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**Hint:**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.

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