JEE Main 2023 · 10 April · morning · Single correct · +4 / −1
Given below are two statements:
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 statements, choose the correct answer from the options given below :
- (a) Statement I is true but Statement II is false
- (b) Statement I is false but Statement II is true
- (c) Both Statement I and Statement II are false
- (d) Both Statement I and Statement II are true
Answer and solution
Answer (a) Statement I is true but Statement II is false
Solution
Physics sir · 4 steps
More turns give more torque per ampere, but also more wire and resistance. That sinks Statement II.
- Current sensitivity. At equilibrium the magnetic torque balances the spring torque, NIAB = kθ. So the deflection per unit current is θ/I = NAB/k, which is directly proportional to N.
- Statement I. Doubling N with A, B and k unchanged doubles θ/I. Statement I is true.
θ/V = θ/IR = NAB/kR
- Voltage sensitivity. Doubling the turns doubles the length of wire in the coil, so its resistance R also doubles. The factor of 2 in the numerator cancels the factor of 2 in R, and θ/V stays the same.
- So. Statement I is true and Statement II is false, which is option (a).
The idea to keep. Current sensitivity is NAB/k. Voltage sensitivity is NAB/(kR), and R grows with N. Changing only the number of turns changes current sensitivity but leaves voltage sensitivity the same.
Answer from the NTA final answer key. Solution by PrepWiser.