Question

Two inductor coils with inductance 10
mH and 20 mH are connected in series.
What is the resultant inductance of the
combination of the two coils?
(A) 20 mH (B) 30 mH
20
(C) 10 mH (D) - mH
3​

Answer 1

Net L = L1+L2 = 10+20 = 30mH

Answer 2

Given:

Two inductor coils with inductance 10

mH and 20 mH are connected in series.

To find:

Resultant inductance of the combination of the coils ?

Calculation:

For the inductors in series combination , the net voltage will be equal to the sum of the individual voltage drops along each inductor.

But the rate of change of current with time will be same for the inductors (i.e. di/dt will be same).

$\therefore \: V_{net} = V_{1} + V_{2}$

$\implies \: L_{net} \bigg(\dfrac{di}{dt} \bigg) = L_{1} \bigg( \dfrac{di}{dt} \bigg) + L_{2} \bigg( \dfrac{di}{dt} \bigg)$

$\implies \: L_{net} = L_{1} + L_{2}$

Putting the required values :

$\implies \: L_{net} = 10+ 20$

$\implies \: L_{net} =30 \: mH$

So, resultant induction is 30 mH. Here the mutual induction (M) factor has been ignored.