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Circuit Analysis: AC, Linear Circuits and Transients

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?

  1. A1 V
  2. B4 V
  3. C8 V
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Answer: B. 4 V

In a linear circuit the output can be written as a sum of terms proportional to each source, Vo = aE1 + bE2 (the superposition theorem and proportionality). The measurements give a = 2 and b = −1, so Vo = 2 × 3 + (−1) × 2 = 4 V. The answer follows from linearity alone, without knowing what is inside the circuit.

  • A. 2 + (−1) = 1 V just adds the two measured values without scaling each in proportion to the source size (3 times and 2 times).
  • B. Correct. Vo = 2E1 − E2 = 4 V.
  • C. This takes the term due to E2 as positive, giving 6 + 2 = 8 V.
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