Question

A battery of emf ${ϵ}_0=10V$ is connected across a $1m$ long uniform wire having resistance $10\Omega /m$. Two cells of emf ${ϵ}_1=2V$ and ${ϵ}_2=4V$ having internal resistances $1\Omega$ and $5\Omega$ respectively are connected as shown in the figure. If a galvanometer shows no deflection at the point $P$, find the distance of point $P$ in cm from the point $A$. (Round off the answer to the nearest integer)

Answer 1

If galvanometer shows a zero reading,
$i_1=\frac{10}{10+10}=0.5A$

So, $V_{AP}=i_1\times \frac{x}{1}10=5x$
And, $i_2=\frac{4-2}{5+1}=\frac{1}{3}A$
So, $V_{AP}=2+i_2\times 1=2+\frac{1}{3}=\frac{7}{3}$

$\Rightarrow 5x=\frac{7}{3}$

$\Rightarrow x=0.466m=46.6cm\approx 47cm$