Question

Two coils having self inductances 60 mH each, are coupled with each other. If the coefficient of coupling is 0.75, calculate the mutual inductance between them.

Hint:

The coefficient of coupling (\(k\)) tells you how much of the magnetic flux from one coil links with the other. \(k=1\) means perfect coupling, \(k=0\) means no coupling. The mutual inductance is just this fraction of the geometric mean of the self-inductances.

Answer 1

The mutual inductance (\(M\)) between two coils is related to their self-inductances (\(L_1\) and \(L_2\)) and the coefficient of coupling (\(k\)) by the formula: \[ M = k \sqrt{L_1 L_2} \] Given:
Self-inductance of the first coil, \(L_1 = 60 \, mH = 60 \times 10^{-3} \, H\)
Self-inductance of the second coil, \(L_2 = 60 \, mH = 60 \times 10^{-3} \, H\)
Coefficient of coupling, \(k = 0.75\)
Substitute the values into the formula: \[ M = 0.75 \times \sqrt{(60 \times 10^{-3}) \times (60 \times 10^{-3})} \] \[ M = 0.75 \times \sqrt{(60 \times 10^{-3})^2} \] \[ M = 0.75 \times (60 \times 10^{-3}) \] \[ M = 45 \times 10^{-3} \, H \] \[ M = 45 \, mH \] The mutual inductance between the coils is 45 mH.