Question

An air cored coil has a self-inductance of 10 mH. If the number of the coil is double, keeping the length and area of cross section of the coil same, the self-inductance will be _______.
1. 20 mH
2. 10 mH
3. 40 mH
4. 5 mH

Answer 1

Correct Answer - Option 3 : 40 mH

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.
  • The self-inductance of a solenoid is given by:

\(L = \frac{{{μ _o}{N^2}A}}{l}\)

Where N = number of turns, A = area of cross-section, l = length of the solenoid and μ0 = absolute permeability 

CALCULATION:

Given:

L₁ = 10 mH

N₂ = 2N₁

Rest all parameters are same,

Now as,

L ∝ N²

\(\frac{L_1=N_1^2}{L_2=4N_1^2}\)

L₂ = 4L₁

L₂ = 4 × 10 = 40 mH