Question

Find the equivalent resistance between points $\text{A}$ and $\text{B}$ in the circuit shown

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

Answer 1

The correct option is D $\frac{3R}{2}$

The given circuit is symmetrical about $\text{AOB}$. So, current from upper part will not enter lower part.

Therefore, resistance between $\text{CO}$ and $\text{OD}$ can be considered to be connected in series.

Likewise, resistance between $\text{EO}$ and $\text{OF}$ can be considered to be connected in series.


Effective resistance between $ACDB$

$R_1=R+\frac{2R(R+R)}{2R+(R+R)}+R=3R$

Similarly, effective resistance between $AEFB$

$R_1=R+\frac{2R(R+R)}{2R+(R+R)}+R=3R$

Hence, the effective resistance between $AB$

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

Option $\left(D\right)$ is the correct answer.