Question

A Wheatstone bridge is used to measure strain as shown in the figure below.
Initially, the bridge was balanced. When a strain is applied to the resistor \( R_{{strain}} \), along its length, the output voltage \( V_{{out}} \) is 10 mV. If \( R_{{strain}} \) is a cylindrical resistor of length \( l \) and cross-sectional area \( A \), the magnitude of the applied strain is _______.
(rounded off to two decimal places)
\includegraphics[width=0.5\linewidth]{63.png}

Hint:

In a Wheatstone bridge, the output voltage is proportional to the resistance change caused by the applied strain. The strain is calculated by relating the output voltage to the original resistance.

Answer 1

The output voltage of the Wheatstone bridge is given by the formula: \[ V_{{out}} = \frac{V}{4} \cdot \frac{\Delta R}{R} \] Where:
\( \Delta R \) is the change in resistance,
\( R \) is the original resistance,
\( V_{{out}} \) is the output voltage (10 mV),
\( V \) is the input voltage (1 V).
Since strain \( \epsilon \) is related to the change in resistance as: \[ \epsilon = \frac{\Delta R}{R} \] Thus, the strain can be calculated by: \[ \epsilon = \frac{V_{{out}}}{V} \cdot 4 \] Substitute the given values: \[ \epsilon = \frac{10 \, {mV}}{1 \, {V}} \cdot 4 = 0.04 \] Thus, the magnitude of the applied strain is \( 0.04 \).