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

Answer 1

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

Mutual inductance between two coils,

$M=-\frac{E_2}{\left(\frac{d{i}_1}{dt}\right)}=-\frac{E_1}{\left(\frac{d{i}_2}{dt}\right)}$

Also , $E_1=-L_1\frac{d{i}_1}{dt}$ and $E_2=-L_2\frac{d{i}_2}{dt}$

$\therefore M^2=\frac{E_1{E}_2}{\left(\frac{d{i}_1}{dt}\right)\left(\frac{d{i}_2}{dt}\right)}=L_1{L}_2$

$\Rightarrow M=\sqrt{L_1{L}_2}$

Hence, $\left(C\right)$ is the correct answer.