Question

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are $380\mu H$ and $240\mu H$. Their mutual inductance in $\mu H$ is

• A. 35

Answer 1

The correct option is A 35
Two possible series connection are shown below:

Let the mutual inductance be $M$

(i) Additive connection,

$L_{eqv}=L_1+L_2+2M=380\mu H$

(ii) Subtractive connection,

$L_{eqv}=L_1+L_2-2M=240\mu H$

$Thus,L_1+L_2+2M=380\mu H$ ... (i)

$and{L}_1+L_2-2M=240\mu H$ ....(ii)

Solving equations (i) and (ii), we get:

$4M=140\mu HorM=35\mu H$

$\therefore Mutualinductance,$

$M=35\mu H$