Electrical Engineering ⇒ Topic : Superposition Theorem with d.c

Superposition Theorem

The superposition theorem states that in any linear network containing two or more sources, the response in any element is equal to the algebraic sum of the responses caused by individual sources acting alone, while the other sources are non-operative; that is, while considering the effect of individual sources, other ideal voltage sources and ideal current sources in the network are replaced by short circuit and open circuit across their terminals. This theorem is valid only for linear systems. This theorem can be better understood with a numerical example.

  Consider the circuit which contains two sources as shown in Fig. (a).Now let us find the current passing through the 3Ω resistor in the circuit.According to superposition theorem, the current I₂ due to the 20V voltage source with 5 A source open circuited = 20/(5 + 3) = 2.5 A. See Fig. (2)

    The current 15 due to 5 A source with 20V source short circuited is

                                                          figure (a)

                                                           figure (b)

The total current passing through the 3 Ω resistor is

                   (2.5 + 3.125) = 5.625 A

Let us verify the above result by applying nodal analysis

The current passing in the 3Ω resistor due to both sources should be 5.625 A.

Applying nodal analysis to Fig.(d),we have

                                       figure (c)

                                         figure (d)

So the superposition theorem is verified.

Let us now examine the power responses.

Power dissipated in the 3Ω  resistor due to voltage source acting alone

We can, therefore, state that the superposition theorem is not valid for power responses. It is applicable only for computing voltage and current responses.