Two closely situated coils have self-inductances of $3 \mathrm{mH}$ and $12 \mathrm{mH}$ respectivel

Question

Two closely situated coils have self-inductances of $3 \mathrm{mH}$ and $12 \mathrm{mH}$ respectively. If the coefficient of coupling between them is $0.5$, the mutual inductance between these coils is

Professor PC Thomas Classes · Answer

(c) : The mutual inductance $M$ between two coupled coils is given by the formula $M = K \sqrt{L_1 L_2}$, where $K$ is the coefficient of coupling and $L_1, L_2$ are the self-inductances of the two coils. Given $K = 0.5$, $L_1 = 3 \mathrm{mH}$, and $L_2 = 12 \mathrm{mH}$, we have $M = 0.5 	imes \sqrt{3 	imes 12} = 0.5 	imes \sqrt{36} = 0.5 	imes 6 = 3 \mathrm{mH}$.