Question

Two different coils of self inductance $ L_1 $ and $ L_2 $ are placed close to each other so that the effective flux in one coil is completely linked with other. If $ M $ is the mutual inductance between them, then

• A. $ M = L_1/L_2 $
• B. $ M = L_1L_2 $
• C. $ M=\sqrt{L_{1}L_{2}} $
• D. $ M=\left(L_{1}\,L_{2}\right)^{2} $

Answer 1

Answer: (C)

We know that, $M=-\frac{e_{2}}{d i_{1} / d t}=-\frac{e_{1}}{d i_{2} / d t}$
Also, $e_{1}=-L_{1} \frac{d i_{1}}{d t}$ and $e_{2}=-L_{2} \frac{d i_{2}}{d t}$
$\Rightarrow M^{2}=\frac{e_{1} e_{2}}{\left(\frac{d i_{1}}{dt}\right)\left(\frac{di_{2}}{d t}\right)}=L_{1} L_{2}$
$\Rightarrow M=\sqrt{L_{1} L_{2}}$