Question

In the circuit shown in figure, the total resistance between points $X$ and $Y$ is $R_{0}$. The value of resistance $R$ is

• A. $R_{0}$
• B. $\frac{R_{0}}{\sqrt{3}}$
• C. $\frac{R_{0}}{2}$
• D. $\sqrt{3} R_{0}$

Answer 1

Answer: (B)

$R_{X Y}=R+\frac{R\left(R+R_{0}\right)}{R+\left(R+R_{0}\right)}$
$\Rightarrow R_{0}=\frac{2 R^{2}+R_{0} R+R^{2}+R R_{0}}{\left(2 R+R_{0}\right)}$
or $2 R R_{0}+R_{0}^{2}=3 R^{2}+2 R R_{0}$
$\Rightarrow R=\frac{R_{0}}{\sqrt{3}}$