Question

A moving coil galvanometer A has $200turns$ and resistance $100$ . Another meter B has $100turns$ 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

The correct option is A

B is double as that of A

Step 1: Given

Number of turns of A: $n_A=200$

Number of turns of B: $n_B=100$

Resistance of A: $R_A=100$

Resistance of A: $R_B=40$

Step 2: Formula Used:

$I=nABk\theta$

where I is the reciprocal of current sensitivity, A is the area of the coil, B is the magnetic field, k is the couple per unit twist, and $\theta$ is the angle of deflection.

Step 3: Find the ratio of sensitivity of both galvanometers

Calculate the reciprocal of the current sensitivity of galvanometer A using the formula

$$\begin{gathered} I_A=n_{A}ABk\theta \\ =200ABk\theta \end{gathered}$$

Calculate the reciprocal of the current sensitivity of galvanometer B using the formula

$$\begin{gathered} I_B=n_{B}ABk\theta \\ =100ABk\theta \end{gathered}$$

Calculate the ratio of current sensitivity by dividing the current sensitivity of A by the current sensitivity of B. Current sensitivity will be the reciprocal of I.

$$\begin{gathered} Ratioofcurrentsensitivity=\frac{{\displaystyle \frac{1}{I_A}}}{{\displaystyle \frac{1}{I_B}}} \\ =\frac{{\displaystyle \frac{1}{200ABk\theta }}}{{\displaystyle \frac{1}{100ABk\theta }}} \\ =\frac{100ABk\theta }{200ABk\theta } \\ =\frac{1}{2} \end{gathered}$$

Hence, the current sensitivity of B is 2 times that of A.

Thus, option A is correct.