GATE 2022 EE – Question 18

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

A balanced Wheatstone bridge $ABCD$ has the following arm resistances:

$R_{AB}=1\ \text{k}\Omega\pm2.1\%$; $R_{BC}=100\ \Omega\pm0.5\%$; $R_{CD}$ is an unknown resistance;

$R_{DA}=300\ \Omega\pm0.4\%$. The value of $R_{CD}$ and its accuracy is

$30\ \Omega\pm3\ \Omega$
$30\ \Omega\pm0.9\ \Omega$
$3000\ \Omega\pm90\ \Omega$
$3000\ \Omega\pm3\ \Omega$

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Correct answer: (B) $30\ \Omega\pm0.9\ \Omega$

Explanation

For a balanced bridge $\frac{R_{AB}}{R_{BC}}=\frac{R_{DA}}{R_{CD}}$, so $R_{CD}=\frac{R_{BC}R_{DA}}{R_{AB}}=\frac{100\times300}{1000}=30\ \Omega$. The limiting errors add: $2.1+0.5+0.4=3.0\%$, which is $0.03\times30=\pm0.9\ \Omega$.