C
CraftExam
high importancemedium8 min

Power Factor and Average Power in AC Circuits

Average power consumed in an AC circuit is P = Vrms Irms cos phi, where cos phi is the power factor and phi is the phase difference between voltage and current.

Concept Practice Coming Soon

Learn the concept

Student-friendly explanation

In AC, instantaneous power changes with time because voltage and current vary continuously. The useful average power over a complete cycle depends on how much of the current is in phase with voltage. The factor cos phi measures this in-phase part. A pure resistor has phi = 0, so cos phi = 1 and power is maximum for given Vrms and Irms. In a pure inductor or pure capacitor, phi = pi/2, so cos phi = 0 and average power is zero; this is called wattless current because energy is alternately stored and returned rather than consumed over a full cycle.

How to write this in exams

  1. 1

    Start with the exact idea

    Average power consumed in an AC circuit is P = Vrms Irms cos phi, where cos phi is the power factor and phi is the phase difference between voltage and current.

  2. 2

    Then show how to use it

    Identify RMS voltage and RMS current. Find cos phi from the given phase angle or from R/Z. Substitute in P = Vrms Irms cos phi. Interpret whether power is maximum, reduced, or zero depending on phi.

  3. 3

    Add one concrete example

    If Vrms = 200 V, Irms = 5 A, and power factor = 0.8, the average power is P = 200 x 5 x 0.8 = 800 W.

  4. 4

    Avoid this incomplete answer

    Writing P = V0 I0 cos phi directly without averaging is incomplete. If peak values are used, average power is P = (V0 I0/2) cos phi.

Definition

Average power consumed in an AC circuit is P = Vrms Irms cos phi, where cos phi is the power factor and phi is the phase difference between voltage and current.

Example

If Vrms = 200 V, Irms = 5 A, and power factor = 0.8, the average power is P = 200 x 5 x 0.8 = 800 W.

Rule to remember

Average power: P = Vrms Irms cos phi. Power factor: cos phi = R/Z for a series LCR circuit. P is in watt, Vrms in volt, Irms in ampere, and phi is the phase angle between voltage and current. Use RMS values, not peak values, unless converting them first.

Memory hook

Only the current component in step with voltage earns power: I cos phi does the work.

Examples and method

Worked example

A series AC circuit has Vrms = 240 V, Irms = 3 A, and phase angle phi = 60 degrees. Average power P = Vrms Irms cos phi = 240 x 3 x cos 60 degrees = 240 x 3 x 0.5 = 360 W. The apparent power is 720 VA, but only 360 W is consumed as average power.

Method to apply

Identify RMS voltage and RMS current. Find cos phi from the given phase angle or from R/Z. Substitute in P = Vrms Irms cos phi. Interpret whether power is maximum, reduced, or zero depending on phi.

Diagram support

A power-factor phasor may show current I, voltage V, phase angle phi, and the in-phase component I cos phi. For pure L or C, the V-I phase difference is 90 degrees, making average power zero.

How CBSE asks it

Questions ask for average power, power factor, wattless current, comparison of pure R/L/C power, or why power factor correction is useful in AC systems.

Avoid common mistakes

Common confusion

Students often calculate AC power as only VI without multiplying by cos phi. That is correct only when voltage and current are in phase.

Common wrong answer

Writing P = V0 I0 cos phi directly without averaging is incomplete. If peak values are used, average power is P = (V0 I0/2) cos phi.

Exam tip

Whenever an AC circuit contains L or C, check the phase angle before calculating average power. Write the power factor clearly.

Quick check

What is wattless current in an AC circuit?

Wattless current refers to the current in a purely reactive AC circuit where the phase difference is pi/2. Since cos phi = 0, the average power P = Vrms Irms cos phi is zero even though current flows.

Answer writing and exam use

1-mark answer

Average power consumed in an AC circuit is P = Vrms Irms cos phi, where cos phi is the power factor and phi is the phase difference between voltage and current.

2-mark answer

Average power consumed in an AC circuit is P = Vrms Irms cos phi, where cos phi is the power factor and phi is the phase difference between voltage and current. Average power: P = Vrms Irms cos phi. Power factor: cos phi = R/Z for a series LCR circuit. P is in watt, Vrms in volt, Irms in ampere, and phi is the phase angle between voltage and current. Use RMS values, not peak values, unless converting them first. If Vrms = 200 V, Irms = 5 A, and power factor = 0.8, the average power is P = 200 x 5 x 0.8 = 800 W.

3-mark answer

In AC, instantaneous power changes with time because voltage and current vary continuously. The useful average power over a complete cycle depends on how much of the current is in phase with voltage. The factor cos phi measures this in-phase part. A pure resistor has phi = 0, so cos phi = 1 and power is maximum for given Vrms and Irms. In a pure inductor or pure capacitor, phi = pi/2, so cos phi = 0 and average power is zero; this is called wattless current because energy is alternately stored and returned rather than consumed over a full cycle. Average power: P = Vrms Irms cos phi. Power factor: cos phi = R/Z for a series LCR circuit. P is in watt, Vrms in volt, Irms in ampere, and phi is the phase angle between voltage and current. Use RMS values, not peak values, unless converting them first. A series AC circuit has Vrms = 240 V, Irms = 3 A, and phase angle phi = 60 degrees. Average power P = Vrms Irms cos phi = 240 x 3 x cos 60 degrees = 240 x 3 x 0.5 = 360 W. The apparent power is 720 VA, but only 360 W is consumed as average power. Questions ask for average power, power factor, wattless current, comparison of pure R/L/C power, or why power factor correction is useful in AC systems. Writing P = V0 I0 cos phi directly without averaging is incomplete. If peak values are used, average power is P = (V0 I0/2) cos phi.
Practice

Concept practice is coming soon

Join the waitlist for concept-level MCQs and weak-concept practice.

10 MCQs5 MinutesInstant Results
Join Waitlist for Practice

Help improve this page

Found something confusing, incorrect, or missing?

Open Learning Map