- 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.
Let us understand the statement.
Here, two 1.5 Volt batteries present in the circuit. At this condition, the current through 1 ohm resistance is 1.2 ampere.
The ammeter indicates this value in the above picture.
Now, we replace the left side battery by a short circuit as shown. In this case the current flowing through the 1 ohm resistance is 0.6 ampere. The ammeter indicates this value as shown in the picture above.
Now, we replace the right side battery by a short circuit as shown. In this case the current flowing through the 1 ohm resistance is also 0.6 ampere. The ammeter indicates this value as shown in the picture above.
1.2 = 0.6 + 0.6
Therefore, if we connect a branch of an electrical circuit with multiple voltage and current sources, the total current through this branch is the sum of the individual currents from each source. This principle is known as the Superposition Theorem.
Instead of having two sources as shown above, there are n number of sources acting in a circuit due to which I current flows through a particular branch of the circuit.
If someone replaces all the sources from the circuit by their internal resistance except first source which is now acting along in the circuit and giving current I1 through the said branch, then he reconnects the second source and replaces the first source by its internal resistance.
Now the current through that said branch for this second source alone can be assumed I2.
Similarly, if he reconnects the third source and replaces the second source by its internal resistance. Now the current through that said branch for this third source, alone is assumed I3.
Similarly, when nth source acts alone in the circuit and all other sources are replaced by their internal electrical resistances, then said In current flows through the said branch of the circuit.
Now according to Superposition theorem, current through the branch when all the sources are acting on the circuit simultaneously, is nothing but summation of these individual current caused by individual sources acting alone on the circuit.
Electrical sources can be voltage source or current source. When removing a voltage source, replace it with a short circuit or its internal resistance to maintain zero electric potential difference. Removing a current source means replacing it with an open circuit or its internal resistance, as zero current implies an open circuit. For the superposition theorem, voltage sources are replaced by short circuits, and current sources are replaced by open circuits.
This theorem only applies to linear circuits, where Ohm’s law is valid. It does not work for circuits with non-linear resistances like thermionic valves or metallic rectifiers. Though more laborious than other methods, the superposition theorem avoids solving simultaneous equations. With practice, equations can be written directly from the circuit diagram, saving time. Here are the steps to apply the Superposition Theorem:
Step – 1
Replace all but one of the sources by their internal resistances.
Step – 2
Determine the currents in various branches using simple Ohm’s law.
Step – 3
Repeat the process using each of the sources turn – by turn as the sole source each time.
Step – 4
Add all the currents in a particular branch due to each source. This is the desired value of current at that branch when all the sources acting on the circuit simultaneously.
Example of Superposition Theorem
Suppose there are two voltage sources V1 and V2 acting simultaneously on the circuit.
Because of these two voltage sources, say current I flows through the resistance R.
Now replace V2 by short circuit, keeping V1 at its position and measure current through the resistance, R. Say it is I1.
Then replace, V1 by short circuit, reconnect V2 to its original position and measure current through the same resistance R and say it is I2.
Now if we add these two currents, I1 and I2 we will get the current which is equal to the current – was actually flowing through R, when both voltage sources V1 and V2 were acting on the circuit simultaneously. That is I1 + I2 = I.
