---
title: "Average, rms, form and peak factor of sawtooth"
subject: "Basic Electrical Engineering"
chapter: 5
key: "semester_1/basic_electrical_engineering:sawtooth-average-rms-form-peak"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/sawtooth-average-rms-form-peak
site: BCT Engineering
---

# Average, rms, form and peak factor of sawtooth

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2068 Chaitra, 6 marks
- Video: [Average,  rms of saw tooth waveform](https://www.youtube.com/watch?v=ZcruC3Rg3No) — Electrical and Electronics Engineering Department Christ College of Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/sawtooth-average-rms-form-peak
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Calculate the average value, rms value, form factor and peak factor of the saw tooth wave as shown in figure below. [Figure: sawtooth wave rising linearly from 0 to 50 V over each period of 2π; three periods shown up to 6π.]

## Short answer

Average = 25 V, rms = 50/√3 ≈ 28.87 V. Form factor = 1.155, peak factor = 1.732.

## Answer

From the figure: the wave rises linearly from 0 to 50 V over each period 2π, then drops instantly to 0. So in one period v = Vm θ/2π, with Vm = 50 V.

#### Average value
Vav = (1/2π) ∫₀^{2π} (Vm θ/2π) dθ = (Vm/4π²)(2π)² / 2 = Vm/2

**Vav = 25 V**

#### RMS value
Vrms² = (1/2π) ∫₀^{2π} (Vm θ/2π)² dθ = (Vm²/(2π × 4π²)) × (2π)³/3 = Vm²/3

Vrms = Vm/√3 = 50/1.732 = **28.87 V**

#### Form factor
Vrms / Vav = 28.87 / 25 = **1.155**

#### Peak factor
Vm / Vrms = 50 / 28.87 = **1.732**

## Check yourself

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

1. What describes one period of the sawtooth rising from 0 to 50 V over 2π?
   A. v = Vm
   B. v = Vm (θ/2π)^2
   C. v = Vm θ/2π
   D. v = Vm sin θ
   Answer: C. The wave rises linearly, so v = Vm θ/2π with Vm = 50 V. (Key point: Equation of wave)

2. What is the average value of this sawtooth?
   A. 28.87 V
   B. 35.4 V
   C. 50 V
   D. 25 V
   Answer: D. Averaging the linear ramp gives Vm/2 = 25 V. (Key point: Average value)

3. Which result comes from the rms integral of the ramp?
   A. Vrms = Vm/2
   B. Vrms = Vm/√3 = 28.87 V
   C. Vrms = Vm/√2
   D. Vrms = Vm/3
   Answer: B. Mean of squares gives Vm^2/3, so Vrms = Vm/√3. (Key point: RMS value)

4. Which pair of factors is correct?
   A. Form factor 1, peak factor 1
   B. Form factor 1.11, peak factor 1.414
   C. Form factor 1.732, peak factor 1.155
   D. Form factor 1.155, peak factor 1.732
   Answer: D. Form factor = Vrms/Vav = 28.87/25 = 1.155; peak factor = Vm/Vrms = 1.732. (Key point: Form and peak factors)

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