Superposition theorem:
The superposition theorem is applicable for linear networks, that is, R, L, C.
In a linear network with more independent sources acting simultaneously, the response in a particular branch is the algebraic sum of the individual response calculated by treating one independent source at a time.
Here the voltage source should be short-circuited and the current source should be open-circuited.
Instead of using nodal and mesh analysis, we can proceed with this method to easily find out the current flowing through any of the resistors.
Two steps are to be followed to solve the circuits using the superposition theorem.
The first step is to short circuit the independent voltage source and find the current through the respective resistor.
The second step is to open the circuit to the independent current source to find the current flowing through the same resistor.
Then summation of the currents from the previous steps will provide the expected results.
Consider the following linear circuit as shown in the figure.
We have to find the current flowing through the resistor R2 using superposition theorem and also compare it with by solving using any of the methods like nodal, mesh analysis also provides us the same results.
Now let us know about the superposition theorem using this example.
We don't have any dependent sources here.
So we can simply short circuit the independent voltage source and find the current for each response The summation of both the currents provides us the expected results.
Therefore in a simple equation,
In the first step, we will short circuit the independent voltage source, therefore we get the circuit as shown in the figure. As V = 0,
To find the current flowing through the resistor R2, we apply the current division rule so we get
Therefore the summation of both the currents,
Problems with Superposition theorem:
Let us have a look at this problem, where we have to find the current flowing through the resistor.
Instead of using nodal and mesh analysis. We can use the superposition theorem to solve it in a minute.
Keep one independent source alone and the remaining sources should be short-circuited if voltage source and open-circuited if in case of the current source.
Keeping independent voltage source and open circuiting the independent current sources.
Step 1:
Here it is trivial from the circuit that the negative terminal of the voltage is not connected to the circuit and it is an open path.
So, I = I1 = 0 A .
Step 2:
Keeping 1A independent current source and short-circuiting the independent voltage source and open circuiting the independent current source.
Applying the current division rule, we get ,
After the summation of all the three currents, we get the expected result.
