CURRENT
I = V / Z
rms
rms
RESONANT FREQUENCY
f = 1
2π (LC)
0
1/2
Forward
Bias
Connecting
battery
across
p

n
junction
Reverse
Bias
INDUCTORS
There is also no energy lost in an inductor.
Energy is alternately stored in the magnetic field and then given back to the circuit.
Energy associated with the magnetic field.
CAPACITORS
No energy is lost because the capacitor alternately stores charge and then gives it back again.
In this case, energy is stored in the electric field between the capacitor plates.
Energy associated with an electric field
Electrons (current) flow steadily in one direction.
Capacitors and Capacitive Reactance
Chapter 23: Alternating Current Circuits
By Hiba, Muhammad and Anusha
RMS  Root Mean Square
SEMICONDUCTOR
DEVICES
> Material that has conductivity between that of an insulator and a metal.
Semiconductor
Brief Overview
ELECTRICITY
Application:
Audio System
AC Voltage
>
DC Voltage
Amplifies
AC Voltage
Definition: Electrons moving along a conductor, like a wire, that have been harnessed for energy
ptype
and
ntype
semiconductors
Semiconductor
Example : Batteries, Solar cells and
Fuel cells
Example : Power plant
Electrons keep switching direction.
Alternating Current
Direct Current
ntype
Semiconductor
Material Example: Silicon doped with Phosphorus
Contributes mobile electrons 
negative charge
Creates immobile phosphorus atom  positive charge
RESULT!
ptype
Semiconductor
Material Example: Silicon doped with Boron
Contributes positive holes 
positive charge
Creates immobile boron atoms  negative charge
RESULT!
Doping
 Process of adding foreign atoms to a material to its change conductive properties
Semiconductor Diode
Formation of the
p

n
junction diode:
Averaging Method.
Square the voltage to make everything positive, find the average, take the square root.
Voltages
and
Currents
for
AC circuits
are expressed as
rms values
.
For a sine wave, the relationship between the peak and the rms average is:
rms value = 0.707 peak value
Where does the energy go?
RESISTORS
Power is simply dissipated as heat.
Electrical Energy In AC Circuit
RCL
CIRCUITS
IMPEDANCE
The total opposition to the flow of charge.
The ratio of voltage to current.
Resistance
Capacitive Reactance
X
c
Inductive Reactance
X
L
FORMULAS
IMPEDANCE OF THE CIRCUIT Z
Z = (R + (X  X ) )
2
2
1/2
PHASE ANGLE
tan x = ( (X  X ) / R)
L
C
Rectifier Circuits
L
C
Transistors
POWER
P = I V cos x
rms
rms
Application:
Solar Cells
Alternating Current Circuits:
Capacitors and Capacitive reactance
TWO CONDUCTING PLATES SEPARATED BY AN INSULATOR
INNER WORKINGS OF A CAPACITOR
ALTERNATING
CURRENT
French High speed trains operating from Alternating current electricity
CAPACITIVE REACTANCE
Formula for Average Voltage across a capacitor : V = I R
rms
rms
For Capacitive Reactance the R is replaced by Xc :
V = I X
rms
rms
Capacitive reactance is like resistance measured in OHMS
Determines how much Current exists in a Capacitor if given the average voltage across the capacitor.
EXAMPLE 1
Found experimentally through the equation :
The Capacitive reactance Xc
is inversely proportional to the
frequency f according to the equation.
The capacitance of the capacitor is 1.50 µF and the rms voltage of the generator is 25.0V. What is the rms current in the circuit when the frequency of the generator is
a) 1.00 x 10^2 Hz
b) 1.00 x 10^3 Hz
Capacitive reactance is inversely portional to the frequency
Therefore:
Givens:
C = 1.50 µF
V = 25.0 V
f = 1.00 x 10^2 Hz
f = 1.00 x 10^3 Hz
C = ?
1
2
>
Pure
Silicon not good conductors
Electrons
form bonds only to
hold crystal shape together
Phosphorus
> Only
4
out of
5
outershell
electrons
fit in structure
Boron
> Missing forth
electron
creates
"hole"
in structure
Combination of
p
type and
n
type
semiconductor
Mobile
electrons
from
n
type semiconductor combine with
positive
holes from
p
type semiconductor
Leaves behind
positive
ions on
n
type side
Leaves behind
negative
ions on
p
type side
RESULT!
Negative
Terminal attached to
n
material
Positive
Terminal attached to
p
material
Negative
Terminal attached to
p
material
Positive
Terminal attached to
n
material
Concen
tration
difference:
Repels carriers toward junction
Recombination
Current flows
RESULT!
RESULT!
Attracts carriers away from junction.
Depletion region increases.
No current flows.
Only
positive
cycle present 
Forward
Bias > Current
RESULT!
Current flow in
one direction
!
Bipolar junction transistor Consists of two
p

n
junctions
FOR AC CIRCUITS
p

n
type junctions create
positive
and
negative
terminals
ALTERNATIVE APPROACH:
Keep in mind limiting behavior of inductors and capacitors at the extreme limits of frequency.
Zero Frequency.
Very Large Frequency.
RESONANCE
In a series RCL circuit characterized by
minimum impedance
and
zero phase.
FORMULAS
EFFECT OF RESISTANCE
RESONANT FREQUENCY FOR AN AC CIRCUIT
Electric field
Potential difference
Depletion Layer
OSCILLATOR
CIRCUITS
WHAT IS RESONANCE?
It occurs when the
frequency
of a
vibrating force
exactly
matches
a
natural (resonant)
frequency of the object
to which the force is applied.
STRING
SPRING
TUNING FORK
TUBE
The effect on electrical resonance is to make the sharpness of the circuit less pronounced.
Oscillation of energy between a capacitor and an inductor.
Once a capacitor/inductor is energized the energy will oscillate indefinitely.
As long as there is some provision to dissipate any losses that occur because of resistance.
HETRODYNE METAL DETECTOR
*Note!
Adding capacitor
keeps voltage from
dropping to zero!
KIRCHOFF'S
LOOP RULES
I
=
I

I
I
Treat phasors as vectors.
I
=
I

I
Sunlight > Ionization > Ejection of electron
C
V = I R
Instantaneous Current and Voltage withResistance
Phasor Diagram of a Resistor
rms
rms
Instantaneous Current and Voltage in a Capacitor
Phasor Diagram of Capacitor
Current
Leads voltage
I sin (2pift + pi/2) = I cos (2pift)πππ
o
o
Power being the product of current and voltage, it alternates between positive and negative values for equal periods of time
Power = 0 on average therefore, a capacitor uses no energy in an AC circuit
Current fluctuates between these values
Inductors and Inductive Reactance
Inductors
Faraday's Law used to show Average voltage across a inductor:
Inductane :
L
Frequency Vs. Inductance
Instantaneous Inductive Reactance
A coil or wire
Faraday's Law of electromagnetic induction states....
An inductor develops a voltage that opposes a change in the current.
L
V = I X
rms
rms
Inductive Reactance : X
Measured in Ohms
Determines average current existing in an inductor
Found experimentally
L
X = 2pifL
L
X is directly proportional to frequency and the inductance
L
Phasor Diagram
An Inductor in an AC circuit
A Circuit contains a 3.60mH inductor. The rms voltage of the generator is 25.0 V. Find the rms current in the circuit when the generator frequency is
a) 1.00 x 10^2 Hz
b) 5.00 x 10^3 Hz
Givens:
L = 3.60 x 10 ^ 3
f = 1.00 x 10^2 Hz
f = 5.00 x 10^3 Hz
V = 25.0 V
1
2
Therefore the inductor offers more opposition to the changing current when frequency is larger.
p

n
JUNCTION
Halfwave rectifier
p

n
junction diode: unidirectional
Large change in output voltage
Small changes in input voltage from ac generator
C
E
B
C
E
B
E
> Device used in amplification
RESULT!
The END
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CHAPTER 23
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