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Question 15

Two coils of self inductance $$L_1$$ and $$L_2$$ are connected in series combination having mutual inductance of the coils as $$M$$. The equivalent self inductance of the combination will be

Solution

Given:
$$Two\ inductors\ of\ self\ induc\tan ce\ L_1\ and\ L_2\ connected\ in\ series\ with\ mutual\ induc\tan ce\ M.$$

Concept:
For series combination of coupled inductors:

$$If\ currents\ are\ in\ same\ direction\ (aiding):\ L=L1+L2+2M$$
$$If\ currents\ are\ in\ opposite\ direction\ (oppo\sin g):L=L_1+L_2−2M$$

Here:
Currents are in opposite direction ⇒ opposing case

Result:

$$Leq=L_1+L_2−2M$$

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