Question

Sixteen identical resistors, each having resistance $R$ are connected as shown in the figure. Find the net resistance between points $X$ and $Y$.

• A. $\frac{5R}{7}$
• B. $\frac{7R}{6}$
• C. $\frac{6R}{7}$
• D. $\frac{3R}{7}$

Answer 1

The correct option is C $\frac{6R}{7}$


The given circuit can be modified as shown below.

The current in the arms $\text{FB}$ and $\text{BG}$ will be zero, due to symmetry, so we can remove the resistors in those arms.

After this, the junction $B$ will act like a pseudo junction due to symmetry, which can be removed.


$\therefore \frac{1}{R_{XY}}=\frac{1}{3R}+\frac{1}{2R}+\frac{1}{3R}=\frac{7}{6R}$

$\Rightarrow R_{XY}=\frac{6R}{7}$

Hence, option $\left(c\right)$ is the correct answer.