Example of superposition theorem

Example

Calculate the current  flowing through the resistor 3Ω as shown in fig.(a), using the superposition theorem

                                                     (a)

Solution:

Assume that the current source 3 A is acting alone in the circuit and the internal resistances replace the other sources. The current flowing through 3Ω resistor can be obtained from fig(b).

and it is given by

Current flowing through 3Ω resistor due to 2V source (only) can be obtained from fig(c)

                                               (c)

and it is seen from no current is flowing

Current through 3Ω resistor due to 1V voltage source only (see fig.(d)) is given by

(d)

Current through 3Ω resistor due to 3 A current source only (see fig(e)) is obtained by

                                   (e)

Current through 3Ω resistor due to 2V voltage source only (see fig.7.3(f)) is given by

                                       (f)

Resultant current  flowing through 3Ω resistor due to the combination of all sources is obtained by the following expression (the algebraic sum of all currents obtained in eqs with proper direction of currents)