Question

Two coils of self inductance $L_{1}$ and $L_{2}$ 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

• A. $M = L_{1}L_{2}$
• B. $M = L_{1}/L_{2}$
• C. $M = \sqrt{L_{1}L_{2}}$
• D. $M = (L_{1}L_{2})^{2}$

Answer 1

Answer: (C)

$M = \sqrt{L_{1}L_{2}}$

Answer 2

$M = - \frac{e_{2}}{di_{1}/dt} = - \frac{e_{1}}{di_{2}/dt}$

Also $e_{1} = - L_{1}\frac{di_{1}}{dt}.e_{2} = - L_{2}\frac{di_{2}}{dt}$

$M^{2} = \frac{e_{1}e_{2}}{\left( \frac{di_{1}}{dt} \right)\mspace{6mu}\left( \frac{di_{2}}{dt} \right)} = L_{1}L_{2} \Rightarrow M = \sqrt{L_{1}L_{2}}$