Question

# A meter bridge is set-up as shown, to determine an unknown resistance. X using a standard $10$ohm resistor. The galvanometer shows null point when tapping key is a $52cm$ mark. The end-corrections are $1cm$ and $2cm$ respectively for the ends A and B. The determined value of X is

A

$10.2\Omega$

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B

$10.6\Omega$

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C

$10.8\Omega$

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D

$11.1\Omega$

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Solution

## The correct option is B $10.6\Omega$Step 1. Given data:Resistance = $10$ohm Tapping key initial mark = $52cm$ End-corrections at A and B = $1cm$ and $2cm$ respectively.Step 2. Finding unknown resistance:Applying the condition of the balanced Wheatstone bridge, we get$\frac{X}{10}=\frac{\left(52+1\right)}{\left(\left(100-52\right)+2\right)}=\frac{53}{50}\phantom{\rule{0ex}{0ex}}X=\frac{53}{50}×10=10.6\Omega$Thus, the correct option is option B.

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