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

Statement I:

The current sensitivity (\( S_I \)) of a moving coil galvanometer is defined as the deflection per unit current and is given by:

\( S_I = \frac{NAB}{k} \)

Where:

• \( N \): Number of turns
• \( A \): Area of the coil
• \( B \): Magnetic field strength
• \( k \): Torsional constant of the suspension

If the number of turns \( N \) is doubled, \( S_I \) also doubles. Thus, Statement I is true.

Statement II:

The voltage sensitivity (\( S_V \)) of a moving coil galvanometer is defined as the deflection per unit voltage and is given by:

\( S_V = \frac{NAB}{kR} = \frac{S_I}{R} \)

Where:

• \( R \): Resistance of the galvanometer coil

When the number of turns \( N \) is increased:

• \( S_I \) increases proportionally to \( N \).
• However, the resistance \( R \) of the coil also increases because the length of the wire doubles, and resistance is directly proportional to the length of the wire.

As both the numerator (\( S_I \)) and denominator (\( R \)) double, \( S_V \) remains unchanged. Thus, Statement II is false.

Conclusion:

Statement I is true, and Statement II is false.