Question

If the potential difference between $A$ and $D$ is $V$, what will be potential difference between $F$ and $C$. Each of the resistance is $R$.

Answer 1

The given figure is,

Resultant resistance of Arm,

$FD=2R$

$CD=R$

$AC=2R$

$AF=R$

Now, applying the Wheatstone bridge principle, there will be no current through arm.

$\therefore$ total resistance across the arm $AD$ will be

$\frac{1}{R_{eq}}=\frac{1}{3R}+\frac{1}{3R}$

$=\frac{2}{3R}$

or $R_{eq}=\frac{3R}{2}$

Now $V=I{R}_{eq}$

$⟹I=\frac{2V}{3R}$

Now for arm $FC$

Now $I^{\prime }=\frac{2V}{3R}$ and $R_{eq}^{\prime }=\frac{3R}{5}$

Then, $V^{\prime }=I^{\prime }{R}^{\prime }$

$=\frac{2V}{3R}\times \frac{3}{4}R$

$V^{\prime }=\frac{2}{5}V$

$\therefore$ the potential difference across arm $FC$ will be $\frac{2}{5}$ of $V$.