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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

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B

A is 2.5 times of B

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C

A is 5 times of B

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D

B is 5 times of A

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Solution

The correct option is A

B is double as that of A


Step 1: Given

Number of turns of A: nA=200

Number of turns of B: nB=100

Resistance of A: RA=100

Resistance of A: RB=40

Step 2: Formula Used:

I=nABkθ

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 θ 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

IA=nAABkθ=200ABkθ

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

IB=nBABkθ=100ABkθ

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.

Ratioofcurrentsensitivity=1IA1IB=1200ABkθ1100ABkθ=100ABkθ200ABkθ=12

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

Thus, option A is correct.


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