Question

In the arrangement of resistances shown in the circuit, the potential difference between points $B$ and $D$ will be zero, when the unknown resistance $X$ is equal to -

• A. $4\Omega$
• B. $3\Omega$
• C. $2\Omega$
• D. $1\Omega$

Answer 1

The correct option is C $2\Omega$

This given circuit is a Wheatstone bridge circuit.

Here, points $B$ and $D$ will be at same potential if,

$\frac{R_{AB}}{R_{AD}}=\frac{R_{BC}}{R_{DC}}$

$\Rightarrow \frac{12+4}{1+3}=\frac{X}{\frac{1\times 1}{1+1}}$

$\Rightarrow X=2\Omega$

Hence, option $\left(C\right)$ is the correct answer.