Two indentical coils, each of inductance `L`, are interconnected (a) in series, (b) in parallel. Assuminng the mutual insducane of the coils to be negliglible, find the inductance fo the system in both cases.

Explanation

(a) In series, the current `I` flows through both coils, and the total `e.m.f` induced. When the current changes is,
`-2L (d I)/(dl) = -L (dI)/(dt)`
or,
(b) In parallel, the current flowing though either coil is, `(I)/(2)` and the `e.m.f` induced is
`-L((1)/(2) (dI)/(dt))`
Equating this to `-Ll (dI)/(dt)`, we find `L' = (1)/(2) L`.