The superposition theorem states that the response in any element of a linear, bilateral network containing more than one independent source can be obtained as the algebraic sum of the response, obtained by each independent source acting separately at a time with all independent source set as zero.
In other or simpler words if several current or voltage source is acting simultaneously in a linear network the resultant current in any branch is the algebraic sum of the current that would be produced in it. When each source acts alone replacing other independent sources by their internal resistance.
Here independent voltage source is made short-circuited and independent current source if made open-circuited..
Note. while calculating, the direction of current should be taken care of with superposition theorem.
Also, the limitation of this theorem is that this theorem can only be used to calculate voltage and current of the circuit. This theorem cannot be used/applied to determine the power of the circuit. The reason for this is the relation between power and (voltage and current is quadratic).
Now to determine the power first voltage and current of the branch should be determined and then they should be used to determine power.
Theorem is important from the following two aspects.
A given response in a network that results from several independent sources may be calculated by summing the response of each individual source with all other sources made inoperative. It can also be called as the additive property linear network.
If all source are m multiplied by the same constant response available from the network is multiplied by the same constant. This describes the property of homogeneity. The only requirement for this is a linear network/system.
The network can be time-variant or invariant.
Steps for the solution of a network by using superposition theorem.
Select an independent source (it may be a voltage source/current source). and deactivate the other independent sources. Deactivating other sources by shorting the voltage source and opening the current sources. The obtain the branch current,
Repeat the above for steps for other independent sources.
Now to determine the net branch current, just add all current obtained from the above steps with their polarity. I.e. if the same direction then add and if opposite direction then subtract.
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