---
title: "Cycle, period, frequency, average and rms"
subject: "Basic Electrical Engineering"
chapter: 5
key: "semester_1/basic_electrical_engineering:define-cycle-period-frequency-avg-rms"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/define-cycle-period-frequency-avg-rms
site: BCT Engineering
---

# Cycle, period, frequency, average and rms

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2071 Shrawan, 6 marks
- Video: [RMS & Average Values of Standard Waveforms](https://www.youtube.com/watch?v=KygtYb2EsQE) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/define-cycle-period-frequency-avg-rms
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Define cycle, Time period, angular velocity, frequency, average and rms value of an alternating quantity.

## Short answer

Cycle: one complete alternation. Time period T=1/f. Angular frequency ω=2πf rad/s. Frequency f in Hz. Average value over half cycle for sine: 0.637 Im. RMS (effective) value: 0.707 Im, the equivalent DC heating effect.

## Answer

- **Cycle:** One complete set of positive and negative values of an alternating quantity. It corresponds to 360° or 2π radians.
- **Time period (T):** Time taken to complete one cycle, in seconds. T = 1/f.
- **Angular velocity (ω):** Rate at which the rotating coil (or phasor) sweeps angle, in rad/s. ω = 2πf = 2π/T.
- **Frequency (f):** Number of cycles completed per second, in hertz (Hz). In Nepal f = 50 Hz.
- **Average value:** The mean of all instantaneous values over half a cycle (the full-cycle mean of a symmetrical wave is zero).

  Iav = (1/π) ∫₀^π i dθ. For a sine wave, Iav = 2Im/π = 0.637 Im.
- **RMS (effective) value:** The value of steady direct current that produces the same heating effect in a resistor as the alternating current does in the same time. It is the square root of the mean of the squares of the instantaneous values.

  Irms = √[ (1/2π) ∫₀^{2π} i² dθ ]. For a sine wave, Irms = Im/√2 = 0.707 Im.

## Check yourself

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

1. omega?
   A. pi f
   B. f/2pi
   C. 2 pi/f
   D. 2 pi f
   Answer: D. rad/s. (Key point: Angular velocity)

2. RMS value is?
   A. Half cycle average
   B. DC giving same heating
   C. Peak/2
   D. Mean of instantaneous values
   Answer: B. Effective value. (Key point: RMS meaning)

3. Sine average?
   A. 0.5 Im
   B. 0.707 Im
   C. Im
   D. 0.637 Im
   Answer: D. Over half cycle. (Key point: Average)

4. T relates to f?
   A. T = f
   B. T = f/2
   C. T = 1/f
   D. T = 2 pi f
   Answer: C. Seconds. (Key point: Period)

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