Question

A certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of ${45}^{\circ }$. If the current be reduced by a factor of $\sqrt{3}$​, the deflection would
A. Decrease by${30}^{\circ }$
B. Decrease by${15}^{\circ }$
C. Increase by${30}^{\circ }$
D. Increase by${15}^{\circ }$

Answer 1

Hint: An early measuring tool for measuring electric current is a tangent galvanometer. It operates by comparing the magnetic field produced by an unknown current to the magnetic field of the Earth using a compass needle. Current steadiness is measured using a tangent galvanometer.

Formula used:
The formula to measure current using tangent galvanometer is,
$I=K\tan \theta$
where $\theta$ defines the angle through which the needle deflects and $K$ is the constant.

Complete step by step solution:
Tangent galvanometer is a device used for calculating current, and it is used to measure steady flows. It lowers the bar set by Tangent law. A beautiful needle strung at a location where two crossed fields are at right angles to one another will stop moving in the direction of the result of the two fields.

The magnetic field of Earth immediately causes the instrument needle to start moving. Development continues until the plane of the loop and the earth's attractive field are aligned. At that time, a second attractive field on the pivot of the loop that is opposed to the attractive field of the Earth is created using an unknown current.

As a result, the vector sum of the two fields triggers a response from the compass needle. This divergence corresponds to the ratio of those two fields' tangents at this position. We know that the expression of current is,
$I=K\tan \theta$
$\Rightarrow I\propto \tan \theta$
$\Rightarrow {\displaystyle \frac{I_1}{I_2}}={\displaystyle \frac{\tan {\theta }_1}{\tan {\theta }_2}}$
Substituting the given value $\theta ={45}^{\circ }$and$I_2={\displaystyle \frac{I_1}{\sqrt{3}}}$ we get,
${\displaystyle \frac{I_1}{I_1/\sqrt{3}}}={\displaystyle \frac{\tan 45}{\tan {\theta }_2}}$
$$\begin{gathered} \Rightarrow \tan {\theta }_2={\displaystyle \frac{1}{\sqrt{3}}} \\ \therefore \theta ={30}^{\circ } \end{gathered}$$
Since current is reduced the angle of deflection will also decrease due to proportional dependency.

Hence option B is correct.

Note: The tangent law of attraction states that the proportion of characteristics between two opposing attractive fields is directly related to the tangent of the point of a compass needle, which is due to the development impacted by an attractive field. In simpler terms, the moving needle's tangent point under the attractive field properly illustrates the merits of the opposing attractive fields.