Two coils, each one having self - inductance of 10 H, are coupled such that the mutual inductance between them is 4 H. Find the coefficient of the coupling between the coils.

Concept:

Coefficient of Coupling (k):
The coefficient of coupling (k) between two coils is defined as the fraction of magnetic flux produced by the current in one coil that links the other.

Two coils have self-inductance L1 and L2, then mutual inductance M between them then Coefficient of Coupling (k) is given by 

\(k=\frac{M}{\sqrt {L_1L_2}}\)

Where,

\(M=\frac{\mu_o \mu_rN_1N_2A}{ l}\)

\(L_1=\frac{\mu_o \mu_rN_1^2A}{ l}\)

\(L_2=\frac{\mu_o \mu_rN_2^2A}{l}\)

N1 and N2 is the number of turns in coil 1 and coil 2 respectively
A is the cross-section area
l is the length

Calculation:

Given,

L1 = 18 H

L2 = 2 H

M = 3 H

From the above concept,

\(k=\frac{M}{\sqrt {L_1L_2}}\)

\(k=\frac{4}{\sqrt {10\times10}}=\frac{4}{10}=0.4\)