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

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Q. 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 $22.5 \,cm$. The value of $X$ is _______

JEE MainJEE Main 2023Current Electricity

Solution:

$ \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$