Question

The effective resistance between $A$ and $B$ in the figure is $\frac{7}{12}\Omega$. If each side of the cube has $1\Omega$ resistance. The effective resistance between the same two points, when the link $AB$ is removed, is

• A. $\frac{7}{12}\Omega$
• B. $\frac{5}{12}\Omega$
• C. $\frac{7}{5}\Omega$
• D. $\frac{5}{7}\Omega$

Answer 1

The correct option is C $\frac{7}{5}\Omega$

Let the effective resistance between A and B with $1\Omega$ resistance between them removed be $R$.

This resistance is in parallel with the resistance between A and B to form overall effective resistance of circuit.

Hence $\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{1}$

$⟹\frac{12}{7}=\frac{1}{R}+\frac{1}{1}$

$⟹\frac{1}{R}=\frac{5}{7}$

$⟹R=\frac{7}{5}$