Superposition Theorem
Uploaded by
truptiSuperposition Theorem
Uploaded by
truptiExperiment No.
01
AIM: Verification of Superposition Theorem in A.C. circuits.
APPRATUS:
Sr. No Name of the Equipment Specification Quantity
1. Superposition circuit kit R1=470Ω,R2=220Ω,R3=330Ω 1
V=(0-12V)
2. Digital Multimeter 1
3. DC Dual power Supply 30 V DC,2A 1
4. Connecting wires
SUPERPOSITION THEOREM STATEMENT: -
The Superposition Theorem can be used to analyze multi-source AC linear bilateral
networks.
It may be stated as follows.
In any multisource (containing initial condition energy sources of emf or current source)
complex network consisting of linear bilateral elements, the responses (loop current or node
voltage) caused by the individual sources of the network may be found by determining the
algebraic sum of the response (current) at that element while considering the effect of
individual source. The other ideal voltage sources are replaced by its internal resistance (or
by a short circuit) and ideal current sources in the network are replaced open circuit across
the terminals. This theorem is valid only for linear systems.
If the internal impedances of independent voltage sources are known then the sources are
replaced by a short circuit, while the independent current sources must replace by open
circuit.
If there are dependent current and voltage sources present in the circuit then they should not
be replaced by an open or short circuit. But they should kept as they are ,
Proof of Superposition theorem :
Consider a network shown in figure 1(a), having two voltage sources V1 and V2 .
Figure1(a) .When Both V1 and V2 Source are Active
Let us calculate current through branch AB by using Superposition theorem. According to
superposition theorem, consider each sources independently. Let source V1 0 0 V acting
independently. At this time other sources must be replaced by short circuit as shown in Figure
1(b).
I1' A I2'
470 I3' 220
330
10V
B
Figure1(b) .When V1 Source are Active
Now obtain the current through branch AB by using any law such as KVL,KCL etc.
And it is given by I’AB.
Now consider source E2 alone with E1 replaced by short circuit to obtain current
through branch AB The corresponding circuit is as shown in figure 1(c).Obtain I” AB due to
V2 alone by using any of the network techniques.
Figure1(c) .When V2 Source are Active
According to superposition theorem the total current through branch AB is algebraic sum
of current through branch AB produces by each source acting indendently that is
I330= I’3+I”3
Where IAB=Total current through branch AB.
I’3= Current due to V1 alone.
I”3= Current due to V2 alone.
Step to apply Superposition Theorem:-
1. Select single source alone .Short the other voltage sources and open the current
sources, if internal impedances are not known and if known replace these sources
with internal impedance.
2. Find the current through or the voltage across required element, due to these
sources under consideration using suitable network simplification technique.
3. Repeat above two steps for all the sources in the circuit.
4. Add all the individual current produce by individual sources to obtain current in
Sr. V1 = V; V2 = 0V V2 = V; V1 = 0V V1 = V; V2 =
No. I3’ (mA) I3’’ (mA) I3 = I3’ + I3’’ (mA)
Practical Theoretical Practical Theoretical Practical Theoretical
element or voltage across element.
Advantage:
1. It can be used for multi source complex networks consisting of linear bilateral
elements.
2. This method is used when there is more than one current or voltage source.
Disadvantage :
1. This method does not apply to the power circuit because power is proportional to
the square of the current which is not linear function.
2. Each source has some internal resistance due to which some errors are introduced.
Application:
1. This is applicable for only linear and bilateral circuits.
2. This can be used for DC as well as AC a circuit which is linear and bilateral.
Procedure :
1. As Shown in the circuit diagram, connect the circuit with the help of connecting
probes.
2. In first case consider two sources and apply 5 V DC to the kit by dual power
supply at the respective terminal. Measure the voltage across each resistor and
across R2 and find current through it.
3. Consider only one source and short other sources. Now measure voltage across
resistor and calculate current through it.
4. Similarly, short the first source and now second source should act. Measure
voltage across resistor and calculate current.
Observation Table:-
R1= R2= R3=
Calculations :
1. When V2 is Short circuited and V1 is open
2. When V2 is acting and V1 is Shorted.
3. When both V1 and V2 are acting.
Result Table:-
Sr.No Observed Values(mA) Calculated Values(mA)
Conclusion :-
Pre Lab Questions:-
1. State Superposition theorem?
2. How to find power using Superposition theorem?
3. Write applications of super position theorem?
Post Lab Question :-
1. Is it possible to apply Superposition theorem to nonlinear circuit?
2. Is it possible to apply Superposition theorem to ac as well as dc circuit?