Ch#4 Circuit Theorem - Complete
Ch#4 Circuit Theorem - Complete
Ch#4 Circuit Theorem - Complete
Spring 2019
Chapter 4
Circuit Theorems
LEARNING OUTCOMES / OUTLINE
Introduction
Linearity Circuits & Superposition
Source Transformation
Thevenin’s Theorem
Norton’s Theorem
• Since these theorems are applicable to linear circuits, we first discuss the
concept of circuit linearity.
• Statement
The voltage across (current through) an element is the
algebraic sum of the voltage across (current through)
that element due to each independent source acting alone.
PRINCIPLE OF SUPERPOSITION(2)
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Example 1
v v v
1 1
2 8 10 V
Example 2
i i ' i"
0 0 0
= +
Example 3
i i i i
1 2 3
Example 4.5 : In the circuit below, find the current i by
superposition
24V
DC
Repeat step 2
23
Example: In the circuit below, find the current i by superposition
24V
DC
DC
12V
3A
24
24V
DC
DC
12V
3A
(8+4) // 4
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Example: In the circuit below, find the current i by superposition
24V
DC
12V
3A
26
Example: In the circuit below, find the current i by superposition
24V
DC
12V
3A
27
24V
DC
i i i i 1A 2A 1A 2A
1 2 3
DC
12V
3A
24V
DC
i1 i
2
v1 v
2
12V DC
12V
i
3A i2
O.C. 3 O.C.
i i2 i
1
3
i1 1 i2 2 i3 1
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NOTE
• Source transform is done only in one or
two parts (few part ) of the circuit
containing voltage or current sources.
• We don’t need to transform the whole
circuit
Thevenin's Theorem
Thevenin’s theorem states that a linear two-terminal resistive circuit can be
replaced by an equivalent circuit consisting of a voltage source VTh in series with
a resistor RTh, where VTh is the open-circuit voltage at the terminals, and RTh is
the input or equivalent resistance at the terminals when the independent sources
are all turned off.
i a i a
RTh
Linear
Circuit RL RL
DC VTh
b b
Rin Rin
46
Thevenin's Theorem
Thevenin’s theorem states that the two circuits given below are equivalent as seen
from the load RL that is the same in both cases.
i a
i a
RTh
Linear
RL RL
Circuit DC VTh
b b
Rin Rin
47
Thevenin's Theorem
i a i a
RTh
Linear
RL RL
Circuit DC VTh
b b
Rin Rin
RTh = Thevenin’s resistance = the input resistance with all independent sources
turned off (voltage sources replaced by short circuits and current sources
replaced by open circuits). This is the resistance seen at the terminals ab when
all independent sources are turned off.
48
Thevenin's Theorem
DC VTh 5V
b
a
2 10
DC
10V iSC 102 3 2.5A
2 4
3 b
a
2 2
b R 1 2
Th
22
55
b
56
57
Norton’s Theorem
RN RTh Rin
Norton equivalent circuit
Example
I N RN
=
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