Question

In the circuit shown, the resistance of each resistor is $R=100 \, \Omega $ . Find the resistance in $\Omega $ to the nearest integer, which is to be connected between points $C$ and $D$ so that the resistance of entire circuit between $A$ and $B$ does not depend on the number of elementary cells.

Answer 1

Let resistance added across $CD$ is $x$ , then the equivalent resistance between $A$ and $B$ will be independent of the number of elementary cells if the combination of $x$ with the resistors of the elementary cells is $x$ itself. So $R_{AB}=x$
$\therefore \, x=\frac{\left(2 R + x\right) \times R}{\left(3 R + x\right)}$
$\Rightarrow \, x=\left(\sqrt{3} - 1\right)\times R$
$=\left(1.73 - 1\right)\times 100$
$=73\Omega $