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

# Form and peak factor of triangular wave

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2073 Chaitra, 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/form-peak-factor-triangular-wave
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Calculate the form factor and peak factor of the following triangular waveform. [Figure: train of triangular pulses of peak 100 V; first triangle rises from 0 at 0 to 100 V at π and falls to 0 at 2π; second triangle peaks at 3π and ends at 4π.]

## Short answer

The triangular wave of peak 100 V has average 50 V, RMS 100/√3 ≈ 57.74 V. Form factor = RMS/average = 1.155, peak factor = peak/RMS = √3 ≈ 1.732.

## Answer

The figure shows triangles of peak 100 V. Each rises linearly from 0 at θ = 0 to 100 V at π and falls to 0 at 2π; the pattern repeats with period 2π. Because the wave is always positive and the rise and fall are symmetrical, one rising slope 0 to π is enough.

Let Vm = 100 V. On the rise, v = Vm θ/π.

#### Average value
Vav = (1/π) ∫₀^π (Vm θ/π) dθ = (Vm/π²)(π²/2) = Vm/2 = **50 V**

#### RMS value
Vrms² = (1/π) ∫₀^π (Vm θ/π)² dθ = (Vm²/π³)(π³/3) = Vm²/3

Vrms = Vm/√3 = 100/1.732 = **57.74 V**

#### Factors
- Form factor = Vrms / Vav = 57.74 / 50 = **1.155**
- Peak factor = Vm / Vrms = 100 / 57.74 = **1.732** (= √3)

## Check yourself

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

1. Average value?
   A. Vm = 100
   B. 0
   C. Vm/2 = 50 V
   D. Vm/pi
   Answer: C. Integral of linear ramp. (Key point: Average)

2. RMS value?
   A. Vm/sqrt2
   B. Vm/3
   C. Vm/2
   D. Vm/sqrt3 = 57.74 V
   Answer: D. Vm^2/3. (Key point: RMS)

3. Form and peak factor?
   A. 1.155 and 1.732
   B. 1.732 and 1.155
   C. 1 and 1
   D. 1.11 and 1.414
   Answer: A. Vrms/Vav and Vm/Vrms. (Key point: Factors)

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