Question

In the following circuit diagram, the value of resistance $X$, for which the potential difference between the points $\text{B}$ and $\text{D}$ is zero is equal to

• A. $4\Omega$
• B. $6\Omega$
• C. $8\Omega$
• D. $9\Omega$

Answer 1

The correct option is C $8\Omega$

By using the concept of succesive reduction,


For, $V_B-V_D=0$, the circuit behaves as a balanced wheatstone bridge.

$\Rightarrow \frac{21}{18}=\frac{\frac{8X}{8+X}+3}{6}$

$\Rightarrow \frac{21}{3}=\frac{8X+24+3X}{8+X}$

$\Rightarrow 56+7X=11X+24$

$\Rightarrow 4X=32$

$X=8\Omega$

Why this Question? Tip: To solve complex circuits, first identify any series or parallel combinations and reduce the circuit. $V_B-V_D=0\Rightarrow$The circuit is a balanced wheatstone bridge.