The document discusses various concepts related to electric circuits including: - Ideal and non-ideal voltage and current sources and their characteristics - Converting between voltage and current sources using Ohm's law - Thevenin's and Norton's theorems for simplifying two-terminal circuits - Superposition theorem for analyzing circuits with multiple sources - Maximum power transfer occurring when load resistance equals source resistance

1. Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall
Chapter 8

2. An ideal voltage source
plots a vertical line on the
VI characteristic as shown
for the ideal 6.0 V source.
Voltage sources
Actual voltage sources
include the internal source
resistance, which can drop
a small voltage under load.
The characteristic of a non-
ideal source is not vertical.
Current
(A)
Voltage (V)
0
0
1
2
2
3
4
4 6
5
8 10

3. 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
+

4. 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?
Use the voltage-divider
equation:
L
L S
L S
68
5 V = 4.96 V
68 0.5
R
V V
R R
 
  

 
W
 
  
W  W
 
RS
RL
VS
VOUT
+
5.0 V
0.5W
68 W

5. An ideal current source
plots a horizontal line on the
VI characteristic as shown
for the ideal 4.0 mA source.
Current sources
Practical current sources
have internal source
resistance, which takes some
of the current. The
characteristic of a practical
source is not horizontal.
Current
(A)
Voltage (V)
0
0
1
2
2
3
4
4 6
5
8 10

6. 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.
Current sources
RS
IS

7. 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:
S
L S
L S
4.7 k
10 mA = 9.8 mA
100 4.7 k
R
I I
R R
 
  

 
W
 
  
W  W
 
RS
IS RL
100W
4.7 kW
10 mA

8. Source conversions
Any voltage source with an internal resistance can be
converted to an equivalent current source and vice-
versa 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,
S
S
S
V
I
R

S S S
V I R

To convert a current source to a voltage source,

9. Current Sources
A battery supplies fixed voltage and the source current may
vary according to load. Similarly, a current source is one
where it supplies constant current to the branch where it is
connected and the voltage and polarity of voltage across it
may vary according to the network condition.
A
I
I
E
VS
4
3
7
I
KCL
Applying
A,
3
4
12V
I
V
12
2
1
2






W




10. Source Conversion
A Voltage source can be converted to a current source and vice
versa. In reality, Voltage sources has an internal resistance Rs
and current sources has a shunt resistance Rsh. In ideal cases,
Rs equal to 0 and Rsh equal to .

11. Source Conversion
For us to be able to convert sources, the voltage source must have a series
resistance and current source must have some shunt resistance.
Eg.

12. 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.
What does the
ammeter read for
I2? (See next slide
for the method and
the answer).
+
-
-
+
-
+
R1 R3
R2
I2
VS2
VS1
12 V
2.7 kW 6.8 kW
6.8 kW
18 V

13. 6.10 kW
What does the ammeter
read for I2?
1.97 mA 0.98 mA
8.73 kW 2.06 mA
+
-
-
+
-
+
R1 R3
R2
I2
VS2
VS1
12 V
2.7 kW 6.8 kW
6.8 kW
18 V
0.58 mA
1.56 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.

14. 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

15. 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.

16. Thevenin’s theorem
R
R
1
R2
R2 L
VS
VS
12 V
10 kW
68 kW
27 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.

17. 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
A and ground is R1||R3 and the
resistance from B to ground is
R2||R4. The voltage on each
side of the bridge is found
using the voltage divider rule.
R3 R4
R2
RL
R1
VS
-
+
A B

18. Thevenin’s theorem
For the bridge shown, R1||R3 = and
R2||R4 = . The voltage from A to ground
(with no load) is and from B to ground
(with no load) is .
The Thevenin circuits for each of the
bridge are shown on the following slide.
165 W
179 W
7.5 V
6.87 V
R3 R4
R2
RL
R1
VS
-
+
A B
330W 390W
330W 330W
+15 V
150 W

19. Thevenin’s theorem
Putting the load on the Thevenin circuits and
applying the superposition theorem allows you to
calculate the load current. The load current is:
RL
A B
150 W
VTH VTH
RTH RTH
'
'
165W 179W
7.5 V 6.87 V
A B
VTH VTH
RTH RTH
'
'
165W 179W
7.5 V 6.87 V
1.27 mA

20. 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:
Norton’s theorem
RN
IN

21. Norton’s theorem
the output current when the output
terminals are shorted.
the total resistance appearing between
the two output terminals when all sources have been
replaced by their internal resistances.
IN is defined as
RN is defined as
RN
IN

22. Norton’s theorem
Output terminals
What is the Norton current for the circuit? 17.9 mA
What is the Norton resistance for the circuit? 359 W
R2
R1
RL
VS +
10 V
560W
820 W
1.0 kW
The Norton circuit is shown on the following slide.

23. Norton’s theorem
RN
IN
17.9 mA 359 W
The Norton circuit (without the load) is:

24. 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 +

25. 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 W
10 V
 
2
2
L
L
5.0 V
= 0.5 W
50
V
P
R
 
W

26. Current source
Maximum power
transfer
Norton’s
theorem
Superposition
theorem
Transfer of maximum power from a source
to a load occurs when the load resistance
equals the internal source resistance.
A method for simplifying a two-terminal
linear circuit to an equivalent circuit with only
a current source in parallel with a resistance.
A device that ideally provides a constant value
of current regardless of the load.
Key Terms
A method for analysis of circuits with more
than one source.

27. Terminal
equivalency
Thevenin’s
theorem
Voltage source
A method for simplifying a two-terminal
linear circuit to an equivalent circuit with only
a voltage source in series with a resistance.
The concept that when any given load is
connected to two sources, the same load
voltage and current are produced by both
sources.
Key Terms
A device that ideally provides a constant value
of voltage regardless of the load.

28. 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
b. 1.50 V
c. 1.53 V
d. 1.60 V
RS
RL
VS
VOUT
+
1.5 V
1.5W
75 W

29. 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

30. 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

31. 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

32. 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

33. 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.

34. 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.

35. Quiz
7. A Wheatstone bridge is shown with the Thevenin circuit
as viewed with respect to ground. The total Thevenin
resistance (RTH + RTH’) is
a. 320 W
b. 500 W
c. 820 W
d. 3.47 kW.
R3 R4
R2
RL
R1
VS
-
+
A B
1.0 kW 1.0 kW
1.0 kW 470W
100 W
VTH VTH
RTH RL RTH
'
'

36. Quiz
8. The Norton current for the circuit is
a. 5.0 mA
b. 6.67 mA
c. 8.33 mA
d. 10 mA
R2
R1
RL
VS +
10 V
1.0 kW
1.0 kW 1.0 kW

37. Quiz
9. The Norton resistance for the circuit is
a. 500 W
b. 1.0 kW
c. 1.5 kW
d. 2.0 kW
R2
R1
RL
VS +
10 V
1.0 kW
1.0 kW 1.0 kW

38. 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

39. Quiz
Answers:
1. a
2. c
3. b
4. d
5. b
6. b
7. c
8. d
9. a
10. b