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The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be

Question

The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be

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Solution

The self-inductance (L) of a coil is directly proportional to the square of the number of turns (N) in the coil. This relationship can be expressed as L ∝ N².

If the number of turns in the coil is increased to four times, the new number of turns will be 4N.

Substituting this into the relationship, the new self-inductance (L') will be L' ∝ (4N)² = 16N².

Since L ∝ N², we can say that L = kN², where k is a constant of proportionality.

Therefore, L' = 16kN² = 16L.

So, if the number of turns in the coil is increased to four times, the self-inductance of the coil will increase to sixteen times.

This problem has been solved

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