Question

Given below are two statement :  
Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.  
Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio.
In the light of the above statement, choose the correct answer from the options given below : 

• A. Statement I is false but Statement II is true
• B. Both Statement I and Statement II are true
• C. Both Statement I and Statement II are false
• D. Statement I is true but Statement II is false

Answer 1

The Correct Option is D

To determine the correct answer, we will evaluate each statement individually and justify why one is true and the other is false.

Statement I: If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.

The current sensitivity of a moving coil galvanometer is given by the formula:

S_I = \frac{nBAG}{k}

where:

• n = number of turns
• B = magnetic field strength
• A = area of the coil
• G = torque constant
• k = spring constant

From the formula, we can see that the current sensitivity S_I is directly proportional to the number of turns n. Therefore, if n is doubled, S_I also doubles. Thus, Statement I is true.

Statement II: Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio.

The voltage sensitivity of a moving coil galvanometer is given by:

S_V = \frac{S_I}{R}

where:

• S_V = voltage sensitivity
• S_I = current sensitivity
• R = resistance of the coil

Even if S_I doubles (due to doubling the number of turns), the resistance R of the coil will also generally increase because resistance is also directly proportional to the number of turns. This increase in resistance could offset the increase in current sensitivity, leading to the conclusion that voltage sensitivity does not necessarily double. Hence, Statement II is false.

Therefore, in light of the explanations above, the correct answer is that Statement I is true but Statement II is false.