---
title: "Peak and form factor of triangular wave"
subject: "Basic Electrical Engineering"
chapter: 5
key: "semester_1/basic_electrical_engineering:peak-form-factor-triangular-wave-im"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/peak-form-factor-triangular-wave-im
site: BCT Engineering
---

# Peak and form factor of triangular wave

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2072 Kartik, 4 marks
- Video: [Triangular Waveform - Calculation of Form and Peak Factors | Satyanarayana Sir | Tharagathi](https://www.youtube.com/watch?v=4o2U9RgS0WM) — Tharagathi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/peak-form-factor-triangular-wave-im
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Find the peak factor and form factor of the triangular wave shown in figure below. [Figure: current i versus ωt; rises linearly from 0 to +Im at π/2, falls through zero at π to -Im at 3π/2, and returns to 0 at 2π.]

## Short answer

For the symmetric triangular current wave, half-cycle average = Im/2, RMS = Im/√3. Form factor = 1.155, peak factor = 1.732.

## Answer

The current rises linearly from 0 to +Im at π/2, falls through zero at π to −Im at 3π/2, and returns to 0 at 2π. It is a symmetrical alternating triangular wave, so one quarter cycle (0 to π/2) is enough.

In the first quarter, i = Im θ/(π/2) = 2Imθ/π.

#### Average value (half cycle)
Iav = (1/(π/2)) ∫₀^{π/2} (2Imθ/π) dθ = (2/π)(2Im/π)(π²/8) = Im/2

#### RMS value
I² = (2/π) ∫₀^{π/2} (2Imθ/π)² dθ = (2/π)(4Im²/π²)(π³/24) = Im²/3

Irms = Im/√3 = 0.577 Im

#### Factors
- Form factor = Irms / Iav = 0.577 Im / 0.5 Im = **1.155**
- Peak factor = Im / Irms = **1.732** (= √3)

## Check yourself

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

1. Why one quarter?
   A. Symmetric wave
   B. Periodic only
   C. Sine
   D. DC
   Answer: A. Symmetry. (Key point: Quarter cycle)

2. Irms?
   A. Im/sqrt3
   B. Im/sqrt2
   C. Im/2
   D. Im/3
   Answer: A. Square the ramp. (Key point: RMS)

3. Form and peak?
   A. 1.155 and 1.732
   B. 1.11 and 1.414
   C. 1.414 and 1.11
   D. 2 and 1
   Answer: A. 0.577/0.5, 1/0.577. (Key point: Factors)

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