Two coils of self inductances \( L_1 \) and \( L_2 \) are kept close to each other so that the effective flux in one is completely linked with the other. What is the mutual inductance M between them?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( (L_1 L_2)^{1/2} \)
The mutual inductance of two coils is related to their self inductances by
\( \displaystyle M = k\sqrt{L_1 L_2} \)
where \( k \) is the coefficient of coupling (\( 0 \le k \le 1 \)). When the flux of one coil is completely linked with the other, there is no flux leakage and \( k = 1 \).
\( \displaystyle M = \sqrt{L_1 L_2} = (L_1 L_2)^{1/2} \)
Shortcut: Dimensions: M, \( L_1 \) and \( L_2 \) are all inductances in henry. Only \( (L_1 L_2)^{1/2} \) has the unit henry; the other options have units \( \mathrm{H^2} \), no unit and \( \mathrm{H^4} \).