---
title: "Average power in pure inductor"
subject: "Basic Electrical Engineering"
chapter: 6
key: "semester_1/basic_electrical_engineering:average-power-pure-inductor"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/average-power-pure-inductor
site: BCT Engineering
---

# Average power in pure inductor

Basic Electrical Engineering · Chapter 6: Single-phase AC Circuits

- Asked in: 2067 Asoj, 2 marks
- Video: [AC voltage across pure inductor (derivation) | Alternating current | Physics | Khan Academy](https://www.youtube.com/watch?v=vOJxWKOMCPM) — Khan Academy India - English
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/average-power-pure-inductor
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-6

## Question

What is the average power consumed by a circuit containing an inductance only, when supplied by an ac source?

## Short answer

Average power is zero. Voltage and current are 90° out of phase, so instantaneous power alternates positively and negatively equally; net energy consumption per cycle is nil.

## Answer

**The average power is zero.**

In a pure inductor the current lags the voltage by 90°. The instantaneous power is p = v i = −(Vm Im/2) sin 2ωt, which has equal positive and negative half-loops. Its mean over a cycle is 0. Equivalently, P = V I cos 90° = 0.

The inductor stores energy in its magnetic field while the current rises and returns it to the source while the current falls, so no net energy is consumed.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The average power in a pure inductor over a cycle is:
   A. Zero
   B. Vm Im/2
   C. VI
   D. VI/2
   Answer: A. P = VI cos 90° = 0. (Key point: Average power)

2. The instantaneous power is:
   A. Always positive
   B. −(VmIm/2) sin 2ωt, with equal positive and negative loops
   C. Constant
   D. Equal to I^2R
   Answer: B. The mean of sin 2ωt over a cycle is zero. (Key point: Power wave)

3. What happens to the energy supplied?
   A. Dissipated as heat
   B. Stored in magnetic field and returned to the source
   C. Stored as electric field
   D. Lost in the core
   Answer: B. The inductor stores ½Li^2 while current rises and returns it as current falls. (Key point: Energy)

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