EE2010 Fundamentals of Electric
Circuits
Lecture 09
Network Theorems
Introduction
A large
complex circuits
Simplify
circuit analysis
Circuit Theorems
‧Thevenin’s theorem
‧ Superposition
‧ Norton theorem
‧ max. power transfer
linear circuit
A linear circuit is one whose output is linearly
related (or directly proportional) to its input
Superposition principle
The superposition principle states that the voltage
across (or current through) an element in a linear
circuit is the algebraic sum of the voltages across (or
currents through) that element due to each
independent source acting alone.
Turn off, killed, inactive source:
 independent voltage source: 0 V (short circuit)
 independent current source: 0 A (open circuit)
Dependent sources are left intact.
Superposition principle
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.
 Turn off voltages sources = short voltage sources; make it
equal to zero voltage
 Turn off current sources = open current sources; make it
equal to zero current
 Superposition involves more work but simpler circuits.
 Superposition is not applicable to the effect on power.
Superposition principle
Removing the effect of ideal sources
Voltage source is
replaced by a S/C
Removing the effect of practical sources
Current source is
replaced by a O/C
Superposition principle
Dependent Source
(a) Dependent Voltage Source
A voltage source whose parameters are controlled by voltage/current
else where in the system
v = ρix
v = µVx
CDVS
VDVS
(Current Dependent
(Voltage Dependent
Voltage source)
Voltage source)
(b) Dependent Current Source
A current source whose parameters are controlled by voltage/current
else where in the system
v = βix
v = αVx
CDCS
VDCS
(Current Dependent
(Voltage Dependent
Current source)
Current source)
For Superposition, All dependent sources must be left intact!!
You can’t apply O/C and S/C on dependent sources
Example -1
Using the superposition theorem, determine current
I1 for the network in Fig.
Solution: Since two sources are present,
there are two networks to be analyzed.
First let us determine the effects of the
voltage source by setting the current
source to zero amperes as shown in Fig.
Example -1
Since I1’ and I1’’ have the same defined
direction, the total current is defined by
The voltage source is in parallel with the current source and load
resistor R1, so the voltage across each must be 30 V. The result is
that I1 must be determined solely by
Example -2
Using the superposition theorem, determine the current
through the 12Ω resistor in Fig.
Considering the effects of the 54 V
source requires replacing the 48 V
source by a short-circuit equivalent
as shown in Fig. The result is that
the 12Ω and 4Ω resistors are in
parallel.
Example -2
The total resistance seen by the source is
and the source current is
Using the current divider rule results in the contribution to I2 due
to the 54 V source:
Example -2
The total resistance seen by the 48 V source is
Applying the current divider rule results in
Example -3
Use the superposition theorem to find v in the
circuit in Fig.
13
Example -3
Since there are two sources,
let
v  v1  v2
Voltage division to get
v1 
4
(6)  2V
48
Current division, to get
Hence
8
i3 
(3)  2A
48
v2  4i3  8V
And we find
v  v1  v2  2  8  10V
14
Example -4
a. Using the superposition theorem, determine
the current through resistor R2 for the
network in Fig.
b. Demonstrate that the superposition theorem
is not applicable to power levels.
Example -4
Solutions:
(a) Simple series circuit with a current equal to
Parallel combination of resistors R1 and
R2. Applying the current divider rule
The total solution for current I2 is the
sum of the currents established by the two
sources.
Example -4
(b) The power delivered to the 6 Ω resistor is
Using the total resultant current
Example -5
Using the principle of superposition, find the
current l2 through the 12 k resistor in Fig.
Example -5
Solution:
Considering the effect of the 6 mA current source
Current divider rule:
Example -5
Considering the effect of the 9 V voltage source