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MCQEasyJEE 2023Electric Current & Drift Velocity

JEE Physics 2023 Question with Solution

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.

  • A

    Both Statement I and Statement II are true

  • B

    Both Statement I and Statement II are false

  • C

    Statement I is true but Statement II is false

  • D

    Statement I is false but Statement II is true

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Two statements about current sensitivity and voltage sensitivity of a moving coil galvanometer.

Find: Which statement is true.

For a moving coil galvanometer, the current sensitivity is

SI=NABkS_I = \frac{NAB}{k}

where NN is the number of turns, AA is the area of the coil, BB is the magnetic field, and kk is the torsional constant.

If the number of turns NN is doubled, then

SI∝NS_I \propto N

So the current sensitivity also becomes double. Therefore, Statement I is true.

The voltage sensitivity is

SV=NABkR=SIRS_V = \frac{NAB}{kR} = \frac{S_I}{R}

where RR is the resistance of the galvanometer coil.

If only the number of turns is increased, the length of the wire in the coil also increases, so the resistance RR increases in the same ratio. Hence both SIS_I and RR increase proportionally, and

SV=SIRS_V = \frac{S_I}{R}

does not increase in the same ratio.

Therefore, Statement II is false.

So, Statement I is true but Statement II is false. The correct option is C.

The solution labels the correct option as D, but its own working and conclusion clearly match Statement I is true but Statement II is false, which corresponds to option C in the given options.

Common mistakes

  • Assuming that voltage sensitivity must increase whenever current sensitivity increases. This is wrong because voltage sensitivity depends on both SIS_I and coil resistance RR. Use SV=SIRS_V = \frac{S_I}{R} and check how RR changes when the number of turns increases.

  • Ignoring the increase in resistance when the number of turns is doubled. This is wrong because adding turns increases the wire length and hence the resistance. Account for the simultaneous change in RR before concluding about voltage sensitivity.

  • Reading the option label from the solution without matching it to the actual statement text. This is wrong because the page marks D, but the written conclusion says Statement I is true and Statement II is false. Always verify the final statement against the listed options.

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