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 is mutual inductance between them, then

• A. $M=L_1{L}_2$
• B. $M=\frac{L_1}{L_2}$
• C. $M=\sqrt{L_1}{L}_2$
• D. $M=(L_1{L}_2{)}^2$

Answer 1

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

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