Question

If N is the number of turns in a coil, the value of self inductance varies as
1. N⁰
2. N
3. N²
4. N^-2

Answer 1

Correct Answer - Option 3 : N²

Concept:

Self-Induction

• Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.
• As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
• This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.
• Self-inductance of a solenoid is given by –

\(L=\frac{{{\mu }_{o}}{{N}^{2}}A}{l}\)

Where μo = Absolute permeability, N = Number of turns, l = length of the solenoid and A = Area of the solenoid.

Explanation:

We know self-inductance,

\(L=\frac{{{\mu }_{o}}{{N}^{2}}A}{l}\)

⇒ L ∝ N²

Hence the correct answer is N²