Question

The deflection of a moving coil galvanometer falls from $60$ divisions to $12$ divisions for the same value of current in the circuit, when a shunt of $12\Omega$ is connected. If the resistance (in ohm) of the galvanometer is $G$, then find the value of ${\left(\frac{G}{6}\right)}^{1/3}$.

Answer 1

Answer: 2

The current $i$ in the galvanometer is directly proportional to the angle of deflection, i.e, $i\propto \theta$

Then, $\frac{i_g}{i}=\frac{12}{60}=\frac{1}{5}$
or, $i_g=\frac{i}{5}...(i)$
For shunted galvanometer,
$\left(i-i_g\right)S=i_{g}G$
or, $G=\left(i-i_g\right)\frac{S}{i_g}...(ii)$
Putting $i_g=\frac{i}{5}$ from equation (i) in equation (ii) and
$S=12\Omega$, we get
$G=48\Omega$