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. $M=L_1{L}_2$
• C. $M=\sqrt{L_1{L}_2}$
• D. $M=(L_1{L}_2{)}^2$

Answer 1

The correct option is C $M=\sqrt{L_1{L}_2}$

We know that, $M=-\frac{e_2}{d{i}_1/dt}=-\frac{e_1}{d{i}_2/dt}$
Also, $e_1=-L_1\frac{d{i}_1}{dt}$ and $e_2=-L_2\frac{d{i}_2}{dt}$
$\Rightarrow M^2=\frac{e_1{e}_2}{\left(\frac{d{i}_1}{dt}\right)\left(\frac{d{i}_2}{dt}\right)}=L_1{L}_2$
$\Rightarrow M=\sqrt{L_1{L}_2}$