CPHY 122
Class Notes 17
Instructor: H. L. Neal
1 Impedance in AC Circuits
The impedance is deโฆned as
Z=Vma x
Ima x
2 Power in AC Circuits
The instantaneous power is
P(t) = Vs(t)I(t)
=Vma x Ima x sin (!t) sin (!t ๎๎):
The important quantity is the average power
Pav (t) = 1
TZT
0
P(t)dt;
where the period of one cycle is
T=2๎
!:
We may write
Pav (t) = Vm ax Im ax
!
2๎Z2๎
!
0
sin (!t) sin (!t ๎๎)dt
=Vma x Ima x
!
2๎Z2๎
!
0
sin (!t) [sin (!t) cos ๎๎cos (!t) sin ๎]dt:
We have
!
2๎Z2๎
!
0
sin2(!t)dt =1
2;
!
2๎Z2๎
!
0
sin (!t) cos (!t)dt = 0;
so that
Pav (t) = Im ax Vm ax cos ๎:
2.1 Series RLC Circuit
From the previous Class Notes
๎=tan๎1 !L ๎(!C )๎1
R!:
1
