Question

For the circuit given below, the inductance measured across the terminals 1 and 2 was 15 H with open terminals 3 and 4. It was 30 H when terminals 3 and 4 were short-circuited. Both the inductors are having inductances 2H. The coefficient of coupling is ______________

(a) 1

(b) 0.707

(c) 0.5

(d) Inderminate due to insufficient data

This question was addressed to me by my school principal while I was bunking the class.

My doubt is from Advanced Problems on Magnetically Coupled Circuits in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct answer is (d) Inderminate due to insufficient data

To elaborate: When 2 coils are connected in series, then effective inductance,

LEFF = L1 + L2 ± 2M

For this case, LEFF = L1 + L2 – 2M

However, L1 + L2 + 2M or L1 + L2 – 2M cannot be determined.

Hence, data is insufficient to calculate the value of coupling coefficient (k).