In a metre-bridge when a resistance in the left gap is and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with , the balance length changes by

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Solution

Q.
In a metre-bridge when a resistance in the left gap is $2 Ω$ and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with $2 Ω$ , the balance length changes by [2024]

1 22.5 cm

2 20 cm

3 62.5 cm

4 65 cm

Ans.
(1)

Given for $l_{1} = 40$ cm
$\frac{R}{l_{1}} = \frac{X}{l_{2}} \Rightarrow \frac{2}{40} = \frac{X}{60}$

$x = 3 Ω$

After shunting

$R_{eq} = \frac{2 \times 3}{3 + 2} = \frac{6}{5} Ω$

$\frac{R}{l} = \frac{R_{eq}}{100 - l} \Rightarrow \frac{2}{l} = \frac{6}{5 (100 - l)}$

$\Rightarrow 10 (100 - l) = 6 l$

$500 - 5 l = 3 l$

$500 = 8 l$

$l = \frac{500}{8} = \frac{125}{2} = 62.5 cm$

Balance length change

by $= 62.5 - 40 = 22.5 cm$

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