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: