Question

In a moving coil galvanometer, the deflection of the coil \[\theta \] is related to the electric current i by the relation
A. $i\propto \tan \theta $
B. $i\propto \theta $
C. $i\propto {{(\theta )}^{2}}$
D. $i\propto (\sqrt{\theta })$

Answer 1

Hint: Recall the formula for the angular deflection of a moving coil galvanometer to determine the correct option. Then observe the relationship between the specified quantities and the moving coil galvanometer's angular deflection. Check to see how the current is related to the deflection.

Formula used:
$\theta =(\dfrac{NAB}{k})i$, where $\theta $ is the deflection of the coil, N is the number of turns in the coil, B is the magnetic field, k is the torsional constant and A is the area of the coil.

Complete answer:
Let’s analyze the given options according to the formula
$\theta =(\dfrac{NAB}{k})i$
Where $\theta $ is the deflection of the coil, N is the number of turns in the coil, B is the magnetic field, k is the torsional constant and A is the area of the coil.

In option A, we can see that the current is directly proportional to $\tan \theta $and according to the formula there is no such relation between them, so it’s a wrong option.

In option C and D, the current is directly proportional to ${{(\theta )}^{2}}$and $(\sqrt{\theta })$respectively and according to the formula that we are using, there is no such relation between them.

As we can observe in the formula, if we suppose $(\dfrac{NAB}{k})$ as a constant then deflection of moving coil galvanometer is directly proportional to the current.

Hence, the correct option is B. $i\propto \theta $

Note: An electromagnetic tool used to measure tiny electric currents is a moving coil galvanometer. The galvanometer is made up of a coil with several turns that can freely revolve around a fixed axis. This current-carrying coil experiences a torque and rotates about the fixed axis when current runs through it and the gadget is put in a uniform magnetic field. The existence and deflection of current are indicated by this deflection.