Question

A moving coil galvanometer A has $200$ turns and resistance $100$ Another meter B has $100$ turns and resistance $40$ All the other quantities are same in both the cases. The current sensitivity of
A. B is double as that of A
B. A is $2.5$ times of B
C. A is $5$ times of B
D. B is $5$ times of A

Answer 1

In order to solve this question, we should know about current sensitivity of moving coil galvanometers. The deflection produced in a moving coil of galvanometer due to per unit flow of current is called current sensitivity and here, we will use the general formula of moving coil galvanometer and then will compare in both cases to find the correct option.

Complete step by step answer:
According to the question, we have given that the coil A has number of turns $n = 200$ and the current sensitivity of galvanometer is calculated by using the formula
$I = nABk\theta$
Where, $I$ is reciprocal of current sensitivity, $n$ is number of turns of coil, $A$ is area of coil, B is a magnetic field, $k$ is a couple per unit twist and $\theta$ is angle of deflection.

Here, current sensitivity is independent of resistance and keeping all other quantities same and depending only upon number of turns so,
For coil A ${I_A} = 200(ABk\theta )$
For coil B ${I_B} = 100(ABk\theta )$
Dividing both equations we get,
$\dfrac{{{I_A}}}{{{I_B}}} = \dfrac{{200(ABk\theta )}}{{100(ABk\theta )}}$
$\Rightarrow \dfrac{{{I_A}}}{{{I_B}}} = 2$
And since $\dfrac{1}{I}$ is the current sensitivity so ${\varphi _B} = 2{\varphi _A}$ where $\varphi$ is the current sensitivity. So, the current sensitivity of meter B is twice as that of meter A.

Hence, the correct option is A.

Note: It should be remembered that, I is the actual current flowing through the coil but the deflection per unit current which may be written as reciprocal of current is the actual calculation of current sensitivity of a moving coil galvanometer. The SI unit of current sensitivity is radian per ampere written as $rad{A^{ - 1}}$.