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. ${22.5}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

We know that, the current in the tangent galvanometer is,

$i=K\tan \theta$

Here, Reduction factor, $K=\frac{2B_{H}a}{{\mu }_{0}n}$

Where,
$a\to \text{Radius of the coil}{B}_H\to \text{Horizontal component of the magnetic field}N\to \text{Number of turns of the coil}\theta \to \text{Angle of deflection}$

$K=\frac{i}{\tan \theta }$

For $K=i$,

$\tan \theta =1$

$\Rightarrow \theta ={\tan }^{-1}\left(1\right)$

$\therefore \theta ={45}^{\circ }$

So the reduction factor will be equal to the current passing through the tangent galvanometer to produce a deflection of ${45}^{\circ }$.

Hence, option $\left(B\right)$ is correct.