Question

The reduction factor of a tangent galvanometer may be defined as the current passing through it to produce a deflection of:
A) $90^\circ$
B) $45^\circ$
C) $30^\circ$
D) $60^\circ$

Answer 1

To solve this question we should know what a tangent galvanometer is. After that, we can understand what the reduction factor for a tangent galvanometer is and the conditions associated with it. Using this we can easily solve the required solution for the question.

Formulae used:
$I = K\tan \theta$
Where $I$ is the current supplied, $K$ is the reduction factor and $\theta$ is the angle of deflection shown by the galvanometer.
$\tan \theta = \dfrac{{{B_V}}}{{{B_H}}}$
Here $\theta$ is the angle of deflection shown by the galvanometer, ${B_V}$ is the vertical component of magnetic field and ${B_H}$ is the horizontal component of magnetic field.

Complete step by step solution:
We know that,
$I = K\tan \theta$
Where $I$ is the current supplied, $K$ is the reduction factor of the galvanometer, and $\theta$ is the angle of deflection shown by the galvanometer.
To obtain the reduction factor, the tangent galvanometer should be in balanced condition i.e.
$\Rightarrow {B_V} = {B_H}$
Let this be equation 1.
Here ${B_V}$ is the vertical component of the magnetic field of earth and ${B_H}$ is the horizontal component of magnetic field of the earth.
We know that
$\Rightarrow \tan \theta = \dfrac{{{B_V}}}{{{B_H}}}$
Substituting the of equation 1 here, we get,
$\Rightarrow \tan \theta = \dfrac{{{B_V}}}{{{B_V}}} = 1$
$\Rightarrow \tan \theta = \tan 45^\circ$
$\Rightarrow \theta = 45^\circ$
So we get the angle of deflection as $45^\circ$. So the reduction factor of a tangent galvanometer may be defined as the current passing through it to produce a deflection of $45^\circ$.

Hence the required solution will be option (B).

Note: A tangent galvanometer is a measuring instrument used for the measurement of electric current. It works on the principle of the tangent law of magnetism. It uses a copper coil wound on a nonmagnetic frame. It has a compass needle placed horizontally to the surface. It compares the magnetic field generated by the unknown current to the magnetic field of the Earth.