1. The document summarizes key concepts about AC circuits including sinusoidal waveforms, complex numbers, phasor analysis, complex power, and three-phase AC circuits. 2. Phasor analysis allows AC circuits to be studied in the phasor domain using complex numbers where differential equations are replaced by algebraic equations. Circuit elements like resistors, inductors, and capacitors can be represented by their impedances. 3. Complex power in AC circuits includes both active power P and reactive power Q. Active power represents the energy consumption in the circuit while reactive power is a fictitious power.

1. 1
University of Waterloo
Department of Electrical & Computer Engineering
GEN E ME 123: Electrical Engineering for
Mechanical Engineers
AC CIRCUITS
Dr. Claudio Ca~izares
n December 1998
1 Sinusoidal Waveforms
A sinusoidal or alternate current ac circuit is made up of resistances R,
inductors L, capacitors C , and sinusoidal voltage and or current sources. In
steady-state, any voltage or current in the circuit is a sinusoid of the form
v(t)
V
ωt
π 2π
θ
-V
vt = V sin!t +

2. = V cos!t +

3. , 90o
= A sin!t + B cos!t
where
A = V cos

4. AC Circuits 2
B = V sin

5. p
V = A2 + B 2

7. = tan A ,1 B
The frequency f and period T = 1=f of this signal are de ned as:
! = 2 f = 2T
As in any periodic signal, the average av and root-mean-square rms
values may be computed as:
1ZT
Vav = T vt dt
0
= 0
s
Vrms = 1 Z T v2t dt
T 0
V
= p
2
2 Complex Numbers
AC circuits can be studied with the help of complex numbers. A complex
number C in the complex plane can be represented in polar or rectangular
coordinates as: Imaginary
C
b
C
θ
Real
a