Question

In the circuit shown in the figure, all wires have equal resistance r. The equivalent resistance between A and B is

• A. $\frac{3r}{5}$
• B. $\frac{2r}{5}$
• C. $\frac{7r}{5}$
• D. $\frac{3r}{4}$

Answer 1

The correct option is A $\frac{3r}{5}$

$\begin{array}{c}\frac{x-v}{R}+\frac{2x-v}{R}+\frac{x-y}{R}=0\\ \Rightarrow 4x-y=2v..............\left(1\right)\\ \frac{y-x}{R}+\frac{2y-x}{R}+\frac{y-x}{R}=0\\ \Rightarrow 4y-x=2v............\left(2\right)\\ \Rightarrow x=y\\ \&3x=2v\\ x=\frac{2v}{3}=y\\ \therefore i=\frac{v-x}{R}+\frac{v-y}{R}+\frac{v}{R}\\ =\frac{v}{3R}+\frac{v}{3R}+\frac{v}{R}=\frac{2v}{3R}+\frac{v}{R}=\frac{5v}{R}\\ v=\left(\frac{3R}{5}\right)i\\ \therefore R_{eq}=\frac{3R}{5}\end{array}$

$\therefore$ Option $A$ is correct .