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

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, $\quad G=\left(i-i_{g}\right) \frac{S}{i_{g}}\,\,\,...(ii)$
Putting $i_{g}=\frac{i}{5}$ from equation (i) in equation (ii) and
$S=12 \,\Omega$, we get
$G=48 \,\Omega$