Question
What is the magnitude of the impedance of a parallel RLC circuit at resonance?
Answer Options
- A) Approximately equal to circuit resistance
- B) Approximately equal to inductive reactance
- C) Low compared to the circuit resistance
- D) High compared to the circuit resistance
Correct Answer: D
Explanation
In a parallel RLC circuit, the individual currents flowing through the inductor (L) and the capacitor (C) are almost exactly 180 degrees out of phase with each other. At the resonant frequency, X_L = X_C, meaning the current flowing through the inductor is exactly canceled by the current flowing through the capacitor.
Since the parallel LC combination acts as an extremely high impedance (theoretically infinite, neglecting component losses) due to the reactive currents cancelling, the total impedance is dominated by the only component that is left: the parallel resistor (R). This means the magnitude of the impedance of a parallel RLC circuit at resonance is at its maximum value and is high compared to the circuit resistance (if the resistor is assumed to be the loading resistance). The actual parallel resonant impedance is given by Z_P \approx Q \times X_L or, more simply, the equivalent resistance of the network, which is much higher than the resistance of the components themselves.
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