Question

The effective resistance between points $A$ and $B$ is

• A. R
• B. $\frac{R}{3}$
• C. $\frac{2R}{3}$
• D. $\frac{3R}{5}$

Answer 1

Answer: (C)

Here points $B$ and $D$ are common.
So, $2R$ in arm $DC$ and $2R$ in arm $CB$ are in parallel between $C$ and $B$.
Their effective resistance $=\frac{2R\times 2R}{2R+2R}=R$
The modified and simpler circuit will be shown in figure. The effective resistance between $A$ and $B$ is

$R_{\text{eff }}=\frac{R\times (R+R)}{R+(R+R)}=\frac{2}{3}R$