Question

If reduction factor of a tangent galvanometer is 900 mA, then the current through it to produce a deflection of 45$^{\circ}$ is:
A.) 600 mA
B.) 700 mA
C.) 750 mA
D.) 900 mA

Answer 1

Hint: Tangent galvanometer is a current measuring device and the amount of current passing through the galvanometer is directly proportional to its reduction factor and tangent of angle of deflection.
Formula used:
$I = K\tan \theta$
where I is the current through the galvanometer, K is the reduction factor and $\theta$ is the angle of deflection in the galvanometer.

Step by step solution:
Tangent galvanometer is a current measuring device used to measure small currents. It comprises a copper wire which is insulated and wound around a circular frame which is non-magnetic in nature.

Working principle of tangent galvanometer: The tangent galvanometer works on the basic principle of tangent law of magnetism. The needle used is magnetic in nature and is subjected to two fields. One of these fields is due to the horizontal component of earth’s magnetic field while the other one is created by the current passing through the galvanometer. When these two fields balance each other, the needle comes to rest and the angle that it makes with the horizontal component of earth’s magnetic field is $\theta$.

The amount of current that must be passed through the galvanometer to obtain deflection of 45$^{\circ}$ is called the reduction factor of that galvanometer. It has the same units as current.

The current through the galvanometer is directly proportional to the reduction factor and tangent of the angle of deflection. They are related to each other as follows:

$I = K\tan \theta$

We are given the angle of deflection and the reduction factor.

$\theta = 45^\circ \\\ K = 900mA \\\ \therefore I = 900\tan 45^\circ \\\ \Rightarrow I = 900 \times 1 \\\ \Rightarrow I = 900mA \\\$

Hence, the correct answer is option D.

Note: The tangent galvanometer can measure only small amounts of currents. Large amounts of current can damage the device. The device should be kept away from other magnetic substances as fields can affect the reading of the galvanometer.