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Figure shows a meter bridge in which a known resistance R and an unknown resistance X connected to it. The length of the total wire AB is 100cm. Then the balancing length for which the percentage error in measuring the value of x is minimum (neglect end corrections)

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100 cm

50 cm

0 cm

33.3 cm

answer is C.

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Detailed Solution

$x = \frac{R l}{100 - l} \Rightarrow d x = \frac{100 R}{(100 - l)^{2}} d l$

$\Rightarrow \frac{d x}{x} = \frac{100 dl}{100 l - l^{2}}$

$\frac{d x}{x}$ is minimum when $100 l - l^{2}$ is maximum

$y = 100 l - l^{2}; \frac{dy}{dl} = 0$

$100 - 2 l = 0; l = 50 cm$

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