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Circuit Analysis: AC, Linear Circuits and Transients

In the parallel RLC circuit in the figure, the source frequency is set to the resonant frequency f0 = 1/(2π√(LC)). Which of the following correctly describes the circuit?

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. AThe impedance seen from the source is at its minimum, and the current drawn from the source is at its maximum
  2. BThe current drawn from the source leads the source voltage by 90°
  3. CThe currents in L and C cancel, so the current drawn from the source is only the current in R and is at its minimum
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Answer: C. The currents in L and C cancel, so the current drawn from the source is only the current in R and is at its minimum

Method 1 (admittance): the admittance of the parallel circuit is Y = 1/R + j(ωC − 1/(ωL)); at f0 the imaginary part becomes 0 and |Y| takes its minimum value 1/R. The impedance takes its maximum value R, and the source current V/R is at its minimum and in phase with the voltage. Method 2 (phasor diagram): at f0, IL and IC are equal in size and opposite in direction, so they cancel and only IR remains in the source current. A large current circulates between L and C but is invisible to the source, which is why parallel resonant circuits are used as tank circuits that pick out a particular frequency.

  • A. This describes series resonance. At parallel resonance the impedance is at its maximum and the source current at its minimum.
  • B. At resonance the currents in L and C cancel, so the source current is in phase with the voltage.
  • C. Correct. At parallel resonance the source current is only IR and is at its minimum.
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