Question

When two coupled coils of equal self-inductance are connected in series in one way the net inductance is 20 mH and when they are connected in the other way, the net inductance is 12 mH. The maximum value of net inductance when they are connected in parallel is __________

(a) 2 mH

(b) 5 mH

(c) 4 mH

(d) 6 mH

I got this question by my college director while I was bunking the class.

I would like to ask this question from Advanced Problems on Magnetically Coupled Circuits in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct option is (b) 5 mH

To explain: LEFF = L1 + L2 ± 2M (when the two coils are connected in series)

Now, L1 = L2 = L

∴ LEFF = 2L ± 2M

Or, 2L + 2M = 20

Or, 2L – 2M = 12

∴ L = 8, M = 2

Now, to get maximum value in parallel connection,

LMAX = \(\frac{(L+M)(L+M)}{2L+2M}\)

= \(\frac{(8+2)(8+2)}{(16+4)}\)

= \(\frac{100}{20}\) = 5 mH.