Question

Thirteen resistances each of resistance $R\Omega$ are connected in the circuit as shown in the figure. The effective resistance between $\text{A}$ and $\text{B}$ is : -

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

Answer 1

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

Let us identify, the series and parallel combinations and simplify further as,

$\Downarrow$


This is a balanced Wheatstone bridge so $R$ will be removed.


$\therefore$ Equivalent resistance of the given circuit is,

$R_{eq}=\frac{\frac{4R}{3}\times \frac{4R}{3}}{\frac{4R}{3}+\frac{4R}{3}}=\frac{2R}{3}\Omega$

Hence, option $\left(d\right)$ is correct.