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Circuit Analysis: AC, Linear Circuits and Transients

A sinusoidal voltage of 100 V RMS is applied to a load consisting of a resistor R = 8 Ω in series with a coil of reactance X = 6 Ω. Which of the following is the active power of the load?

  1. A600 W
  2. B800 W
  3. C1,000 W
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Answer: B. 800 W

Method 1 (from the current): |Z| = √(8² + 6²) = 10 Ω, so I = 100/10 = 10 A, and the active power, consumed in the resistor, is P = I²R = 10² × 8 = 800 W. Method 2 (from the power factor): the power factor is cos φ = R/|Z| = 0.8, so P = VI cos φ = 100 × 10 × 0.8 = 800 W. Method 3 (complex power): S = V²/(conjugate of Z) = 10000/(8 − j6) = 800 + j600 VA, whose real part is 800 W. The coil's reactance consumes no power; 600 var of reactive power shuttles back and forth between it and the source.

  • A. 600 is I²X, the reactive power [var].
  • B. Correct. P = I²R = 800 W.
  • C. 1,000 is the apparent power VI [VA].
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