---
title: "Gauge factor of resistance strain gauge"
subject: "Instrumentation I"
chapter: 3
key: "semester_4/instrumentation_i:strain-gauge-factor"
source: https://www.bctengineer.com/q/semester_4/instrumentation_i/strain-gauge-factor
site: BCT Engineering
---

# Gauge factor of resistance strain gauge

Instrumentation I · Chapter 3: Transducer

- Asked in: year not given, 8 marks
- Video: [Strain Gauge & Derivation Of Gauge Factor Of Strain Gauge. || Piezoresistive  Effects. In Hindi.](https://www.youtube.com/watch?v=1k4tIh2ZhNc) — Mintoss Mood
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_i/strain-gauge-factor
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_i/chapter-3

## Question

Define gauge factor of a resistance strain gauge and obtain the expression for the same.

## Short answer

Gauge factor G = (ΔR/R)/(ΔL/L) = 1 + 2ν + (dρ/ρ)/ε, combining dimensional (1+2ν) and piezoresistive effects. For metals G ≈ 2; for semiconductors the resistivity term dominates, giving G ≈ 100–200.

## Answer

The **gauge factor (G)** of a strain gauge is the ratio of the fractional change in resistance to the fractional change in length (strain):

**G = (ΔR/R) / (ΔL/L) = (ΔR/R) / ε**

It is the sensitivity of the gauge; a higher G gives a larger output.

#### Derivation
The resistance of a conductor of resistivity ρ, length L and cross-section area A is:

R = ρL/A

Take logarithms and differentiate:

dR/R = dρ/ρ + dL/L − dA/A

For a circular wire A = πD²/4, so dA/A = 2 dD/D.

Poisson's ratio ν = −(lateral strain)/(axial strain) = −(dD/D)/(dL/L), thus dD/D = −ν dL/L, and

dA/A = −2ν dL/L

Substituting:

dR/R = dL/L + 2ν dL/L + dρ/ρ = (1 + 2ν) dL/L + dρ/ρ

Dividing by dL/L = ε:

**G = 1 + 2ν + (dρ/ρ)/ε**

#### Meaning of the terms
- **1 + 2ν:** change in resistance due to the geometry (dimensions) change.
- **(dρ/ρ)/ε:** change due to the piezoresistive effect (change in resistivity with strain).

For metallic gauges, ν ≈ 0.3, so 1 + 2ν ≈ 1.6; with the resistivity term G ≈ 2 (constantan 2.0 to 2.1). For semiconductor gauges, the piezoresistive term dominates and G ≈ 100 to 200.

If the resistivity change is negligible, G ≈ 1 + 2ν. Note ν = 0.5 would imply no volume change, G = 2.

## Check yourself

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

1. The gauge factor G is:
   A. Ratio of strain to resistance
   B. (DeltaR/R) divided by (DeltaL/L)
   C. Change in length per unit resistance
   D. Resistance per unit length
   Answer: B. G = (DeltaR/R)/strain, the sensitivity of the gauge. (Key point: Definition)

2. For a circular wire, with Poisson's ratio nu, dA/A equals:
   A. +2 nu dL/L
   B. -nu dL/L
   C. -2 nu dL/L
   D. +dL/L
   Answer: C. A = pi D^2/4 so dA/A = 2 dD/D, and dD/D = -nu dL/L, giving -2 nu dL/L. (Key point: Derivation step)

3. The expression for gauge factor is:
   A. G = 1 + nu + (d rho/rho)/strain
   B. G = 1 - 2 nu
   C. G = 2 nu + d rho/rho
   D. G = 1 + 2 nu + (d rho/rho)/strain
   Answer: D. dR/R = (1 + 2nu) dL/L + d rho/rho; dividing by strain gives G. (Key point: Final expression)

4. Why is the gauge factor of a semiconductor gauge (100 to 200) much larger than that of a metal gauge (about 2)?
   A. The piezoresistive (resistivity change) term dominates
   B. Poisson's ratio is much larger
   C. The geometry term is larger
   D. Semiconductors have no lateral strain
   Answer: A. In semiconductors the resistivity change with strain is large; in metals G is about 1 + 2nu plus a small term. (Key point: Metal vs semiconductor)

## Related in Instrumentation I

- [Maxwell bridge balance equation and suitability](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Amaxwell-bridge-inductance) — Instrumentation I, chapter 2

## Related in other subjects

- [Derivation of strain gauge factor](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Astrain-gauge-factor-derivation) — Instrumentation and Measurement, chapter 6
- [Ballast circuit for a strain gauge](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aballast-circuit-strain-gauge-sensitivity) — Instrumentation and Measurement, chapter 6
- [Gauge resistance change and quarter-bridge output](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Agauge-resistance-change-quarter-bridge) — Instrumentation and Measurement, chapter 6
- [Short note: Strain gauge](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Ashort-note-strain-gauge) — Basic Electronics Engineering, chapter 7, asked 6×