First slide

Inductance

Question

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

Moderate

A

$M = L_{1} L_{2}$
B

$M = L_{1} / L_{2}$
C

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

$M = {(L_{1} L_{2})}^{2}$

Solution

$\begin{array}{l} M = - \frac{e_{2}}{{di}_{1} / dt} = - \frac{e_{1}}{{di}_{2} / dt} \\ Also e_{1} = - L_{1} \frac{{di}_{1}}{dt} . e_{2} = - L_{2} \frac{{di}_{2}}{dt} \\ M^{2} = \frac{e_{1} e_{2}}{(\frac{{di}_{1}}{dt}) (\frac{{di}_{2}}{dt})} = L_{1} L_{2} \Rightarrow M = \sqrt{L_{1} L_{2}} \end{array}$

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