Question

An accumulator of emf $2Volt$ and negligible internal resistance is connected across a uniform wire of length $10m$ and resistance $30\Omega$. The appropriate terminals of a cell of emf $1.5Volt$ and internal resistance $1\Omega$ is connected to one end of the wire, and the other terminal of the cell is connected through a sensitive galvanometer to a slider on the wire. If the length of the wire which is required to produce zero deflection of the galvanometer is $\frac{x}{2}m$. Find $x$.

Answer 1

When there is no any deflection in the galvanometer $\Rightarrow$ voltage of secondary circuit = voltage drop across the wire AJ

voltage drop on the balancing length of the wire

$\Rightarrow i\rho X$

where $i=$ current flowing in primary circuit

$\rho$ = resistance per unit length of the wire

X=balancing length of wire AB when deflection in galvanometer is zero

When deflection is zero $\Rightarrow \frac{3}{2}=\left(\frac{2}{30}\right)\left(\frac{30}{10}\right)\left(y\right)$

where $y$ is the length of the wire AJ

$y=\frac{15}{2}m.$

$\Rightarrow x=15$