Question

The equivalent resistance between $A$ and $B$ for the given circuit is $20\,x$ ohm where, $R=100\sqrt{3}\,\Omega$ . Value of $x$ is,

Answer 1

From infinite series

$\frac{x R}{R+x}+2 R=x$
$x R+2 R^{2}+2 R x=x R+x^{2}$
$x^{2}-2 R x-2 R^{2}=0$
$x=\frac{2+\sqrt{4+8}}{2} R$
$x=(\sqrt{3}+1) R$
$\frac{1}{R_{e q}}=\frac{1}{x}+\frac{1}{R}+\frac{1}{x}$
$R_{e q}=100 \,\Omega=20 \times 5 \, \Omega$