First slide

Electrical measuring instruments

Question

A resistance of $2 Ω$ is connected across one gap of a meter bridge (the length of the wire is 100 cm ) and an unknown resistance, greater than $2 Ω$ , is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

Moderate

A

$3 Ω$
B

$4 Ω$
C

$5 Ω$
D

$6 Ω$

Solution

$R > 2 Ω$
100-x > x
Applying, $\frac{P}{Q} = \frac{R}{S}$
We have, $\frac{2}{R} = \frac{x}{100 - x}$
$\frac{R}{2} = \frac{x + 20}{80 - x}$
Solving the equations,
$R = 3 Ω$

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