Question

In the electrical circuit shown in figure the current through the galvanometer will be zero if the value of resistance x is

• A. 4 ohm
• B. 8 ohm
• C. 16 ohm
• D. 24 ohm

Answer 1

The correct option is D 24 ohm

The given circuit is Wheatstone's bridge.The current through the galvanometer will be zero if the bridge is balanced
$\frac{P}{Q}+\frac{R}{S}$ where P = 2+3 =5 ohm, Q = 10 ohm and R=4 ohm
The value of S is given by
$\frac{5}{10}=\frac{4}{S}$
or S= 8 ohm
thus the effective resistance of the parallel combination of 12 ohm and x ohm must be 8 ohm
therefore
$\frac{1}{12}+\frac{1}{x}=\frac{1}{8}$
which gives x = 24 ohm