---
title: "Ballast circuit for a strain gauge"
subject: "Instrumentation and Measurement"
chapter: 6
key: "semester_4/instrumentation_and_measurement:ballast-circuit-strain-gauge-sensitivity"
source: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/ballast-circuit-strain-gauge-sensitivity
site: BCT Engineering
---

# Ballast circuit for a strain gauge

Instrumentation and Measurement · Chapter 6: Strain Gage

- Asked in: year not given, 5 marks
- Video: [5.5 strain guage potentiometer circuit. RGPV ME 8001 Advanced Machine Design](https://www.youtube.com/watch?v=KTDMMi9YzMw) — 25A521-Sourabh jain
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/ballast-circuit-strain-gauge-sensitivity
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_and_measurement/chapter-6

## Question

Explain the ballast (potentiometer) circuit for a strain gauge. Derive the change in output voltage for a small change in gauge resistance and find the condition for maximum sensitivity. For $R_g = R_b = 120\ \Omega$, supply 6 V, gauge factor 2.0 and strain 1000 microstrain, calculate the output change.

## Short answer

Ballast circuit is a potential divider with gauge and fixed resistor. Output change is dVo = V Rb Rg/(Rg+Rb)^2 times dRg/Rg; maximum sensitivity occurs when Rb = Rg, giving dVo = V/4 dRg/Rg. For V = 6 V, G = 2 and 1000 microstrain, dR/R = 0.002, so dVo = 3 mV.

## Answer

A ballast circuit is a simple potential-divider circuit in which the strain gauge $R_g$ is in series with a fixed ballast resistor $R_b$ across a supply $V$. The output is taken across the gauge. It is used mostly for dynamic strain, since any slow drift appears as a false signal.

```text
   V (+) o---- R_b ----+-------o
                       |
                      R_g      V_o (across R_g)
                       |
   V (-) o-------------+-------o
```

#### Output change
$$
V_o = V\frac{R_g}{R_g + R_b}
$$

Differentiate with respect to $R_g$:

$$
\frac{dV_o}{dR_g} = V\frac{R_b}{(R_g + R_b)^2}
$$

For a small change $\Delta R_g$:

$$
\Delta V_o = V\frac{R_bR_g}{(R_g + R_b)^2}\cdot\frac{\Delta R_g}{R_g}
$$

#### Maximum sensitivity
Let $m = R_b/R_g$. Then $\Delta V_o = V\dfrac{m}{(1+m)^2}\dfrac{\Delta R_g}{R_g}$. Setting $d/dm[m/(1+m)^2] = 0$ gives $m = 1$, i.e. $R_b = R_g$. The maximum output change is

$$
\Delta V_o = \frac{V}{4}\frac{\Delta R_g}{R_g}
$$

(This is the same as a quarter bridge, but the output sits on a dc level of $V/2$, which must be blocked by a capacitor before amplification.)

#### Numerical
$\Delta R_g/R_g = G\varepsilon = 2.0 \times 1000\times10^{-6} = 2\times10^{-3}$, $R_b = R_g$.

$$
\Delta V_o = \frac{6}{4}(2\times10^{-3}) = 3\times10^{-3}\ \text{V}
$$

**Answer: $R_b = R_g$ for maximum sensitivity; $\Delta V_o = 3$ mV.**

## Check yourself

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

1. What is the ballast circuit?
   A. A bridge with four active gauges
   B. A potential divider of the gauge in series with a fixed ballast resistor, with output taken across the gauge
   C. A gauge in parallel with a capacitor
   D. An amplifier with feedback gauge
   Answer: B. Vo = V Rg/(Rg + Rb), and a change in Rg changes Vo. (Key point: Ballast circuit)

2. For what ratio m = Rb/Rg is the sensitivity m/(1+m)^2 maximum?
   A. m = 0.5
   B. m = 1, i.e. Rb = Rg
   C. m = 2
   D. m very large
   Answer: B. Setting the derivative to zero gives m = 1, where the factor equals 1/4. (Key point: Maximum sensitivity)

3. For Rg = Rb = 120 ohm, V = 6 V, G = 2.0 and 1000 microstrain, the output change is:
   A. 12 mV
   B. 6 mV
   C. 3 mV
   D. 1.5 mV
   Answer: C. dVo = (V/4)(G e) = (6/4)(2e-3) = 3 mV. (Key point: Numerical output)

## Related in Instrumentation and Measurement

- [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
- [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
- [Elastic transducers and strain gauge load cells](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aelastic-force-transducers-load-cells) — Instrumentation and Measurement, chapter 7
- [Potentiometer transducer and loading error](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Apotentiometer-transducer-loading-error) — Instrumentation and Measurement, chapter 5
- [Shaft torque measurement using strain gauges](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Ashaft-torque-strain-gauge-numerical) — Instrumentation and Measurement, chapter 7

## Related in other subjects

- [Gauge factor of resistance strain gauge](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Astrain-gauge-factor) — Instrumentation I, chapter 3
- [Piezoelectric transducer sensitivity and output voltage](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Apiezoelectric-transducer-output-voltage) — Instrumentation I, chapter 3
- [Zener circuit output voltage and current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Azener-circuit-120v-5k) — Basic Electrical and Electronics Engineering, chapter 3
- [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×