- Superposition Theorem Definition: The superposition theorem is defined as a method to find the total current in a branch by summing the currents from each source acting alone.
- Voltage Sources: Replace voltage sources with short circuits or their internal resistance when removing them from the circuit.
- Current Sources: Replace current sources with open circuits or their internal resistance when removing them from the circuit.
- Linear Circuit Requirement: The theorem applies only to linear circuits where Ohm’s law is valid.
- Application Steps: The steps include replacing all but one source by their internal resistances, calculating currents, repeating for each source, and summing the currents for the total effect.
The Superposition Theorem says that when several sources act at once, the current in any branch is the sum of the currents that each source would produce alone.
The next figures apply that rule to two 1.5 volt batteries. With both sources active, the current through the 1 ohm resistance is 1.2 ampere.
The ammeter shows that value in the picture above.
Replace the left-hand battery with a short circuit as shown. The current through the 1 ohm resistance is then 0.6 ampere. The ammeter shows that value in the picture above.
Replace the right-hand battery with a short circuit as shown. The current through the 1 ohm resistance is again 0.6 ampere. The ammeter shows that value in the picture above.
1.2 = 0.6 + 0.6
So in an electrical circuit with several voltage and current sources, the total current in a branch is the sum of the currents from each source acting alone. That result is the Superposition Theorem.
The same rule holds when n sources produce current I in one branch.
Leave the first source in place and replace every other source by its internal resistance. The first source acting alone then produces I1 in that branch. Next reconnect the second source and replace the first source by its internal resistance.
The second source acting alone produces I2 in the same branch.
Reconnect the third source and replace the second source by its internal resistance. The third source acting alone produces I3.
When the nth source acts alone and every other source is replaced by its internal electrical resistances, the branch current is In.
By the Superposition theorem, the branch current with every source active is the algebraic sum of those individual currents.
An independent source may be a voltage source or a current source. To deactivate a voltage source, replace it with a short circuit or its internal resistance so the electric potential difference is zero. To deactivate a current source, replace it with an open circuit or its internal resistance, because zero current is an open path. In the ideal case used here, voltage sources become short circuits and current sources become open circuits.
The theorem applies only to linear circuits, where Ohm’s law holds for the resistances. It does not apply to circuits with non-linear resistances such as thermionic valves or metallic rectifiers. The method takes more drawings than some other solutions, but it avoids a simultaneous-equation set. With practice the branch equations can be written from the diagram. Apply the Superposition Theorem as follows:
Step – 1
Replace every source except one by its internal resistance.
Step – 2
Find the branch currents from Ohm’s law.
Step – 3
Repeat the same steps with each remaining source acting alone in turn.
Step – 4
Add the currents found in that branch for every source. The sum is the branch current when all sources act together.
Example of Superposition Theorem
Suppose two voltage sources V1 and V2 act together on the circuit.
Those two sources send current I through resistance R.
Short V2, leave V1 in place, and measure the current through resistance R. Call it I1.
Then short V1, restore V2, and measure the current through the same resistance R. Call it I2.
The sum of I1 and I2 equals the current that flowed through R while V1 and V2 were both active. So I1 + I2 = I.
