Two coils of self inductance L1 and L2 are placed closer to each other so that total flux in one coil is completely linked with other. If M is mutual inductance between them, then

(1) M = L1 L2

(2) M = L1/L2

(3) $M=\sqrt{{L}_{1}{L}_{2}}$

(4) M = (L1 L2)2

Concept Videos :-

#14 | Mutual Induction
#15 | Reciprocity Theorm & Mutual Induction

Concept Questions :-

Mutual-inductance

(3) $M=-\frac{{e}_{2}}{d{i}_{1}/dt}=-\frac{{e}_{1}}{d{i}_{2}/dt}$

Also ${e}_{1}=-{L}_{1}\frac{d{i}_{1}}{dt}.{e}_{2}=-{L}_{2}\frac{d{i}_{2}}{dt}$

${M}^{2}=\frac{{e}_{1}{e}_{2}}{\left(\frac{d{i}_{1}}{dt}\right)\text{\hspace{0.17em}}\left(\frac{d{i}_{2}}{dt}\right)}={L}_{1}{L}_{2}⇒M=\sqrt{{L}_{1}{L}_{2}}$

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