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Electric Circuits I “Dr. Ahmed El-Shenawy”
Electrical Circuits I
Lecture 7
<Dr Ahmed El-Shenawy>
Electric Circuits I “Dr. Ahmed El-Shenawy”
Superposition Theory
 Whenever a linear system is excited, or driven, by more than one
independent source of energy, the total response is the sum of the individual
responses.
An individual response is the result of an independent source acting alone.
Because we are dealing with circuits made up of interconnected linearcircuit elements, we can apply the principle of superposition directly to the
analysis of such circuits when they are driven by more than one independent
energy source
Electric Circuits I “Dr. Ahmed El-Shenawy”
The superposition principle states that the voltage across (or current through)
an element in a linear circuits is the algebraic sum of the voltage across (or
current through) that element due to each independent source acting alone.
Step to apply:
1- Turn off all independent sources except one source. Find the required
(voltage or current) due to that active source.
Current Source  open circuit(0 A)
Voltage Source  short circuit (0 V)
2- Repeat step 1 for each other independent sources.
3- Find the total contribution by adding algebraically all the contribution due
to the independent source.
Electric Circuits I “Dr. Ahmed El-Shenawy”
Consider only the voltage source E1
Electric Circuits I “Dr. Ahmed El-Shenawy”
Consider only the current source I
i1  i11  i12
i 2  i 21  i 22
i3  i31  i32
i 4  i 41  i 42
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example:
Use the principle of superposition to find vo in the circuit shown.
Electric Circuits I “Dr. Ahmed El-Shenawy”
Example:
Use the principle of superposition to find the current io in the circuit shown.