In a meter bridge experiment the balance point in 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 $22.5\,cm$. The value of $X$ is $................$
JEE MAIN 2023, Medium
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$\frac{2}{\left(\frac{3 x}{3+x}\right)}=\frac{40+22.5}{60-22.5}=\frac{62.5}{37.5}=\frac{5}{3}$
$\frac{6}{5}=\frac{3 x}{3+x}$
$6+2 x=5 x \Rightarrow x=2$
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