__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 = V_{1} + V_{2} 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__

According to the rules of parallel connection applies:

I = I_{1} + I_{2} Eq. (3)

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

__dI__ = __dI___{1} + __dI___{2} 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 L_{1} L_{2}

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