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.

ɱ ϵ ∫ #  a Na [ y ∫ ǃ ∫

                

MESH- a loop which does not contain any other loop.

            Kirchhoff’s Voltage Law is the basis of mesh analysis. Like nodal analysis, mesh analysis is also used in analyzing AC circuits. It also provides another general procedure for analyzing circuits using mesh currents as the circuit variables. Using mesh currents as circuit variables is more convenient than using element currents because through this, it lessens the number of equations to be solved. Keep in mind that mesh analysis is only applicable to a planar circuit that’s why it is not that general as the nodal analysis.

            There are also circuits containing supermesh which doesn't have current of its own and two meshes shares in one current source.

            For further understanding of MESH analysis, see sample problem below on how to get equations from a given circuit.

                     EQUATION:

             I've learned that in mesh analysis, we must first assign mesh currents in a given circuit but it is also necessary to apply some strategies that could simplify the circuit to lessen the number of mesh currents and to come out in a few number of equations. There were also some circuits that fit the case 1 in which the current source existing only in one mesh is already the current of that mesh. For me, mesh analysis is convenient to use if current is unknown. If ever voltage is the unknown and we are asked to use mesh analysis. It is also easy to solved by just applying Ohm's Law.