15eee111-07 Superposition Theorem
15eee111-07 Superposition Theorem
15eee111-07 Superposition Theorem
The Superposition principal states that the voltage across (or current
through) an element in a linear circuit is the algebraic sum of the voltages
across (or current through) that element due to each independent source
acting alone.
1. Short ALL independent voltage sources and open ALL independent current
sources EXCEPT ONE source. Find the output (voltage or current) due to
that active source using a suitable method.
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.
EXAMPLE
SOLUTION
Since there are two sources , let
V= v1 +v2
Where v1 and v2 are the contributions due to the 6 v voltage source (acting
alone)and the 3 A current source(acting alone), respectively.
8 i1 + 4 i1 – 6 = 0
12 i1 = 6
I1 = 0.5 A
Thus v1 = 4 i1 = 4 × 0.5 = 2 V
Step 2 To obtain v2 set the voltage source to zero (short the 6V voltage
source) as shown below
Using current division formula, we get
I2 = × 3 = 2A
Thus v2 = 4 i2 = 4 × 2 = 8 V
V = v1 + v2 = 2 + 8 = 10 V
EXAMPLE
SOLUTION
Where v1 and v2 are the contributions due to the 10 v voltage source and
the 1 A current source, respectively.
I = = 1A
V1 = I × 3 = 1 × 3 = 3 V
Step 2 To obtain v2 set the voltage source to zero (short the 10V
voltage source) as shown below
V = v1 + v2 = 3 + 1.5 = 4.5 V
EXAMPLE
SOLUTION
below
I1 = 10 A --------------------------------------------(1)
3 I2 + 6(I2 - I1 ) + 30 ( I2 - I3 ) = 0
39 I2 - 30 I3 = 60 ---------------------------------(2)
12 ( I3 - I1 ) + 30 ( I3 - I2 ) = 0
I2 = 8.29 A i3 = 8.78 A
EXAMPLE
Use superposition theorem to find power across 3 Ω resistor (all R are in Ω) in the
circuit given below.
SOLUTION
= 2 Ω. This gives us
I20V = = 4A
Now consider 15A source (lower) alone, the circuit reduces to circuit 1
and 2 as shown below.
I3Ω = I20V + I15A Upper + I15A Lower = (4 + 4 – 2)A = 6A(2A is minus because
this current is in opposite direction to the other two currents)