Chapter 9
Alternating Current
Advantages of using alternating current
a. Possible to step up and step down voltage. Primary use is in
the transmission of electrical power supply
b. Alternating current is readily adaptable to rotating machinery
such as generator and motors
c. Device such as heaters, lamps, filament foes not depend on
the type of current use
d. Normally, the current that were generated from power station
are in the AC form
e. The AC signal is use in the Electromagnetic wave
transmission.
Comparing AC with DC
Filament lamp worked equally well either with ac or dc
Power (P) = VI = I2R
1
The potential difference across a resistor is proportional to the
current through it.
V= IR
Mean Power (Area under the I-V Curve)
Mean Power = ½ Io2 R
The mean power is define as the average value of power one
complete cycle.
The Root mean Square.
The effective value of an alternating current or potential difference
is the value of direct current or potential difference which should
supply the same power in a given resistors.
Prove:
Let the rms current (effective current)
(I rms)2R = ½ Io2R
1
I rms =
2
1
Vrms =
2
2
Io
Vo
Phasor
A phasor is a rotating vector. It length represent the peak value Vo
(amplitude) and it rotates about one steady end.

Vo
Device Analysis
Resistive Load
3
VR = VOR sin t
V
R=
i
iR =
VR VOR

sin  t
R
R
iR = IOR sin ( t -  )
 = 0o (no phase shift)
VR = IR (R)
A Capacitive Load
4
VC = VOC sin  t
VC = voltage amplitude across capacitor
Q= CV
qc=CVc= C Voc sin  t
ic =
dq
dt
=  C Voc cos  t
ic =  C V c
i=
V
R
I=
V
Xc
1
Xc =
C
From trigonometry solution
cos  t = sin ( t + 90o)
ic = (
Voc
Xc
) sin ( t + 90o)
ic = Ic sin ( t + 90o)
 = -90o
Vc = Ic Xc
An Inductive Resistance
5
VL = VOL sin  t
VL = L
di
dt
=
VL
L
iL = -
VO L
L
=
iL =  diL =
di
dt
VO L
L
sin  t
 sin wt dt
 VOL 

 cos
 wL 
I=
V
R
=
V
XL
XL =  L
6
t
Summary
CIRCUIT
SYMBOL RESISTIVE PHASE
ELEMENT
OR
OF
PHASE AMPLITUDE
ANGLE RELATION
REACTIVE CURRENT
RESITOR
R
R
In phase
0o
VR=IRR
with VR
CAPACITOR
INDUCTOR
C
XC=
L
Lead VC by -90o
1
C
90o
Lags VL by 90o
XL = L
90o
RLC Circuit
Vmax =
VR  V y =
2
2
Tan  =
VR  (VL  VC ) 2
2
VL max  VC max
VR max
Let make substitution
V=IR
VL = I XL
VC = I XC
V max =
IR2  IX L  IX C 2
V max = I max
R2   X L  X C 2
7
VC= ICXC
VL=ILXL
Vmax

I max
R2   X L  X C 2
= Z (Impedance)
Resonance
Vm
I=
Resonance Frequency =
R 2  (L 
1
2 LC
8
1 2
)
c
Application
a. Tuning Circuit (Radio)
b. Filtering circuit
c. Audio application
d. Entertainment circuit
The Nature of Electromagnetic Waves
James Clerk Maxwell predicted:
 Electric field lines originate on positive charges and terminate on
negative charges
 Magnetic field lines always form closed loops – they do not begin or
end anywhere
 A varying magnetic field induces an emf and hence an electric field
(Faraday’s Law)
 Magnetic fields are generated by moving charges or currents
(Ampère’s Law)
9
The Spectrum of Electromagnetic Waves
Maxwell Equation
 Electromagnetic waves are transverse waves
 Electromagnetic waves travel at the speed of light
10
 Because EM waves travel at a speed that is precisely the speed
of light, light is an electromagnetic wave
Properties of Electromagnetic Waves.
 A changing magnetic field produces an electric field
 A changing electric field produces a magnetic field
 These fields are in phase
 At any point, both fields reach their maximum value at the
same time
11
 The ratio of the electric field to the magnetic field is equal to the
speed of light
 Electromagnetic waves carry energy as they travel through space, and
this energy can be transferred to objects placed in their path
12