SUPERPOSITION THEOREM

WHAT IS THE PRINCIPLE OF SUPERPOSITION?

            The principle of superposition states that the voltage across or the current through an element in a linear circuit is the algebraic sum of the voltages or the current through that element due to each independent source acting alone.

            There’s a lot of theorems we’ve been discussed in Circuits 1 and one of those is the superposition theorem in which it is not only applicable to dc circuit but also in an ac circuit. If a given circuit has two or more independent source, one way to determine the value the specific variable is to add up the contribution of each source.

IMPORTANT POINTS TO REMEMBER:

·         Superposition theorem cannot be applied if there’s only one source.

·         We only consider one independent source at a time.

·         Dependent source are left.

HOW TO APPLY SUPERPOSITION IN A GIVEN CIRCUIT?

·         Deadened all independent sources except one source. Then, determine the value of the required circuit variable.

·         Repeat first step in each other sources.

·         Add up the contributions of each independent source.

Voltage source (short circuit)

Current source (open circuit)

MAKE USE OF THE EXAMPLE BELOW:

           This problem is taken from the book of Alexander Sadiku

              (Fundamentals of Electric Circuits)

                                                FINAL ANSWER

            I’ve learned that in ac analysis using superposition theorem that we must add up the responses due to the individual frequencies in the time domain if the sources of the given circuit is operating at different frequencies. It is in the sense that the impedances depend on the frequency. I f a given circuit is composed of two ac sources with different frequencies and a dc source; the final answer would be in three terms. Note that in dc, capacitors act as an open circuit while inductors act as short circuit.