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

Question

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:

TestHub · Accepted Answer

In first circuit:

For balanced condition, we get $\frac{2}{40} = \frac{X}{60} \Rightarrow X = 3 Ω$

In second case:

Net resistance of the right side due to shunting becomes, $X^{'} = \frac{2 \times 3}{2 + 3} = 1.2 Ω$

Again for balanced condition,

$\frac{2}{ℓ} = \frac{1.2}{100 - ℓ}$

$\Rightarrow 200 - 2 ℓ = 1.2 ℓ$

$\Rightarrow ℓ = \frac{200}{3.2} = 62.5 cm$

Clearly, balance length changes by $22.5 cm$ .

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