SUPERPOSITION THEOREM:
Definition:
Statement:
The principle of Superposition theorem is “The voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across that element due to each independent source acting alone. To evaluate the separate currents to be combined, replace all other voltage sources by short circuits and all other current sources by open circuits.
Properties:
Definition:
- In a linear network with several independent sources, the responce in a particular branch when all the sources are acting simultaniously is equal to the linear sum of individual responces calculated by taking one independent source at a time.
- All the ideal voltage sources are eliminated from the network by shorting the sources, all the ideal current sources are eliminated from the network by opening the sources and do not disturb the dependent sources present in the network.
Statement:
The principle of Superposition theorem is “The voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across that element due to each independent source acting alone. To evaluate the separate currents to be combined, replace all other voltage sources by short circuits and all other current sources by open circuits.
Properties:
- This theorem is applicable only to linear networks i.e. the networks with R, L,C, transformer and linear controlled sources as elements.
- thepresence of dependent sources makes the network an active and hence SPT is used for both active as well as passive networks
Superposition theorem problem:
* Find v in the circuit in figure 1 using superposition theorem.
Let, v1 and v2 are the contributions of two sources 12V voltage source and 6A current source. According to linearity we can write,
v = v1 + v2
As per rule we will find only one independent contribution at a time and we set the all sources turned off. To obtain v1 we set current source open circuit or 0A as figure 2 circuit.
Applying KVL we get in the loop,
-12 + 16i1 + 8i1 = 0
or i1 = 0.5A
So, v1 = i18 = 4V
We can find out the value of v1 using voltage divider rule,
v1 = {8/(16+8)} 12 = 4V
To obtain v2, we set voltage source short circuit as figure 3 or 0V.
Now using current divider rule we can find i3,
i3 = {16/(8+16)} 6 = 4A
Thus, v2 = 8i3 = 32V
Finally, v = v1 + v2 = 4 + 32 = 36V
In this way we find voltage or current for a specific resistance for linear circuit.
What Is Superposition Theorem
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