Question

A cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $AC$ and $BD$ as shown in the figure below.

Resistance between point $A$ and $B$ is

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

Answer 1

Answer: (A)

First we connect points of equal potentials and redraw equivalent circuit.


Above equivalent circuit is a combination of two balanced Wheat stones bridge. Hence, simplified circuit is

In above circuit, resistance combination gives,

So, equivalent resistance between $A$ and $B$ is $=\frac{R}{2}\Omega .$