Question

Find equivalent resistance between \(A\) and \(B\)

• A. $\frac{3R}{4}$
• B. $R$
• C. $2R$
• D. $\frac{R}{2}$

Answer 1

The correct option is D $\frac{R}{2}$


Given circuit can be redrawn as follows
The equivalent resistance for the topmost and bottomost part
$R^{\prime }=(R+R)||R$

$\Rightarrow R^{\prime }=\frac{(2R\times R)}{(2R+R)}=\frac{2}{3}R$

The circuit reduces to,

$\Rightarrow R_{AB}=(\frac{2}{3}R+\frac{R}{3}\left)||\right(\frac{2}{3}R+\frac{R}{3})$

$\Rightarrow R_{AB}=R||R$
$\Rightarrow R_{AB}=\frac{R}{2}$
Hence, option $\left(C\right)$ is correct.