Question

The effective resistance between $A$ and $B$ in the figure is $\frac{5}{9}\Omega$, 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 ______$\Omega$

Answer 1

Answer: 1.25

i. For a cube of resistors each of resistance $R$, the equivalent resistance between two edges on the same face is
$R_{eq}=\frac{5R}{9}$
ii. If $AB$ is removed, assuming the equivalent resistance between remaining resistors is $x$,
$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{x}$
$R_{eq}=\frac{Rx}{R+x}$
$\therefore \frac{5}{9}=\frac{1(x)}{1+x}=\frac{x}{1+x}....(\because R=1\Omega )$
$\therefore 5(1+x)=9x$
$\therefore 5+5x=9x$
$\therefore 5=4x$
$\therefore x=\frac{5}{4}\Omega$
$\therefore x=1.25\Omega$