in volt-amperes, VA)

- Reactive Power (Q): Power due to reactance (measured in volt-amperes reactive, VAR)

The relation between these powers is given by:

S² = P² + Q²

What is Power Factor?

The power factor (PF) is the ratio of real power to apparent power. It indicates how effectively the electrical power is converted into useful work.

Power Factor (PF) = P / S = cos(φ)

- If PF = 1: Voltage and current are in phase, circuit is purely resistive.

- If PF < 1: Circuit has reactive components (inductive or capacitive).

- If PF = 0: Circuit is purely reactive (inductive or capacitive), no real power transfer.

Read Also: AC Voltage Applied to a Series LCR Circuit - Class 12 Physics Study Notes

Significance of Power Factor:

- A high power factor means efficient power usage.

- A low power factor causes energy losses and higher electricity bills.

- Industries and power grids aim to maintain a PF close to 1 to improve efficiency.

Power Factor in Resistive, Inductive, and Capacitive Circuits:

1. Purely Resistive Circuit:

- Voltage and current are in phase (φ = 0°).

- Power factor PF = cos(0) = 1.

2. Purely Inductive or Capacitive Circuit:

- Voltage and current are out of phase by 90°.

- Power factor PF = cos(90) = 0 → No real power consumption.

3. RL or RC Circuit (Mixed Load):

- Phase angle lies between 0° and 90°.

- Power factor is between 0 and 1, depending on the reactance.

How to Improve Power Factor?

1. Use Capacitor Banks – They counteract inductive reactance.

2. Synchronous Condensers – Help regulate reactive power.

3. Phase Advancers – Improve PF in AC motors.

Solved Example on Power Factor:

Q: A circuit has an apparent power of 500 VA and a real power of 400 W. Find the power factor.

Solution:

PF = P / S = 400 / 500 = 0.8

Thus, the power factor is 0.8 (lagging).

Conclusion:

Power in AC circuits depends on the power factor, which determines the efficiency of energy usage. A high power factor reduces energy losses, while a low power factor increases power wastage. Understanding power factor correction methods is essential for improving circuit efficiency.