Chapter 8
Chapter 8
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Voltage sources
Principles of Electric Circuits - Floyd
4
Current (A)
An ideal voltage source
plots a vertical line on the
VI characteristic as shown
for the ideal 6.0 V source.
Actual voltage sources
include the internal source
resistance, which can drop
a small voltage under load.
The characteristic of a nonideal source is not vertical.
5
3
2
1
0
0
2
6
4
Voltage (V)
8
10
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Voltage sources
A practical voltage source is drawn as an ideal source
in series with the source resistance. When the internal
resistance is zero, the source reduces to an ideal one.
RS
VS +
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Voltage sources
If the source resistance of a 5.0 V power supply
is 0.5 W, what is the voltage across a 68 W load?
RS
Use the voltage-divider
equation:
VS +
5.0 V
 RL 
VL  
 VS
 RL  RS 
68 W



 5 V = 4.96 V
68
W

0.5
W


Principles of Electric Circuits - Floyd
VOUT
0.5 W
RL
68 W
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Current sources
Principles of Electric Circuits - Floyd
4
Current (A)
An ideal current source
plots a horizontal line on the
VI characteristic as shown
for the ideal 4.0 mA source.
Practical current sources
have internal source
resistance, which takes some
of the current. The
characteristic of a practical
source is not horizontal.
5
3
2
1
0
0
2
6
4
Voltage (V)
8
10
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Current sources
A practical current source is drawn as an ideal source
with a parallel source resistance. When the source
resistance is infinite, the current source is ideal.
IS
Principles of Electric Circuits - Floyd
RS
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Current sources
If the source resistance of a 10 mA current source
is 4.7 kW, what is the voltage across a 100 W load?
Use the current-divider
equation:
IS
10 mA
 RS 
IL  
 IS
 RL  RS 
4.7 kW



10 mA = 9.8 mA
 100 W  4.7 kW 
Principles of Electric Circuits - Floyd
RS
4.7 kW
RL
100 W
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Source conversions
Any voltage source with an internal resistance can be
converted to an equivalent current source and viceversa by applying Ohm’s law to the source. The source
resistance, RS, is the same for both.
To convert a voltage source to a current source, IS 
VS
RS
To convert a current source to a voltage source, VS  IS RS
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Superposition theorem
The 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.
R3
R1
+
-
VS2
18 V
R2
6.8 kW
-
-
VS1
12 V
6.8 kW
I2
+
Principles of Electric Circuits - Floyd
2.7 kW
+
What does the
ammeter read for
I2? (See next slide
for the method and
the answer).
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
+1.56 mA
-
VS1
12 V
6.8 kW
I2
VS2
18 V
R2
6.8 kW
-
Source 1:
Source 2:
2.7 kW
+
Set up a table of
pertinent information
and solve for each
quantity listed:
R3
R1
+
What does the ammeter
read for I2?
RT(S1)= 6.10 kW I1= 1.97 mA I2= 0.98 mA
RT(S2)= 8.73 kW I3= 2.06 mA I2= 0.58 mA
Both sources
I2= 1.56 mA
The total current is the algebraic sum.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
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:
RTH
VTH
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
VTH is defined as the open circuit voltage between the two
output terminals of a circuit.
RTH is defined as the total resistance appearing between
the two output terminals when all sources have been
replaced by their internal resistances.
RTH
VTH
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
What is the Thevenin voltage for the circuit? 8.76 V
What is the Thevenin resistance for the circuit? 7.30 kW
Output terminals
R1
VS
12 V
10 kW
R2
27 kW
Principles of Electric Circuits - Floyd
RL
68 kW
Remember, the
load resistor
has no affect on
the Thevenin
parameters.
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
Thevenin’s theorem is useful for solving the Wheatstone
bridge. One way to Thevenize the bridge is to create two
Thevenin circuits - from A to ground and from B to ground.
The resistance between point
R1
R2
V
A and ground is R1||R3 and the S +
RL
A
B
resistance from B to ground is
R2||R4. The voltage on each
R3
R4
side of the bridge is found
using the voltage divider rule.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
For the bridge shown, R1||R3 = 165 W and
R2||R4 = 179 W . The voltage from A to ground
(with no load) is 7.5 V and from B to ground
(with no load) is 6.87 V .
VS
+15 V
+
-
R1
R2
330 W
390 W
RL
A
B
150 W
R3
R4
330 W
330 W
The Thevenin circuits for each of the
bridge are shown on the following slide.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Thevenin’s theorem
RTH A RL
VTH
7.5 V
165 W
150 W
B RTH'
179 W
VTH'
6.87 V
Putting the load on the Thevenin circuits and
applying the superposition theorem allows you to
calculate the load current. The load current is: 1.27 mA
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Norton’s theorem
Norton’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:
IN
Principles of Electric Circuits - Floyd
RN
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Norton’s theorem
IN is defined as the output current when the output
terminals are shorted.
RN is defined as the total resistance appearing between
the two output terminals when all sources have been
replaced by their internal resistances.
IN
Principles of Electric Circuits - Floyd
RN
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Norton’s theorem
What is the Norton current for the circuit? 17.9 mA
What is the Norton resistance for the circuit? 359 W
R1
VS +
10 V
Output terminals
560 W
R2
1.0 kW
RL
820 W
The Norton circuit is shown on the following slide.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Norton’s theorem
The Norton circuit (without the load) is:
IN
17.9 mA
Principles of Electric Circuits - Floyd
RN
359 W
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
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.
RS
VS +
RL
The maximum power transfer theorem assumes the
source voltage and resistance are fixed.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
Maximum power transfer
What is the power delivered to the matching load?
RS
The voltage to the
load is 5.0 V. The
power delivered is
V 2  5.0 V 
PL 

= 0.5 W
RL
50 W
2
Principles of Electric Circuits - Floyd
VS +
10 V
50 W
RL
50 W
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
D-to-Y and Y-to-D conversion
The D-to-Y and Y-to-D conversion formulas allow a
three terminal resistive network to be replaced with
an equivalent network.
RC
For the D-to-Y conversion, each
resistor in the Y is equal to the
product of the resistors in the two
adjacent D branches divided by the
sum of all three D resistors.
Principles of Electric Circuits - Floyd
R1
RA
R2
R3
RB
© Copyright 2006 Prentice-Hall
Chapter 8
Summary
D-to-Y and Y-to-D conversion
The D-to-Y and Y-to-D conversion formulas allow a
three terminal resistive network to be replaced with
an equivalent network.
R
C
For the Y-to-D conversion, each
R1
resistor in the D is equal to the sum
of all products of Y resistors, taken RA
two at a time divided by the opposite
Y resistor.
Principles of Electric Circuits - Floyd
R2
R3
RB
© Copyright 2006 Prentice-Hall
Chapter 8
Key Terms
Current source A device that ideally provides a constant value
of current regardless of the load.
Maximum power Transfer of maximum power from a source
transfer to a load occurs when the load resistance
equals the internal source resistance.
Norton’s A method for simplifying a two-terminal
theorem linear circuit to an equivalent circuit with only
a current source in parallel with a resistance.
Superposition A method for analysis of circuits with more
theorem than one source.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Key Terms
Terminal The concept that when any given load is
equivalency connected to two sources, the same load
voltage and current are produced by both
sources.
Thevenin’s A method for simplifying a two-terminal
theorem linear circuit to an equivalent circuit with only
a voltage source in series with a resistance.
Voltage source A device that ideally provides a constant value
of voltage regardless of the load.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
1. The source resistance from a 1.50 V D-cell is 1.5 W.
The voltage that appears across a 75 W load will be
a. 1.47 V
RS
b. 1.50 V
c. 1.53 V
d. 1.60 V
Principles of Electric Circuits - Floyd
VS +
1.5 V
VOUT
1.5 W
RL
75 W
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
2. The internal resistance of an ideal current source
a. is 0 W
b. is 1 W
c. is infinite
d. depends on the source
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
3. The superposition theorem cannot be applied to
a. circuits with more than two sources
b. nonlinear circuits
c. circuits with current sources
d. ideal sources
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
4. A Thevenin circuit is a
a. resistor in series with a voltage source
b. resistor in parallel with a voltage source
c. resistor in series with a current source
d. resistor in parallel with a current source
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
4. A Norton circuit is a
a. resistor in series with a voltage source
b. resistor in parallel with a voltage source
c. resistor in series with a current source
d. resistor in parallel with a current source
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
5. A signal generator has an output voltage of 2.0 V with no
load. When a 600 W load is connected to it, the output
drops to 1.0 V. The Thevenin resistance of the generator is
a. 300 W
b. 600 W
c. 900 W
d. 1200 W.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
6. A signal generator has an output voltage of 2.0 V with no
load. When a 600 W load is connected to it, the output drops
to 1.0 V. The Thevenin voltage of the generator is
a. 1.0 V
b. 2.0 V
c. 4.0 V
d. not enough information to tell.
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
7. A Wheatstone bridge is shown with the Thevenin circuit
as viewed with respect to ground. The total Thevenin
resistance (RTH + RTH’) is
R1
R2
a. 320 W
VS
+
1.0 kW
A
-
b. 500 W
R3
1.0 kW
RL
100 W
1.0 kW
B
R4
470 W
c. 820 W
d. 3.47 kW.
RTH
VTH
Principles of Electric Circuits - Floyd
RL
'
RTH
VTH'
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
8. The Norton current for the circuit is
R1
a. 5.0 mA
b. 6.67 mA
c. 8.33 mA
VS +
10 V
1.0 kW
R2
1.0 kW
RL
1.0 kW
d. 10 mA
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
9. The Norton resistance for the circuit is
R1
a. 500 W
b. 1.0 kW
c. 1.5 kW
VS +
10 V
1.0 kW
R2
1.0 kW
RL
1.0 kW
d. 2.0 kW
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
10. Maximum power is transferred from a fixed source
when
a. the load resistor is ½ the source resistance
b. the load resistor is equal to the source resistance
c. the load resistor is twice the source resistance
d. none of the above
Principles of Electric Circuits - Floyd
© Copyright 2006 Prentice-Hall
Chapter 8
Quiz
Answers:
Principles of Electric Circuits - Floyd
1. a
6. b
2. c
7. c
3. b
8. d
4. d
9. a
5. b
10. b
© Copyright 2006 Prentice-Hall