Question

In the above arrangement, each side of the cube have the same resistance, and it is known that the effective resistance between $A$ and $B$ is $\frac{5}{9}\Omega$ . Now, if the resistor between $A$ and $B$ is removed, the new effective resistance (in $\Omega$ ) between the same two points is $\frac{k}{4}$ , find $k$ .

Answer 1

Answer: 5

If $AB$ is removed, assuming the equivalent resistance between remaining resistors is $x,$
$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{x}$
$R_{eq}=\frac{Rx}{R+x}$
$\therefore \frac{5}{9}=\frac{1(x)}{1+x}=\frac{x}{1+x}....\left(\because R=1\Omega \right)$
$\therefore 5(1+x)=9x$
$\therefore 5+5x=9x$
$\therefore 5=4x$
$\therefore x=\frac{5}{4}\Omega$