The superposition theorem is used in theoretical circuit analyis.
Linear electrical circuit analysis is simplified by the application of various rules and theorems. Providing the foundation to the other theorems and insight into the behavior of a circuit is the Superposition Theorem. This theorem yields a particular linear response, such as the voltage or current in a linear circuit, by requiring the algebraic summing of the individual responses arising from sources viewed independently. In practice, this means that a linear response in the circuit is calculated using only one source at a time and those results are added to give the overall linear response from all the sources.
Instructions
1. Check that the circuit schematic you are analyzing has multiple independent voltage or current sources connected in series or parallel. For example, a simple series circuit with one resistor R1 and two batteries, V1 and V2, qualifies as having multiple independent sources (V1 and V2) and will benefit from analysis using the application of the Superposition Theorem.
2. Identify all the sources (for example, batteries) in the circuit and label these, if these sources are not already labeled in the circuit diagram. For example, use V1, V2 and V3 if there are three batteries in the circuit.
3. Calculate the potential difference over, and the current through, each resistor in the circuit with the contribution of only one independent source. For example, in the simple series circuit with only one resistor R1, and sources V1 and V2, keep V1 as part of the circuit and remove the influence of V2 by shorting it out. Label the current flowing through the resistor as I1. The potential difference over R1 is then V1 = R1 x I1. The current through the resistor I1 = V1/R1. Typically, all the voltage sources not being used are replaced by short circuits and all current sources are replaced by open circuits.
4. Continue this procedure by changing the source that remains active and eliminating the influence of all other sources in the circuit. For example, in the simple series circuit with only one resistor R1, and sources V1 and V2, retain V2 as part of the circuit and remove the influence of V1. The current flowing through R1 is now I2, and I2 = V2/R1.
5. Apply the Superposition Theorem to obtain the total current flowing through the resistor. The total current flowing through the resistor is the sum of the individual currents flowing through the resistor. For example, in the simple series circuit with components R1, V1 and V2, the total current flowing through the resistor R1 is I(total) = I1 + I2 = V1/R1 + V2/R1 = (V1 + V2)/R1.
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