Question

Mutual inductance between two closely coupled coils is 2 H. Now, if the number of turns in one coil is reduced by 50 percent and those of the other coil is doubled then, new value of mutual inductance is:
1. 2 H
2. 8 H
3. 1 H
4. 4 H

Answer 1

Correct Answer - Option 1 : 2 H

Concept:

The inductance of a coil is given by,

\(L=\frac{{{\mu }_{0}}{{\mu }_{r}}{{N}^{2}}A}{l}\)

μ0 is magnetic permeability of free space

μr is relative permeability

N is number if turns

A is cross-sectional area

l is length

Calculation:

\(\begin{array}{l} M = K\sqrt {{L_1}{L_2}} \\ L \propto {N^2}\\ \Rightarrow M \propto \sqrt {N_1^2N_2^2} = {N_1}{N_2} \end{array}\)

Given that M = 2 H

If the turns of one coil are decreased to half and the other is doubled.

Now the new value of the mutual inductance would be 2 H.