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Circuit Analysis: AC, Linear Circuits and Transients

In the parallel RLC circuit in the figure, the RMS currents in the resistor R, the coil L and the capacitor C are IR = 4 A, IL = 5 A and IC = 2 A. Which of the following is the RMS value of the current I drawn from the source?

Parallel RLC circuit driven by a sinusoidal AC source V I IR IL IC R L C Y = 1/R + j(ωC − 1/(ωL))
Parallel RLC circuit driven by a sinusoidal AC source · View in diagrams
  1. A5 A
  2. B7 A
  3. C11 A
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Answer: A. 5 A

Method 1 (complex numbers): taking the source voltage as the reference, IR is in phase, IL lags by 90° and IC leads by 90°, so I = 4 − j5 + j2 = 4 − j3 A. Its magnitude is √(4² + 3²) = 5 A. Method 2 (phasor diagram): IL and IC point in opposite directions, so only their difference of 3 A remains, and it combines at a right angle with the 4 A of IR to form a 3-4-5 right triangle. I lags the voltage by about 36.9°, and the circuit as a whole is inductive.

  • A. Correct. |4 − j3| = 5 A.
  • B. 4 + 5 − 2 = 7 A accounts for IL and IC cancelling, but adds the magnitudes while ignoring that IR is at a right angle to them.
  • C. This simply adds the magnitudes of the three currents. Currents with different phases must be added as phasors (vectors).
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