Question

If N is the number of turns in a coil, the value of self inductance varies as

• A. $N^0$
• B. N
• C. $N^2$
• D. $N^{-2}$

Answer 1

The Correct Option is C

The question asks how the self-inductance of a coil is related to the number of turns, \( N \), in the coil. Let's break it down step-by-step.

Concept of Self Inductance:

Self-inductance is a property of a coil or circuit that defines its ability to resist changes in the current flowing through it by inducing an electromotive force (EMF) in itself. This induced EMF is proportional to the rate of change of current.

The formula for the self-inductance \( L \) of a coil is given by:

L = \frac{{\mu N^2 A}}{{l}}

where:

• L is the self-inductance.
• \mu is the permeability of the core material.
• N is the number of turns in the coil.
• A is the cross-sectional area of the coil.
• l is the length of the coil.

From the formula, you can see that the self-inductance \( L \) is directly proportional to the square of the number of turns, \( N^2 \).

Conclusion:

The correct answer is that the self-inductance varies with the square of the number of turns, \(\mathbf{N^2}\).

Why Other Options are Incorrect:

• N^0: This option would mean that the self-inductance is independent of the number of turns, which is incorrect according to the formula.
• N: This would mean self-inductance is directly proportional to the number of turns; however, it's actually proportional to the square of the number of turns.
• N^{-2}: This suggests an inverse proportionality to the square of the number of turns, which is not supported by the formula for self-inductance.

Thus, the value of self-inductance varies as \(\mathbf{N^2}\).