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Fakulti Kejuruteraan Elektrik
CIRCUIT THEOREMS
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Superposition
Thevenin’s
Norton’s
Source Transformation
Fakulti Kejuruteraan Elektrik
CIRCUIT THEOREMS
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Circuits can be analysed using Kirchhoff’s laws
without
tampering
with
their
original
configurations.
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However, for complex and large circuits, using
kirchhoff’s laws will be tedious.
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Thus circuit theorems can be used to simplify
circuit analysis.
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It is the property of an element describing a linear
relationship between cause and effect.
A linear circuit is one whose output is linearly
related (or directly proportional) to its input.
A circuit is said to be linear if it is both additive
and homogenous. A linear circuit consists of only
linear elements, linear dependent sources and
independent sources.
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Homogeneity property requires that if an input is
multiplied by a constant, then the output is
multiplied by the same constant
v=iR

→
kv=kiR
Additivity property requires that the response to a
sum of inputs is the sum of the responses to each
input applied separately.
v1 = i1 R and v2 = i2 R
→ v = (i1 + i2) R = v1 + v2
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Example 4.1
Find I0 when vs = 12 V and vs = 24 V
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Example 4.1
Assume I0 = 1 A, use linearity to find the actual value of I0
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Practice Problem 4.1
Find vo when is = 15 A and is = 30 A
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Practice Problem 4.2
Assume that V0 = 1 V and use linearity to calculate the actual
value of V0 in the circuit below
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Problem 4.4
Use Linearity to determine i0
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Problem 4.5
Assume V0 = 1 V, use linearity to find the actual value of V0
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It states that the voltage across (or current
through) an element in a linear circuit is the
algebraic sum of the voltage across (or currents
through) that element due to EACH independent
source acting alone.
The principle of superposition helps us to analyze a
linear circuit with more than one independent
source by calculating the contribution of each
independent source separately.
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Steps to apply superposition principle
1. Turn
off all independent sources except one
source. Find the output (voltage or current)
due
to that active source using nodal or
mesh
analysis.
2. Repeat step 1 for each of the other independent
sources.
3. Find the total contribution by adding algebraically
all the contributions due to the independent
sources.
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Two things have to be kept in mind:
1.
2.
When we say turn off all other independent
sources:
 Independent voltage sources are replaced by
0 V (short circuit) and
 Independent current sources are replaced by
0 A (open circuit).
Dependent sources are left intact because they are
controlled by circuit variables.
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Example 4.3
Use the superposition theorem to find v
in the circuit shown below.
3A is discarded by
open-circuit
6V is discarded
by short-circuit
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Practice Problem 4.3
Use the superposition theorem to find v0 in the circuit shown
below.
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Example 4.4
Use the superposition theorem to find i0 in the circuit shown below.
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Practice Problem 4.4
Use the superposition theorem to find Vx in the circuit shown
below.
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Example 4.5
Use the superposition theorem to find i in
the circuit shown below.
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Practice Problem 4.5
Find I in the circuit below using superposition
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Problem 4.11
Use superposition principle to find i0 and v0 in the circuit below
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Practice Problem 4.15
Use superposition to find i. Calculate the power delivered to the 3-ohm resistor
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Practice Problem 4.16
Find io in the circuit below using superposition
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