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If the length and cross-sectional area of an inductor remain the same but the number of turns is doubled, its self-inductance will become

1. half
2. four times
3. double
4. one-fourth

Correct answer: four times

Solution

Self-inductance of a coil or solenoid is proportional to the square of the number of turns, $L \propto N^2$. If the number of turns is doubled, $L$ becomes $2^2 = 4$ times. Therefore the self-inductance becomes four times.

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