 The response of a network has two parts: the forced response and the natural response.
 In most circuits, the natural response decays rapidly to zero.
 The forced response for sinusoidal sources persists indefinitely and, therefore, is called
the steadystate response
Sinusoidal Currents and Voltages
 Given by:
v(t) = V
m
cos(
ϖ
t +
θ
)

V
m
: the peak value of the voltage

ϖ
: the angular frequency (radians per second)

θ
: phase angle

ϖ
T = 2
π

T
: period (time it takes for one cycle to be completed)
 Frequency (number of cycles completed in one second):
f = 1/T
Units: hertz (Hz) or inverse seconds (s
1
)
 sin(z) = cos(z  90
°
)
 Rootmeansquare (rms) value of the periodic voltage
v(t)
is defined by:

V
rms
= sqrt(1/T (intr 0 => T) v
2
(t)dt)
 P
avg
= V
2
rms
/R

The rms value is also called the
effective value

I
rms
= sqrt(1/T (intr 0 => T) i
2
(t)dt)
 P
avg
= I
2
rms
R
 V
rms
= V
m
/ sqrt(2)
Phasors
 Phasors: vectors that represent currents and voltages in the complexnumber plane
 For a sinusoidal voltage of the form:
v
1
(t) = V
1
cos(
ϖ
t +
θ
1
)
 we define the phasor as
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 Spring '08
 BEST
 Alternating Current, Reactive Power, AC power

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