Question

A $6V$ battery of internal resistance $1\Omega$ is connected across a uniform wire $AB$ of length $100cm$. The positive terminal of another battery of EMF $4V$ and internal resistance $1\Omega$ is joined to point $A$ as shown. The distance of point $P$ from $A$ is $\alpha \times 10cm$. Find the value of $\alpha$, for which there is no current through the galvanometer. (resistance of $AB$ wire is $5\Omega$ )

Answer 1

Answer: 8

Current flowing through wire AB, $I=\frac{6}{5+1}=1A$

The potential gradient of the wire $AB$,
$\varphi =\frac{V_{AB}}{AB}=\frac{(1\times 5)}{100}=0.05V(cm{)}^{-1}$
For length AP, equating potential difference,
$(AP)\times \varphi =4V$
$\Rightarrow AP=\frac{4}{0.05}=80cm=8\times 10cm$