Electrical measuring instruments

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Question

In an ideal metre-bridge, the balancing length from the left end when standard resistance of $1 Ω$ is in right gap is found to be 20 cm. The value of unknown resistance (in $Ω$ ) is

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Solution

$Let unknown resistance be X . Then condition of Wheatstone's bridge gives \frac{X}{R} = \frac{20 r}{80 r}, where r is resistance of wire per cm .$
$∴ X = \frac{20}{80} \times R = \frac{1}{4} \times 1 = 0.25 Ω$

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