Question 26 of 70

In a metre bridge experiment the balance point is obtained if the gaps are closed by $2\Omega$ and $3\Omega$. A shunt of $X\Omega$ is added to $3\Omega$ resistor to shift the balancing point by $22.5cm$. The value of $X$ is ______.

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Answer: 2

Case $1$: No shunt is added
The initial balancing length $l$ of the bridge is,
$\dfrac{2}{3}=\dfrac{l}{100-l}$
$\Rightarrow 200-2l=3l \Rightarrow l=40cm$

Case $2$: When shunt is added
The new balancing length is, ${l}_{1}=22.5+40=62.5cm$
So, $\dfrac{62.5}{37.5}=\dfrac{2}{\left(\dfrac{3X}{3+X}\right)}$
$\Rightarrow X=2$.