Question

The current sensitivity of a moving coil galvanometer depends on:
A. The number of turns in the coil.
B. Moment of inertia of the coil.
C. Current sent through galvanometer.
D. Eddy current in A1 frame.

Answer 1

Hint: First we have to find the principal on which the galvanometer works, then find the equation of torque due to currents induced in the coil and also the torque in the spring of the galvanometer.

Complete step-by-step answer:
The principle on which a galvanometer works is if we send a current through a coil in the galvanometer a torque is induced.
Now we know that the formula for torque due to currents induced in a coil is,
$\tau =NiAB$ ,……eq.1
Where N is the number of turns in the coil,
‘i’ is the current passing through the coil,
A is the area of the cross-section in the coil,
B is the strength of magnetic strength induced.
 We know that inside the galvanometer a spring is connected to a needle that points at the values for the galvanometer, inside the spring is also connected to the coil of the galvanometer.
So, for the deflection of the spring the torque produced is,
$\tau =c\theta$ ,……eq.2,
Where c is the spring constant, and theta is the deflection by the spring.
Now on comparing equation 1 and equation 2, we get
$NiAB=c\theta$,
Now the galvanometer is used to define in how much current is required to move the pointer with,
That means,
${\displaystyle \frac{\theta }{i}}={\displaystyle \frac{NAB}{c}}$,
Directly proportional to the number of turns.
Directly proportional to the Cross-sectional area or the coil.
Directly proportional to the strength of the magnetic induction.
And inversely proportional to spring constant.

Therefore option A is the correct answer.

Note: ${\displaystyle \frac{\theta }{i}}$ as a whole is called the current sensitivity of the coil, now this sensitivity depends on other factors discussed in the answer above, spring constant c is a constant value for a single type of spring hence it does not change.