First slide

Inductance

Question

Two pure inductor coils of self inductance L each are connected in series, the net inductance is

Easy

A

L
B

2L
C

L/2
D

L/4

Solution

When two coils are connected in series, the sane current i is induced in both the coils and total magnetic flux linked with them will be equal to the sum of the flux linked with them individually, i.e.,
$Φ = L_{1} i + L_{2} i . . . . . . . (1)$
If equivalent inductance be L' then
$\begin{array}{l} Φ = L^{'} i \\ Hence L^{'} i = L_{1}^{i} + L_{2}^{i} \\ or L^{'} = L_{1} + L_{2} \\ Here L_{1} = L_{2} = L \\ ∴ L^{'} = L + L = 2 L \end{array}$

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