SUPERPOSITION THEOREM FOR ELECTRICAL CIRCUITS

1. Prepared by Dr. Sudheer
Electrical Science –I
Lecture 11
Superposition Theorem
T1(4.5)

2. Prepared by Dr. Sudheer
Electrical Circuit Theorems
• Superposition Theorem
• Thevenin's Theorem
• Norton's Theorem
• Maximum Power Transfer

3. Prepared by Dr. Sudheer
Electrical Circuit Theorems
• Superposition Theorem: The Superposition theorem states that in any network
containing more than one source, the current in, or the voltage across, any branch can
be found by considering each source separately and adding their effects: omitted
sources of e.m.f. are replaced by resistances equal to their internal resistances.
• Superposition theorem is applicable to linear circuits only and linear quantities only.
• Ex:- Superposition theorem is applicable to calculate current and voltage but not Power
in any branch ( since it is a non-Linear quantity: P =I2 R).
• The superposition states that the voltage across (or the 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.

4. Prepared by Dr. Sudheer
Not Considered sources/ Replacing with internal
resistances
a
b
s
i
s
i i

Current source:
We replace it by a current
source where 0
s
i 
Voltage source:
DC
+
-
s
v v

s
v
We replace it by a voltage
source where 0
s
v 
An short-circuit
i
An open-circuit

5. Prepared by Dr. Sudheer
Steps for Applying the Superposition Theorem
1. Consider one independent source and replace all other independent sources
with their internal resistances. Find the voltage or current in a branch due to the
active source only.
2. Repeat step 1 for each of the other independent sources.
3. Find the total voltage or current in a branch is calculated by algebraically sum
of all voltage or current obtained in steps 1 & 2.

6. Prepared by Dr. Sudheer
Calculate current using Superposition Theorem
Replacing the voltage
sources with
Their internal resistances

7. Prepared by Dr. Sudheer
Circuit1 Circuit2
A
i
I
A
i
I
A
i
A
i
i
i
b
b 214
.
3
;
57
.
3
214
.
3
;
57
.
3
0
10
20
18
18
19
1
2
1
1
2
1
2
1






























A
i
I
A
i
I
A
i
A
i
i
i
c
c 78
.
6
;
43
.
6
78
.
6
;
43
.
6
20
0
20
18
18
19
1
2
1
1
2
1
2
1

































A
I
I
A
I
I
I
A
I
I
I
c
b
c
b
7
.
0
56
.
3
86
.
2
566
.
3
78
.
6
214
.
3
86
.
2
43
.
6
57
.
3
2
1
2
2
2
1
1
1


















8. Prepared by Dr. Sudheer
DC
12V
 


3A
i
DC
24V
Calculate i using Superposition Theorem

9. Prepared by Dr. Sudheer
Considering 12 V alone
2
i
DC
12V
 


2
i
1
i
O.C.
A
i
i
A
i
A
i
i
i
2
2
;
5
.
0
12
0
7
4
4
16
2
1
2
1
2
1



























10. Prepared by Dr. Sudheer
Considering 24 V alone
A
i
i
A
i
A
i
i
i
1
1
;
75
.
1
0
24
7
4
4
16
2
'
'
2
1
2
1






























11. Prepared by Dr. Sudheer
Considering 3A alone
A
v
i
V
v
V
v
v
v
1
3
3
3
10
;
3
3
0
8
1
4
1
4
1
4
1
4
1
3
1
4
1
1
'
'
'
2
1
2
1

















































12. Prepared by Dr. Sudheer
DC
12V
 


3A
i
DC
24V
Calculate i using Superposition Theorem
A
i
i
i
i 2
1
1
2
'
'
'
'
'
'







A
i
i
i
A
i
A
i
A
i
i
i
i
i
i
i
2
)
3
(
1
1
;
5
.
2
3
12
3
7
4
24
4
4
16
3
2
2
1
3
3
2
1
3
2
1





















