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Circuit Analysis: AC, Linear Circuits and Transients

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
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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.

  • A. Correct. Power is proportional to the square of the current and is not linear.
  • B. Current is proportional to the sources, so it can be found by superposition.
  • C. Node voltages are also proportional to the sources, so they can be found by superposition.
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