Transcript Alternating Current - Deeteekay Community

ALTERNATING VOLTAGES
AND CURRENT
Chapter 1 - Alternating Current


DIRECT CURRENT (DC) – IS WHEN THE CURRENT
FLOWS IN ONLY ONE DIRECTION. Constant flow of
electric charge
EX: BATTERY

ALTERNATING CURRENT AC) – THE CURRENT
FLOWS IN ONE DIRECTION THEN THE OTHER.

Electrical current whose magnitude and
direction vary cyclically, as opposed to direct
current whose direction remains constant.

EX: OUTLETS
Chapter 1 - Alternating Current
 By
rotating a magnetic field within a
stationary coil
 By rotating a coil in a magnetic field
Chapter 1 - Alternating Current
A
voltage supplied by a battery or other DC
source has a certain polarity and remains
constant.
 Alternating Current (AC) varies in polarity
and amplitude.
 AC is an important part of electrical and
electronic systems.
Chapter 1 - Alternating Current
4
 Faraday’s
Laws of electromagnetic Induction.
Induced electromotive field
Any change in the magnetic environment of a coil of wire
will cause a voltage (emf) to be "induced" in the coil.
e.m.f, e = -N d
dt
N = Number of turn
 = Magnetic Flux
Lenz’s law
An electromagnetic field interacting with a conductor
will generate electrical current that induces a counter
magnetic field that opposes the magnetic field generating
the current.
Chapter 1 - Alternating Current
 Faraday
found that a changing magnetic
field produces a current.
 Such a current is called an induced current.
 Therefore, a changing magnetic field
induces an emf.
Chapter 1 - Alternating Current
6
Induced Current
Faraday suspected that a magnetic field would induce a
current, just like a current produces a magnet field.
He found that a steady current in X produced no current in
Y. Only when the current in X was starting or stopping
(i.e., changing) was a current produced in Y.
Chapter 1 - Alternating Current
7
I. Distance between coil and
LEN’Z LAW
magnet decreases.
Therefore, the magnetic field
(and therefore the flux) through
the coil increases.
III. Current is
induced.
II. To oppose this
upward increase in the
magnetic field (flux),
the field produced by
the induced current
points downward,
trying to maintain the
“status quo.”
Chapter 1 - Alternating Current
8
I. Distance between magnet
and coil increases.
III. Current is
So the magnetic field (and
therefore the flux) decreases.
induced in the
opposite direction
as the previous
case.
II. To oppose the decrease
in the upward magnetic
field (flux), the induced
current produces an
upward magnetic field,
trying to maintain the
“status quo.”
Chapter 1 - Alternating Current
9
Since there is no change
in the magnetic flux, no
current is induced.
Chapter 1 - Alternating Current
10




Alternating currents are
repetitious and consist of a
continuing series of cycles.
The time for one complete
cycle is called the period of
the waveform.
A period consists of two,
alternate, opposite polarity,
alternations.
If the positive and negative
waveforms are equal, it is
symmetrical. If not, it is
asymmetrical.
Chapter 1- Alternating Current
11
 The
basis of an AC alternator is a loop of wire
rotated in a magnetic field.
 Slip rings and brushes make continuous
electrical connections to the rotating
conductor.
 The magnitude and polarity of the generated
voltage is shown on the following slide.
Chapter1- Alternating Current
12
Chapter 1 - Alternating Current
13
The sine wave at the
right consists of two,
opposite polarity,
alternations.
 Each alternation is
called a half cycle.
 Each half cycle has a
maximum value called
the peak value.

Chapter 1 - Alternating Current
14
 Sine
waves may represent voltage, current,
or some other parameter.
 The period of a sine wave is the time from
any given point on the cycle to the same
point on the following cycle.
 The period is measured in time (t), and in
most cases is measured in seconds or
fractions thereof.
Chapter 6 - Alternating Current
15
 The
frequency of a sine wave is the number
of complete cycles that occur in one second.
 Frequency is measured in hertz (Hz). One
hertz corresponds to one cycle per second.
 Frequency and period have an inverse
relationship. t = 1/f, and f = 1/t.
 Frequency-to-period and period-to-frequency
conversions are common in electronic
calculations.
Chapter 6 - Alternating Current
16
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The peak value of a sine wave is the
maximum voltage (or current) it reaches.
Peak voltages occur at two different points in
the cycle.
One peak is positive, the other is negative.
The positive peak occurs at 90º and the
negative peak at 270º.
The positive and negative have equal
amplitudes.
Chapter 6 - Alternating Current
17
Another measurement used to describe sine
waves are their peak-to-peak values.
 The peak-to-peak value is the difference
between the two peak values.

Chapter 6 - Alternating Current
18
Amplitude
Amplitude
Chapter 1 - Alternating Current
 The
average value of any measured quantity
is the sum of all of the intermediate values.
 The average value of a full sine wave is zero.
 The average value of one-half cycle of a sine
wave is:
Vavg = 0.637Vp or Iavg = 0.637Ip
Chapter 6 - Alternating Current
20
•
•
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One of the most important characteristics of
a sine wave is its rms or effective value.
The rms value describes the sine wave in
terms of an equivalent dc voltage.
The rms value of a sine wave produces the
same heating effect in a resistance as an
equal value of dc.
The abbreviation rms stands for root-meansquare, and is determined by: Vrms = 0.707Vp
or Irms = 0.707Ip
Chapter 6 - Alternating Current
21
 Form
Factor is defined as the ratio of r.m.s
value to the average value.

Form factor =


=
r.m.s value
average value
1.11
Chapter 1 - Alternating Current
= 0.707  peak value
0.637  peak valur

Crest or Peak or Amplitude Factor
 Peak
factor is defined as the ratio of peak
voltage to r.m.s value.




Peak Factor
= peak value
=
peak value
r.m.s value
0.707 x peak value
= 1.414
Chapter 1 - Alternating Current
Angle describes the amount and direction of
rotation 120°
–210°
Positive Angle- rotates counter-clockwise
(CCW)
Negative Angle- rotates clockwise (CW)
Chapter 1 - Alternating Current
1 Radian = measure of central angle, , that
intercepts the arc that has the same length as
the radius of
the circle
C
A
m AB = 4.31 cm
Chapter 1 - Alternating Current
Length BC on
B
AB = 4.31 cm
Calculate the number of radians in one full circle:

2
C=
 1.571
arc length s

radius r
1
0.5

3.14
0, 2
-1
1
-0.5
-1
3
 4.712
2
Chapter 1 - Alternating Current
2r
0, 6.28
0
2r

 2 radians
r
2
Degrees
Radians
Degrees
0
0
135
30
45
60
90
120
π
6
π
4
π
3
π
2
2π
3
150
180
210
225
240
Chapter 1 - Alternating Current
Radians
3π
4
5π
6
Degrees
π
315
7π
6
5π
4
4π
3
270
300
330
360
Radians
3π
2
5π
3
7π
4
11π
6
2π
To convert from degrees
radians, multiply by
To convert from radians
degrees, multiply by

180
180

Convert to radians:
135 

180
3

4
Chapter 1 - Alternating Current
 80 

180
4

9
To convert from degrees
radians, multiply by

180
To convert from radians
degrees, multiply by
180

Convert to degrees:
 8 180

  480
3

5 180


6 
150
Chapter 1 - Alternating Current
So, you think you got it
now?
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Phase is a relative term to
compare two or more sine
waves that have the same
frequency.
Sine waves that are in phase
have various, identical, points
occurring at exactly the same
time.
The terms leading and lagging
are used to describe the
relative positions of sine
waves with respect to each
other.
Phase angles are measured in
degrees or radians.
Chapter 1 - Alternating Current
30
Refers to the angular displacement between different waveforms of the
same frequency. ( the statement said : in phase
i(ώ t) = Im sin (ώ t +θ )
v1(ώ t) = Vm1 sin (ώ t – θ1)
Peak
Peak
Pea
k
Volta
ge
Volta
ge
Volt
age
t
36
0º
Amplitude
,Vpp
in phase
Current Lead
Chapter 1 - Alternating Current
Current lags
v(ώt) = Vm sin ώ t
i(ώ t) = Im sin (ώ t +θ )
v1(ώ t) = Vm1 sin (ώ t – θ1)
1) i(ώ t) lead v(ώt) with angler θ radian/degree or v(ώt) lag i(ώ t) with
angler θ radian/degree
2) v1(ώ t) lag v(ώt) with angler θ1 radian or v(ώt) lead v1(ώ t) with
angler θ1 radian
Chapter 1 - Alternating Current
Voltage and current are out of phase by 400, and voltage lags.
Using current as the reference, sketch the phasor diagram and the
corresponding waveforms.
Given v= 20sin (ώ t + 400 ) and i=18sin (ώ t - 400 ), draw the phasor
diagram, determine phase relationships, and sketch the waveform.
Chapter 1 - Alternating Current
 We
can express the voltage or current at any
instant during a sine wave’s cycle.
 The instantaneous voltage of a sine wave is
zero at 0º.
 Instantaneous voltages (v) and currents (i)
are found by:
v  VP sin θ
Chapter 6 - Alternating Current
i  I P sin θ
34
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All signals can be viewed from either of two
perspectives: time-domain or frequencydomain.
Fourier developed mathematical principles
that link together time and frequency
domains.
A time-domain signal is one whose
instantaneous voltage changes over time.
Any given waveform can be shown to be
composed of one or more sinusoidal signals
at specific frequencies and phases
(frequency domain)
Chapter 6 - Alternating Current
35
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A phasor consists of a
vector that can be
rotated around a
central point.
The length of the
phasor corresponds to
the peak value of the
sine wave.
The angle of the
phasor corresponds to
the phase angle of the
sine wave.
Chapter 6 - Alternating Current
36
Phasor problems are
solved using
trigonometry.
 There are three basic
equations used to solve
phasor problems:

sin  =
opposite side
hypotenuse
adjacent side
hypotenuse
opposite side
tan  
adjacent side
cos  =
An angle equal to 1/4 turn (90° or π/2 radians)
is called a right angle.
Chapter 6 - Alternating Current
37
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AC circuits composed of resistors can be
analyzed using Ohm’s and Kirchoff’s Laws just as
with dc circuits.
Care must be taken that the correct formulas
are used for peak voltages/currents, average
voltages/currents, etc.
Typically, power ratings are rms values in an ac
circuit.
Chapter 1 - Alternating Current
38
 In
general, Ohm's law cannot be applied
to alternating-current circuits since it
does not consider the reactance which is
always present in such circuits. However,
by a modification of Ohm's law which
does take into consideration the effect of
reactance we obtain a general law which
is applicable to ac circuits. Because the
impedance, Z, represents the combined
opposition of all the reactances and
resistances, this general law for ac is,
 I=E/Z
Chapter 1 - Alternating Current
When an AC circuit consists of a voltage source and a resistor, the current is
in phase with the voltage, meaning that each quantity rises and declines in
step.
This expression is also accurate for the maximum values of the potential and
current. Where;   V sin t
m
V
  iR
therefore
Vm sin t  iR
Vm
sin t
R
i become maximum when sin t  1
V
 i m
or Vm  iR
R
i
Vavg
I avg 
or I max  max
R
R
V peakto peak
I peakto peak 
R
A series circuit consists of two resistors (R1 = 5 Ω and R2 = 15 Ω) and an
alternating voltage source of 120 volts. What is Iavg?
Find the current and voltage drop at all the resistors in the circuit shown below:
Kirchhoff’s Law in Alternating Current
Kirchhoff’s Law can be divided into 2:
•Kirchhoff’s Current Law
•Kirchhoff’s Voltage Law
Kirchhoff’s Current Law
At any point in an electrical circuit where change density is not changing in
time, the sum of current flowing towards that point is equal to the sum of
currents flowing away from that point.
Kirchhoff’s Voltage Law
The algebraic sum of various potential drops across an electrical circuit is
equal to the electromotive force acting on the circuit
Calculate value current that flows to each branch use Kirchhoff’s Law
This power, measured in watts, is the power associated with the total
resistance in the circuit
To calculate true power, the voltage and current associated with the
resistance must be used.
Chapter 1 - Alternating Current
Chapter 1 - Alternating Current
Oscilloscopes are
commonly used to
observe the exact wave
shape of an electrical
signal.
Type of electronic test
instrument that allows
observation of constantly
varying signal voltages
Chapter 1 - Alternating Current
Chapter 1 - Alternating Current
Power
To switch the osiclloscope ON or OFF.
 Focus control
This control adjusts CRT focus to obtain the sharpest,
most-detailed trace. I
 Intensity control
This adjusts trace brightness. Slow traces on CRT 'scopes
need less, and fast ones, especially if they don't repeat
very often.
 Position
To position waveform horizontally or vertically
 Volt/Div
To adjust vertical magnification of a waveform
 Time/Div

to adjust horizontal magnification of a waveform
Chapter 1 - Alternating Current
Thank You