Question

In the circuit shown in figure, the effective resistance between $A$ and $B$ is

• A. $\frac{R}{2}$
• B. $R$
• C. $2R$
• D. $4R$

Answer 1

Answer: (A)

The upper part of the circuit is balanced Wheat stone's bridge. So, resistance $R$ in branch $CD$ is ineffective as no current will flow in this branch. The circuit therefore reduces to three parallel branches having resistance $R,R+R$ and $R+R$.

$\therefore$ Effective resistance $\frac{1}{R^{\prime }}=\frac{1}{R}+\frac{1}{2R}+\frac{1}{2R}$
$\Rightarrow R^{\prime }=R/2$