---
title: "RMS of triangular current waveform"
subject: "Basic Electrical Engineering"
chapter: 5
key: "semester_1/basic_electrical_engineering:rms-triangular-waveform-18a"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/rms-triangular-waveform-18a
site: BCT Engineering
---

# RMS of triangular current waveform

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2071 Chaitra, 6 marks
- Video: [Triangular Wave RMS Value Calculation](https://www.youtube.com/watch?v=uF5d6_55xvI) — Power Electronics Lecturer Notes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/rms-triangular-waveform-18a
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Calculate the rms value of current of the following triangular waveform. [Figure: train of triangular pulses of peak 18 A; first triangle from 0 to 2π peaking at π; second from 2π to 4π peaking at 3π.]

## Short answer

For a triangular wave of peak Im, rms value = Im/√3. With Im=18A, Irms = 18/1.732 = 10.39 A.

## Answer

From the figure: triangles of peak 18 A. The first rises from 0 at θ = 0 to 18 A at π and falls to 0 at 2π; the second repeats from 2π to 4π. So the period is 2π.

Rising portion: i = Im θ/π, with Im = 18 A. The falling portion is its mirror image, so the mean square over 0 to π equals that over the whole cycle.

I_rms² = (1/π) ∫₀^π (Im θ/π)² dθ = (Im²/π³) × (π³/3) = Im²/3

I_rms = Im/√3 = 18 / 1.732

**I_rms = 10.39 A**

(Average value = Im/2 = 9 A, so the form factor is 10.39/9 = 1.155.)

## Check yourself

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

1. Equation of rise?
   A. i = Im theta/pi
   B. i = Im
   C. i = Im sin theta
   D. i = Im theta
   Answer: A. 0 to Im over pi. (Key point: Rising)

2. Mean square?
   A. Im^2/4
   B. Im^2
   C. Im^2/3
   D. Im^2/2
   Answer: C. (1/pi) integral. (Key point: Mean square)

3. I_rms?
   A. 12.73 A
   B. 18 A
   C. 10.39 A
   D. 9 A
   Answer: C. 18/sqrt3. (Key point: RMS)

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