Inductors in Series and Parallel

Inductors in Series

Inductors in Series

We consider two coils connected in series, which are connected to AC voltage.

According to the rules of series connection:

V = V₁  +  V₂    Eq. (1)

We remember: Due to the law of self-induction, the voltage U caused on the coil (due to the change in time that we just have with AC voltage) can be written as follows:

Eq. (2) in Eq. (1) and you get:

Note: The minus sign has been shortened. According to the rules of series connection we have only "one" current. By further shortening it follows:

Inductors in Parallel

Inductors in Parallel

According to the rules of parallel connection applies:

I = I₁ + I₂                Eq. (3)

Since we are considering here the behavior of inductors at AC voltage, we form the differentiation of Eq. (4):

dI = dI₁  +  dI₂        Eq. (5)
dt    dt       dt

from V = - L dI       it follows    dI =  - V    Eq. (6)
.                   dt                         dt        L

Eq. (6) in Eq. (5), the minus sign is shortened. You get:

V  =  V  +  V
L       L₁     L₂

According to the rules of parallel connection, we have only one voltage. Thus follows: