Question

For the three coupled coils shown in figure, KVL equation is ____________

(a) V = (L1 + L2 + L3) \(\frac{di}{dt}\)

(b) V = (L1 – L2 – L3 – M13) \(\frac{di}{dt}\)

(c) V = (L1 + L2 + L3 + 2M12 – 2M23 – 2M13) \(\frac{di}{dt}\)

(d) V = (L1 + L2 + L3 – 2M12 + 2M23 + 2M13) \(\frac{di}{dt}\)

I have been asked this question by my school teacher while I was bunking the class.

This interesting question is from Advanced Problems Involving Complex Circuit Diagram in section Network Theory and Complex Circuit Diagram of Network Theory

Answer 1

The correct option is (c) V = (L1 + L2 + L3 + 2M12 – 2M23 – 2M13) \(\frac{di}{dt}\)

To explain: M12 is positive while M23 and M13 are negative because of dots shown in figure.

So, the KVL equation is given by,

V = (L1 + L2 + L3 + 2M12 – 2M23 – 2M13) \(\frac{di}{dt}\).