electric circuits ee 202 university of hail professor / mohamed a h eleiwa
TRANSCRIPT
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Electric Circuits EE 202
University of Hail
Professor / Mohamed A H Eleiwa
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Summary
Very large and very small numbers are represented with scientific and engineering notation.
Scientific and Engineering Notation
47,000,000 = 4.7 x 107 (Scientific Notation)
= 47 x 106 (Engineering Notation)
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Summary
0.000 027 = 2.7 x 10-5 (Scientific Notation)
= 27 x 10-6 (Engineering Notation)
0.605 = 6.05 x 10-1 (Scientific Notation)
= 605 x 10-3 (Engineering Notation)
Scientific and Engineering Notation
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Summary
Most scientific calculators can be placed in a mode that will automatically convert any decimal number entered into scientific notation or engineering notation.
Metric Conversions
Numbers in scientific notation can be entered in a scientific calculator using the EE key.
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Summary
SI Fundamental Units
Length Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance
Quantity Unit Symbol
Meter m
Kilogram kg
Second s
Ampere A
Kelvin K
Candela cd
Mole mol
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Summary
Some Important Electrical Units
Except for current, all electrical and magnetic units are derived from the fundamental units. Current is a fundamental unit.
CurrentCharge
Voltage
Resistance
Ampere A
Coulomb C
Volt V
Ohm WWatt W
Quantity Unit Symbol
Power
These derived units are based on fundamental units from the meter-kilogram-second system, hence are called mks units.
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Summary
Engineering Metric Prefixes
peta
tera
giga
mega
kilo
1015
1012
109
106
103
P
T
G
M
k
Can you name the prefixes and their meaning?
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Summary
Engineering Metric Prefixes
10-3
10-6
10-9
10-12
10-15
milli
micro
nano
pico
femto
m
m
n
p
f
Can you name the prefixes and their meaning?
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Summary
When converting from a larger unit to a smaller unit, move the decimal point to the right. Remember, a smaller unit means the number must be larger.
Metric Conversions
0.47 MW = 470 kW
Larger number
Smaller unit
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Summary
When converting from a smaller unit to a larger unit, move the decimal point to the left. Remember, a larger unit means the number must be smaller.
Metric Conversions
10,000 pF = 0.01 mF
Smaller number
Larger unit
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Summary
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
Metric Arithmetic
10,000 W + 22 kW =
10,000 W + 22,000 W = 32,000 W
Alternatively,
10 kW + 22 kW = 32 kW
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Summary
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
Metric Arithmetic
200 mA + 1.0 mA =
200 mA + 1,000 mA = 12,000 mA
Alternatively,
0.200 mA + 1.0 mA = 1.2 mA
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Summary
WV
Q
One volt is the potential difference (voltage) between two points when one joule of energy is used to move one coulomb of charge from one point to the other.
Voltage
The defining equation for voltage is
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Summary
Current (I) is the amount of charge (Q) that flows past a point in a unit of time (t). The defining equation is:
QI
t
One ampere is a number of electrons having a total charge of 1 C moving through a given cross section in 1 s.
0.4 AWhat is the current if 2 C passes a point in 5 s?
Current
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Summary
Resistance is the opposition to current.
One ohm (1 W) is the resistance if one ampere (1 A) is in a material when one volt (1 V) is applied.
Conductance is the reciprocal of resistance.
1G
R
Components designed to have a specific amount of resistance are called resistors. Color bands
Resistance material(carbon composition)
Insulation coating
Leads
Resistance
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Summary
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold
Silver
No band
0
1
2
3
4
5
6
7
8
9
±5%
±10%
Digit
±20%
100
101
102
103
104
105
106
107
108
109
10-1
10-2
Multiplier
1% (five band)
5% (four band)
Tolerance
2% (five band)
10% (four band)
Resistance value, first three bands:
First band – 1st digit
Second band – 2nd digit
*Third band – Multiplier (number of zeros following second digit)
Fourth band - tolerance
* For resistance values less than 10 W , the third band is either gold or silver. Gold is for a multiplier of 0.1 and silver is for a multiplier of 0.01.
Resistance color-code
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Summary
What is the resistance and tolerance of each of the four-band resistors?
5.1 k W ± 5%
820 k W ± 5%
47 W ± 10%
1.0 W ± 5%
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Summary
• Two or three digits, and one of the letters R, K, or M are used to identify a resistance value.
• The letter is used to indicate the multiplier, and its position is used to indicate decimal point position.
Alphanumeric Labeling
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Summary
Variable resistors include the potentiometer and rheostat. The center terminal of a variable resistor is connected to the wiper.
13
2
Resistiveelement
Wiper
Shaft
Variable resistors
R
Variable resistor (potentiometer)
R
Variable resistor (rheostat)
To connect a potentiometer as a rheostat, one of the outside terminals is connected to the wiper.
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Summary
The electric circuit
Circuits are described pictorially with schematics. For example, the flashlight can be represented by
Battery (2 cells)
Switch
Lamp
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Summary
The DMM (Digital Multimeter) is an important multipurpose instrument which can measure voltage, current, and resistance. Many include other measurement options.
The DMM
V
Hz
10 A
40 mA
OFF
mV
A
V
H
H
V H
COM
VW
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Summary
An analog multimeter is also called a VOM (volt-ohm-milliammeter). Analog meters measure voltage, current, and resistance. The user must choose the range and read the proper scale.
Analog meters
Photo courtesy of Triplett Corporation
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Summary
Voltage is
Review of V, I, and R
the amount of energy per charge available to
move electrons from one point to another in a circuit and is measured in volts.
Current is the rate of charge flow and is measured in
amperes.
Resistance is the opposition to current and is measured
in ohms.
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Summary
The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance.
Georg Simon Ohm (1787-1854) formulated the equation that bears his name:
VI
R
What is the current in a circuit with a 12 V source if the resistance is 10 W? 1.2 A
Ohm’s law
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Summary
Ohm’s law
If you need to solve for voltage, Ohm’s law is:
What is the voltage across a 680 W resistor if the current is 26.5 mA? 18 V
V IR
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Summary
Ohm’s law
If you need to solve for resistance, Ohm’s law is:V
RI
115 V
V
1 s
1 s
40 m A
1 0 A
C O M
Ra ng eAuto ra ng eTo uc h /Ho ld
Fused
O FF V
V
Hz
m V
A
What is the (hot) resistance of the bulb? 132 W
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In electrical work, the rate energy is dissipated can be determined from any of three forms of the power formula.
Summary
Energy and Power
2P I R P VI2V
PR
Together, the three forms are called Watt’s law.
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Summary
What power is dissipated in a 27 W resistor is the current is 0.135 A?
2
2(0.135 A) 27
0.49 W
P I R
W
Given that you know the resistance and current, substitute the values into P =I 2R.
Energy and Power
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Summary
All circuits have three common attributes. These are:
Summary
Series circuits
1. A source of voltage.
2. A load.
3. A complete path.
R1
VS R2
R3
+
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SummarySummary
Series circuits
A series circuit is one that has only one current path.
VS VS VS
R1
R1
R1
R2 R2
R2
R3
R3
R3
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SummarySummary
Series circuit rule for current:
Because there is only one path, the current everywhere is the same.
R 2
R 1
V S
+ _+ _
++ __
2.0 mA
For example, the reading on the first ammeter is 2.0 mA, What do the other meters read?
2.0 mA
2.0 mA2.0 mA
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SummarySummary
Series circuits
The total resistance of resistors in series is
the sum of the individual resistors.
4.38 kW
For example, the resistors in a series circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance?
R
R
2
3
R 1
V S
6 8 0 W
2 .2 k W
1 .5 k W1 2 V
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Series circuit
Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a series circuit. Continuing with the previous example, complete the parameters listed in the Table.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 4.38 kW VS= 12 V PT= 2.74 mA
2.74 mA
2.74 mA
2.74 mA 1.86 V
4.11 V
6.03 V
5.1 mW
11.3 mW
16.5 mW
32.9 mW
SummarySummarySummaryR
R
2
3
R 1
V S
6 8 0 W
2 .2 k W
1 .5 k W1 2 V
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SummarySummary
Voltage sources in series
Voltage sources in series add algebraically. For example, the total voltage of the sources shown is
+
+
+
9 V
9 V
9 V
27 V
9 VWhat is the total voltage if one battery is accidentally reversed?
+
+
+
9 V
9 V
9 V
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SummarySummary
Kirchhoff’s voltage law
The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that closed path.
KVL applies to all circuits, but you must apply it to only one closed path. In a series circuit, this is (of course) the entire circuit.
Kirchhoff’s voltage law (KVL) is generally stated as:
A mathematical shorthand way of writing KVL is1
0n
ii
V
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Kirchhoff’s voltage law
Notice in the series example given earlier that the sum of the resistor voltages is equal to the source voltage.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 4.38 kW VS= 12 V PT= 2.74 mA
2.74 mA
2.74 mA
2.74 mA 1.86 V
4.11 V
6.03 V
5.1 mW
11.3 mW
16.5 mW
32.9 mW
R
R
2
3
R 1
V S
6 8 0 W
2 .2 k W
1 .5 k W1 2 V
SummarySummary
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SummarySummary
Voltage divider rule
The voltage drop across any given resistor in a series circuit is equal to the ratio of that resistor to the total resistance, multiplied by source voltage.
8 V
Assume R1 is twice the size of R2. What is the voltage across R1?
R 1
R 2R 2
1V SV S
1 2 V
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SummarySummary
What is the voltage across R2?
The total resistance is 25 k . WApplying the voltage divider formula:
22 S
T
10 k20 V
25 k
RV V
R
W W
R1
VS R2+10 kW
15 kW
20 V
Voltage divider
Notice that 40% of the source voltage is across R2, which represents 40% of the total resistance.
8.0 V
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SummarySummary
Resistors in parallel
Resistors that are connected to the same two points are said to be in parallel.
R1 R2 R3 R4
A
B
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SummarySummary
Parallel circuits
A parallel circuit is identified by the fact that it hasmore than one current path (branch) connected to a common voltage source.
VS
+ R1 R2 R3 R4
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SummarySummary
Parallel circuit rule for voltage
Because all components are connected across the same voltage source, the voltage across each is the same.
+ 5 .0 V+-
+ 5 .0 V+-
+ 5 .0 V+-
+ 5 .0 V+-
R 2 R 3R 1V S
6 8 0 W 2 .2 k W1 .5 k W+ 5 .0 V
For example, the source voltage is 5.0 V. What will a volt- meter read if it is placed across each of the resistors?
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SummarySummary
Parallel circuit rule for resistance
The total resistance of resistors in parallel is
the reciprocal of the sum of the reciprocals of the individual resistors.
386 W
For example, the resistors in a parallel circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance?
VS
+ R1 R2 R3
680 W 1.5 kW 2.2 kW
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SummarySummary
Special case for resistance of two parallel resistors
The resistance of two parallel resistors can be found by
either:
R1 R2
T
1 2
11 1
R
R R
or 1 2T
1 2
R RR
R R
18.2 kW
What is the total resistance if R1 = 27 kW and R2 = 56 kW?
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SummarySummary
Parallel circuit
Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a parallel circuit.
Continuing with the previous example, complete the parameters listed in the Table.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
5.0 V
5.0 V
5.0 V
13.0 mA
2.3 mA
3.3 mA
7.4 mA 36.8 mW
16.7 mW
11.4 mW
64.8 mW
VS
+ R1 R2 R3
680 W 1.5 kW 2.2 kW
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SummarySummary
Kirchhoff’s current law
Kirchhoff’s current law (KCL) is generally stated as:
The sum of the currents entering a node is equal to the sum of the currents leaving the node.
Notice in the previous example that the current from the source is equal to the sum of the branch currents.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
5.0 V
5.0 V
5.0 V
13.0 mA
2.3 mA
3.3 mA
7.4 mA 36.8 mW
16.7 mW
11.4 mW
64.8 mW
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SummarySummary
Current divider
When current enters a node (junction) it divides into currents with values that are inversely proportional to the resistance values.
Notice the subscripts. The resistor in the numerator is not the same as the one for which current is found.
21 T
1 2
RI I
R R
and 12 T
1 2
RI I
R R
The most widely used formula for the current divider is the two-resistor equation. For resistors R1 and R2,
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SummarySummary
Current divider
21 T
1 2
4.7 k8.0 mA =
6.9 k
RI I
R R
W W
Assume that R1is a 2.2 kW resistor that is in parallel with R2, which is 4.7 kW. If the total current into the resistors is 8.0 mA, what is the current in each resistor?
5.45 mA
12 T
1 2
2.2 k8.0 mA =
6.9 k
RI I
R R
W W 2.55 mA
Notice that the larger resistor has the smaller current.
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SummarySummary
Power in parallel circuits
Power in each resistor can be calculated with any of the standard power formulas. Most of the time, the voltage is
known, so the equation 2VP
R is most convenient.
As in the series case, the total power is the sum of the powers dissipated in each resistor.
1.04 W
What is the total power if 10 V is applied to the parallel combination of R1 = 270 W and R2 = 150 W?
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SummarySummary
Assume there are 8 resistive wires that form a rear window defroster for an automobile.
(a) If the defroster dissipates 90 W when connected to a 12.6 V source, what power is dissipated by each resistive wire?
(b) What is the total resistance of the defroster?
(a) Each of the 8 wires will dissipate 1/8 of the total power or 90 W
8 wire11. W
s25
22 12.6 V
90 W1.76
VR
P W(b) The total resistance is
What is the resistance of each wire? 1.76 W x 8 = 14.1 W
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SummarySummary
Most practical circuits have various combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components.
Combination circuits
An important analysis method is to form an equivalent circuit. An equivalent circuit is one that has characteristics that are electrically the same as another circuit but is generally simpler.
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SummarySummary
Kirchhoff’s voltage law and Kirchhoff’s current law can be applied to any circuit, including combination circuits.
R5100
R3330
R 2470
R1270 W W
W
W
V S5 .0 V
R4
100
R6
100 Sta rt/Finish
W
WR5100
R3330
R 2470
R1270 W W
W
W
V S5 .0 V
R4
100
R6
100 Sta rt/Finish
W
W
So will this path!
For example, applying KVL, the path shown will have a sum of 0 V.
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SummarySummary
I
+
+
26.5 mA
I
+18.5 mA
I
+8.0 mA
R5100 W
R3330 W
R2470 W
R1270 W
VS5.0 V
R4
100 W
R6
100 W
A- -
-
Kirchoff’s current law can also be applied to the same circuit. What are the readings for node A?
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SummarySummary
Tabulating current, resistance, voltage and power is a useful way to summarize parameters. Solve for the unknown quantities in the circuit shown.
I1= R1= 270 W V1= P1=
I2= R2= 330 W V2= P2=
I3= R3= 470 W V3= P3=
IT= RT= VS= 10 V PT=
4.18 V
4.18 V
5.82 V
21.6 mA
8.9 mA
12.7 mA
21.6 mA 126 mW
53.1 mW
37.2 mW
216 mW
R1
R3
470 W
270 W
R2
330 W
VS +10 V
464 W
Combination circuits
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SummarySummary
Kirchhoff’s laws can be applied as a check on the answer.
I1= R1= 270 W V1= P1=
I2= R2= 330 W V2= P2=
I3= R3= 470 W V3= P3=
IT= RT= VS= 10 V PT=
4.18 V
4.18 V
5.82 V
21.6 mA
8.9 mA
12.7 mA
21.6 mA 126 mW
53.1 mW
37.2 mW
216 mW464 W
R1
R3
470 W
270 W
R2
330 W
VS +10 V
equal to the sum of the branch currents in R2 and R3.Notice that the current in R1 is
The sum of the voltages around the outside loop is zero.
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SummarySummary
Thevenin’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:
Thevenin’s theorem
V T H
R T H
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SummarySummary
V T H
R T H
VTH is defined as
Thevenin’s theorem
RTH is defined as
the open circuit voltage between the two output terminals of a circuit.
the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.
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SummarySummary
Thevenin’s theorem
R
R
1
R 2R 2 L
V SV S
1 2 V1 0 kW
6 8 kW2 7 kW
Output terminals
What is the Thevenin voltage for the circuit? 8.76 V
What is the Thevenin resistance for the circuit? 7.30 kW
Remember, the load resistor has no affect on the Thevenin parameters.
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SummarySummary
Maximum power transfer
The maximum power is transferred from a source to a load when the load resistance is equal to the internal source resistance.
The maximum power transfer theorem assumes the source voltage and resistance are fixed.
RS
RL
VS +
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SummarySummary
Maximum power transfer
What is the power delivered to the matching load?
The voltage to the load is 5.0 V. The power delivered is
RS
RL
VS + 50 W
50 W10 V
22
LL
5.0 V= 0.5 W
50
VP
R
W
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SummarySummary
Superposition theoremThe superposition theorem is a way to determine currents and voltages in a linear circuit that has multiple sources by taking one source at a time and algebraically summing the results.
What does the ammeter read for I2? (See next slide for the method and the answer).
+-
-
+
-
+
R 1 R 3
R 2
I 2
V S 2V S 1
1 2 V
2 .7 kW 6 .8 kW
6 .8 kW
1 8 V
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SummarySummary
6.10 kW
What does the ammeter read for I2?
1.97 mA 0.98 mA
8.73 kW 2.06 mA
+-
-
+
-
+
R 1 R 3
R 2
I 2
V S 2V S 1
1 2 V
2 .7 kW 6 .8 kW
6 .8 kW
1 8 V
0.58 mA
1.56 mA
Source 1: RT(S1)= I1= I2= Source 2: RT(S2)= I3= I2= Both sources I2=
Set up a table of pertinent information and solve for each quantity listed:
The total current is the algebraic sum.
+ -
-
+
R1 R3
R2
I2VS1
12 V
2.7 kW 6.8 kW
6.8 kW
+ -
-
+
R1 R3
R2
I2
VS2
2.7 kW 6.8 kW
6.8 kW
18 V+-
-
+
-
+
R 1 R 3
R 2
I 2
V S 2V S 1
1 2 V
2 .7 kW 6 .8 kW
6 .8 kW
1 8 V1.56 mA
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Node Voltage Method (Nodal Analysis)
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Summary
The Basic Capacitor
Capacitors are one of the fundamental passive components. In its most basic form, it is composed of two conductive plates separated by an insulating dielectric.
The ability to store charge is the definition of capacitance.
Dielectric
Conductors
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Summary
Die le c tric
Pla te sLe a d s
Ele c tro ns
BA
-
-
--
+
+
+
+
-
-
+
+
+
+
-
Initially uncharged
+ -BA
-
-
-
-
-
-
-
+
+
+
--
-
-
- - - - - -
-
---
+
+
+
+
Charging
+ -BA
V S
+
+
+++++++++
-
-
---------
Fully charged
BA
VS
-+
-+
-+-+-+-+-+-+-+-+-+
Source removed
The charging process…
A capacitor with stored charge can act as a temporary battery.
The Basic Capacitor
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Capacitance is the ratio of charge to voltage
QC
V
Rearranging, the amount of charge on a capacitor is determined by the size of the capacitor (C) and the voltage (V).
Q CV
If a 22 mF capacitor is connected to a 10 V source, the charge is 220 mC
Capacitance
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A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates. The energy of a charged capacitor is given by the equation
Capacitance
2
2
1CVW
where
W = the energy in joulesC = the capacitance in faradsV = the voltage in volts
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The capacitance of a capacitor depends on three physical characteristics.
Summary
128.85 10 F/m r AC
d
-
C is directly proportional to
and the plate area.
the relative dielectric constant
C is inversely proportional to
the distance between the plates
Capacitance
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128.85 10 F/m r AC
d
-
Summary
Find the capacitance of a 4.0 cm diameter sensor immersed in oil if the plates are separated by 0.25 mm.
The plate area is
The distance between the plates is
Capacitance
4.0 for oilr
3 2
123
4.0 1.26 10 m 8.85 10 F/m
0.25 10 mC
--
-
30.25 10 m-
178 pF
2 2 3 2π 0.02 m 1.26 10 mA r -
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Summary
Series capacitors
When capacitors are connected in series, the total capacitance is smaller than the smallest one. The general equation for capacitors in series is
T
1 2 3 T
11 1 1 1
...C
C C C C
The total capacitance of two capacitors is
T
1 2
11 1
C
C C
…or you can use the product-over-sum rule
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Summary
Series capacitors
If a 0.001 mF capacitor is connected in series with an 800 pF capacitor, the total capacitance is444 pF
0 .001 µ F 800 pF
C 1 C 2
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Summary
Parallel capacitors
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors. The general equation for capacitors in parallel is
T 1 2 3 ... nC C C C C
1800 pF
If a 0.001 mF capacitor is connected in parallel with an 800 pF capacitor, the total capacitance is
0 .001 µ F 800 pF
C 1 C 2
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Summary
The Basic Inductor
The effect of inductance is greatly magnified by adding turns and winding them on a magnetic material. Large inductors and transformers are wound on a core to increase the inductance.
Magnetic core
One henry is the inductance of a coil when a current, changing at a rate of one ampere per second, induces one volt across the coil. Most coils are much smaller than 1 H.
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Summary
Factors affecting inductance
Four factors affect the amount of inductance for a coil. The equation for the inductance of a coil is
2N AL
l
where L = inductance in henries N = number of turns of wire m = permeability in H/m (same as Wb/At-m) l = coil length on meters
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Summary
What is the inductance of a 2 cm long, 150 turn coil wrapped on an low carbon steel core that is 0.5 cm diameter? The permeability of low carbon steel is 2.5 x10-4 H/m (Wb/At-m).
22 5 2π π 0.0025 m 7.85 10 mA r - 2N A
Ll
22 mH
2 4 5 2150 t 2.5 10 Wb/At-m 7.85 10 m
0.02 m
- -
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Summary
Series inductorsWhen inductors are connected in series, the total inductance is the sum of the individual inductors. The general equation for inductors in series is
2.18 mH
T 1 2 3 ... nL L L L L
If a 1.5 mH inductor is connected in series with an 680 mH inductor, the total inductance is
L 1 L 2
1 .5 m H 680 H
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Summary
Parallel inductorsWhen inductors are connected in parallel, the total inductance is smaller than the smallest one. The general equation for inductors in parallel is
The total inductance of two inductors is
…or you can use the product-over-sum rule.
T
1 2 3 T
11 1 1 1
...L
L L L L
T
1 2
11 1
L
L L
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Summary
Parallel inductors
If a 1.5 mH inductor is connected in parallel with an 680 mH inductor, the total inductance is 468 mH
L 1 L 2
1 .5 m H 680 H
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OBJECTIVES• Become familiar with the characteristics of a sinusoidal waveform, including its general format, average value, and effective value.• Be able to determine the phase relationship between two sinusoidal waveforms of the same frequency.• Understand how to calculate the average and effective values of any waveform.• Become familiar with the use of instruments designed to measure ac quantities.
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SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS
Generation
• Sinusoidal ac voltages are available from a variety of sources. • The most common source is the typical home outlet, which provides an ac voltage that originates at a power plant. • Most power plants are fueled by water power, oil, gas, or nuclear fusion.
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SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS
Definitions
FIG. 13.3 Important parameters for a sinusoidal voltage.
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AVERAGE POWER AND POWER FACTOR• Resistor• Inductor• Capacitor• Power Factor
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AVERAGE POWER AND POWER FACTOR
FIG. 14.33 Purely resistive load with Fp = 1.
FIG. 14.34 Purely inductive load with Fp = 0.
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COMPLEX NUMBERS• A complex number represents a point in a two-dimensional plane located with reference to two distinct axes. • This point can also determine a radius vector drawn from the origin to the point. • The horizontal axis is called the real axis, while the vertical axis is called the imaginary axis.
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COMPLEX NUMBERS
FIG. 14.38 Defining the real and imaginary axes of a complex plane.
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
RECTANGULAR FORM
• The format for the rectangular form is:
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
POLAR FORM
• The format for the polar form is:
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MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS
• Complex Conjugate• Reciprocal• Addition• Subtraction• Multiplication• Division
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IMPEDANCE AND THE PHASOR DIAGRAMResistive Elements
FIG. 15.1 Resistive ac circuit.
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
IMPEDANCE AND THE PHASOR DIAGRAMResistive Elements
• In phasor form,
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IMPEDANCE AND THE PHASOR DIAGRAMResistive Elements
FIG. 15.2 Example 15.1.
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
IMPEDANCE AND THE PHASOR DIAGRAMCapacitive Reactance
• We learned in Chapter 13 that for the pure capacitor in Fig. 15.13, the current leads the voltage by 90° and that the reactance of the capacitor XC is determined by 1/ψC.
• We have
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SERIES CONFIGURATIONR-L-C
FIG. 15.36 Applying phasor notation to the circuit in Fig. 15.35.
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VOLTAGE DIVIDER RULE
FIG. 15.41 Example 15.10.
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FREQUENCY RESPONSE FOR SERIES ac CIRCUITS
Series R-C ac Circuit
FIG. 15.47 Determining the frequency response of a series R-C circuit.
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ILLUSTRATIVE EXAMPLES
FIG. 16.1 Example 16.1.
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ILLUSTRATIVE EXAMPLES
FIG. 16.2 Network in Fig. 16.1 after assigning the block impedances.
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ILLUSTRATIVE EXAMPLES
FIG. 16.3 Example 16.2.
FIG. 16.4 Network in Fig. 16.3 after assigning the block impedances.
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
Δ-Y, Y-Δ CONVERSIONS
• The Δ-Y, Y-Δ (or p-T, T-p as defined in Section 8.12) conversions for ac circuits are not derived here since the development corresponds exactly with that for dc circuits.
FIG. 17.45 Δ-Y configuration.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.46 The T and π configurations.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.47 Converting the upper Δ of a bridge configuration to a Y.
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Electronics Fundamentals 8th edition Floyd/Buchla
Chapter 1
© 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.
Δ-Y, Y-Δ CONVERSIONS
FIG. 17.48 The network in Fig. 17.47 following the substitution of the Y configuration.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.49 Example 17.21.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.50 Converting a Δ configuration to a Y configuration.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.51 Substituting the Y configuration in Fig. 17.50 into the network in Fig. 17.49.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.52 Converting the Y configuration in Fig. 17.49 to a Δ.
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Δ-Y, Y-Δ CONVERSIONS
FIG. 17.53 Substituting the Δ configuration in Fig. 17.54 into the network in Fig. 17.49.