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In a meter bridge experiment, the balance point is obtained if the gaps are closed by $2 Ω a n d 3 Ω .$ A shunt of $x Ω$ is added to $3 Ω$ resistor to shift the balancing point by 20cm, the value of x is ___

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$2.4 Ω$

$4.8 Ω$

$9.6 Ω$

$7.2 Ω$

answer is A.

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Detailed Solution

$\frac{2}{3} = \frac{l}{100 - l} \Rightarrow l = 40 c m$

$\frac{2 (3 + x)}{3 x} = \frac{60}{100 - 60} \Rightarrow 6 + 2 x = \frac{3 x}{2} x^{3}$

$12 + 4 x = 9 x$

$5 x = 12$

$x = 2.4 Ω$

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