First slide

Electrical measuring instruments

Question

In a meter bridge, null point is 20 cm, when the known resistance R is shunted by $10 Ω$ resistance, null point is found to be shifted by 10 cm. Find the unknown resistance X.

Moderate

A

$25 Ω$
B

$50 Ω$
C

$75 Ω$
D

$100 Ω$

Solution

$\frac{R}{X} = \frac{l}{100 - l}$
$X = (\frac{100 - l}{l}) R$
$X = (\frac{100 - 20}{20}) R = 4 R$
When known resistance R is shunted, its net resistance will decrease. Therefore, resistance parallel to this (i.e., P ) should also decrease or its new null point length should also decrease.
$\frac{R^{'}}{X} = \frac{l^{'}}{100 - l^{'}}$
$= \frac{20 - 10}{100 - (20 - 10)} = \frac{1}{9}$
$X = 9 R^{'}$
$4 R = 9 R^{'} = 9 [\frac{10 R}{10 + R}]$
Solving this equation, we get
$R = \frac{50}{4} Ω$
$X = 4 R = 4 (\frac{50}{4})$
$X = 50 Ω$

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