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 $A B$ is removed, is

• A

  $\frac{7}{12} \Omega$
• B

  $\frac{5}{12} \Omega$
• Correct answer
  C

  $\frac{7}{5} \Omega$
• D

  $\frac{5}{7} \Omega$

Solution

Let when link AB is removed, $x$ is an equivalent of remaining part of cube without link. AB and rest part will be in paralel, so according to question $$ \begin{array}{c} \frac{7}{12}=\frac{R_{1} R_{2}}{R_{1}+R}=\frac{1(x)}{1+x}=\frac{x}{1+x} \\ \frac{7}{12}=\frac{x}{1+x} \\ 12 x=7+7 x \\ 12 x-7 x=7 \end{array} 5 x=7 $$ $$ x=\frac{7}{5} \Omega $$

Hence, the correct answer is option: 'C'.