Parallel R–L–C network behavior: When operating above its resonant frequency, a parallel RLC circuit most closely behaves like which simpler parallel network?

Introduction / Context:
A parallel RLC circuit has a resistor, inductor, and capacitor connected across the same AC source. Its overall behavior depends on frequency. Below, at, and above the resonant frequency, the net reactive effect (inductive or capacitive) changes. Knowing which tendency dominates above resonance helps in filter design and tuning.

Given Data / Assumptions:

• Ideal sinusoidal steady state.
• Elements R, L, and C are in parallel.
• Resonant frequency f0 where total susceptance is zero.

Concept / Approach:
For a parallel network, work with admittances: Y = G + jB. The susceptances are B_C = +ωC and B_L = −1/(ωL). At resonance, B_C + B_L = 0. When frequency increases above f0, B_C increases in magnitude (directly proportional to ω), while |B_L| decreases (inversely proportional to ω). The sum B = B_C + B_L becomes positive, meaning net capacitive behavior. Hence the circuit behaves like a parallel RC network as a first-order approximation.

Step-by-Step Solution:
Write susceptances: B_C = ωC, B_L = −1/(ωL).At f0: ω0C = 1/(ω0L) so B_C + B_L = 0.For f > f0: ω increases ⇒ B_C increases; 1/(ωL) decreases ⇒ |B_L| shrinks.Thus B = B_C + B_L > 0 ⇒ net capacitive.Therefore, the circuit resembles a parallel RC.

Verification / Alternative check:
Phasor diagram of branch currents shows the capacitive branch current dominating above f0, pulling total current to lead the voltage, which is the hallmark of capacitive behavior.

Why Other Options Are Wrong:
(a) Net inductive behavior occurs below resonance, not above. (c) While still an RLC, simplification to an equivalent RC captures the dominant effect. (d) Purely resistive occurs only at exact resonance (ideal case), not above it.

Common Pitfalls:
Confusing series and parallel resonance trends; assuming the same lead/lag rules apply in both topologies without checking susceptance signs.

Final Answer:
Parallel RC circuit (net capacitive behavior)