Question 283 of 380

In a metre-bridge when a resistance in the left gap is $2\Omega$ and unknown resistance in the right gap, the balance length is found to be $40cm.$ On shunting the unknown resistance with $2\Omega ,$ the balance length changes by:

A$22.5cm$B$20cm$C$62.5cm$D$65cm$

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Answer: (A) $22.5cm$

In first circuit:
For balanced condition, we get $\dfrac{2}{40}=\dfrac{X}{60}\Rightarrow X=3\Omega$
In second case:
Net resistance of the right side due to shunting becomes, ${X}^{'}=\dfrac{2\times 3}{2+3}=1.2\Omega$
Again for balanced condition,
$\dfrac{2}{\ell }=\dfrac{1.2}{100-\ell }$
$\Rightarrow 200-2\ell =1.2\ell$
$\Rightarrow \ell =\dfrac{200}{3.2}=62.5cm$
Clearly, balance length changes by $22.5cm$.