Question

A moving coil galvanometer has been fitted with a rectangular coil having $50\;$ turns and dimensions$5\;cm \times 3\;cm$. The radial magnetic field in which the coil is suspended is of $0.05\;Wb/{m^2}$. The torsional constant of the spring is $1.5 \times {10^{ - 9}}\;Nm/{\text{degree}}$. Obtain the current required to be passed through the galvanometer so as to produce a deflection of ${30^0}$.

Answer 1

Hint: A moving coil galvanometer is a device that is used to detect or measure very small amounts of the current of the order ${10^{ - 8}}\;A$. It works on the principle that when current flows through a rectangular coil kept in a magnetic field, it is deflected. The angle of deflection is proportional to the current through the coil.
Formula used:
$I = \dfrac{C}{{NAB}}\theta $
where $I$ stands for the current through the galvanometer, $C$ stands for a torsional couple of the spring, $N$ stands for the number of turns of the coil, $A$ is the area of the coil, $B$ stands for the magnetic induction, and $\theta $ stands for the angle of deflection.

Complete step by step solution:
The number of turns, $N = 50$
The magnetic field, $B = 0.05\;Wb/{m^2}$
The torsional constant of the spring, $C = 1.5 \times {10^{ - 9}}\;Nm/{\text{degree}}$.
The length of the coil, $l = 5\;cm$
The breadth of the coil, $b = 3\;cm$
The area of the coil will be, $A = l \times b = \left( {5 \times {{10}^{ - 2}}} \right) \times \left( {3 \times {{10}^{ - 2}}} \right) = 1.5 \times {10^{ - 3}}\;{m^2}$
The angle of deflection, $\theta = {30^0}$
The current through the coil can be obtained by the formula, $I = \dfrac{C}{{NAB}}\theta $
Substituting all the values in the above equation, we get
$I = \dfrac{{1.5 \times {{10}^{ - 9}}}}{{50 \times 0.05 \times 1.5 \times {{10}^{ - 3}}}} \times 30 = 1.2 \times {10^{ - 5}}\;A$

The answer is: $1.2 \times {10^{ - 5}}\;A$

Additional information:
A sensitive galvanometer will give a large deflection for a small current. Current sensitivity can be defined as the deflection produced in the galvanometer for unit current. Voltage sensitivity can be defined as the deflection produced in the galvanometer for unit voltage.

Note:
The current through the galvanometer is directly proportional to the deflection of the galvanometer. To increase the current sensitivity, $N,\;A$ and $B$ should be large and $C$ should be small. To increase the voltage sensitivity $N,\;A$ and $B$ should be large and $C$ and $G$ should be small. Here $G$ is the galvanometer resistance.