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What is Superposition theorem?

The property that a voltage or current in a linear circuit with several sources equals the sum of the results obtained with one source acting at a time and the other independent sources set to 0 (voltage sources shorted, current sources opened). It follows from the linearity of the circuit, so it cannot be applied directly to power, which is proportional to the square of the current. Dependent sources are not set to 0 but kept as part of the circuit.

Japanese name: 重ね合わせの理

Superposition theorem appears in 4 practice questions across 1 topic, including Circuit Analysis: AC, Linear Circuits and Transients.

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Superposition theorem

In a linear circuit with two sources, which of the following cannot be found with the superposition theorem by applying the sources one at a time and adding the results?

  1. AThe power consumed in a resistor
  2. BThe current in a resistor
  3. CThe voltage of a node
Show answer and explanation

Answer: A. The power consumed in a resistor

The superposition theorem holds because voltages and currents are proportional to the sources (the circuit is linear). Power is proportional to the square of the current, so adding the powers due to each source is wrong. For example, if one source drives 1 A and the other 2 A in the same direction through a 1 Ω resistor, the correct power is (1 + 2)² × 1 = 9 W, but adding the separate powers gives 1 + 4 = 5 W. To find a power, first find the current by superposition and then square it.

Superposition theorem in the explanations

Questions that mention Superposition theorem (4)

  1. In a linear circuit with two sources, which of the following cannot be found with the superposition theorem by applying the sources one at a time and adding the results?
  2. In the circuit in the figure, E = 12 V, R1 = 4 Ω, R2 = 12 Ω and the current source is J = 2 A (flowing into node A). Which of the following is the voltage VA of node A with respect to ground?
  3. In the circuit in the figure, E = 12 V, R1 = 4 Ω, R2 = 12 Ω and J = 2 A. Which of the following correctly gives the magnitude and direction of the current in R1?
  4. In a linear resistive circuit whose only sources are two DC voltage sources E1 and E2, the voltage Vo across a resistor is measured. With E1 = 1 V and E2 = 0 V, Vo = 2 V; with E1 = 0 V and E2 = 1 V, Vo = −1 V. Which of the following is Vo when E1 = 3 V and E2 = 2 V?

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Related terms

Admittance Impedance Mesh analysis Nodal analysis Norton's theorem Partial fraction decomposition Phasor Q factor (quality factor) Reactance Reactive power

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