The GATE Grind

GATE 2015 EE – Question 15

Electrical and Electronic Measurements · Bridges and Potentiometers · 1 mark · Multiple choice

When the Wheatstone bridge shown in the figure is used to find the value of resistor $R_X$, the galvanometer G indicates zero current when $R_1 = 50\ \Omega$, $R_2 = 65\ \Omega$ and $R_3 = 100\ \Omega$. If $R_3$ is known with $\pm 5\%$ tolerance on its nominal value of $100\ \Omega$, what is the range of $R_X$ in Ohms?

A Wheatstone bridge with $R_1$ and $R_2$ in the upper arms, $R_3$ and $R_X$ in the lower arms, a galvanometer G across the middle, and a battery V.
  1. [123.50, 136.50]
  2. [125.89, 134.12]
  3. [117.00, 143.00]
  4. [120.25, 139.75]

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Show answer and explanation

Correct answer: (A) [123.50, 136.50]

Explanation

At balance, $R_X = \frac{R_2 R_3}{R_1} = \frac{65 \times R_3}{50} = 1.3\,R_3$. With $R_3$ between 95 and 105 $\Omega$, $R_X$ ranges from $123.5$ to $136.5\ \Omega$.