Question

Two identical solenoid coils, each of self inductance $L$ are connected in series. Their, turns are in the same sense and the distance between them is such that the coefficient of coupling is half. Then, the equivalent inductance of the combination is

• A. $L$
• B. $2L$
• C. $3L$
• D. $\frac{L}{2}$

Answer 1

The correct option is C $3L$

Given,

Coefficient of coupling, $k=\frac{1}{2}$

As the turns are in the same sense, the mutual flux adds to the individual flux.

So, the equivalent inductance will be,

$L_{eq}=L_1+L_2+2M$

$=L+L+2M$

Here, $M=k\sqrt{L_1{L}_2}$

$=\frac{1}{2}\sqrt{L\times L}=\frac{1}{2}L$

$\therefore L_{eq}=2L+2\times \frac{1}{2}L=3L$

Hence, option $\left(C\right)$ is correct