Parallel RLC fundamentals: which statement best characterizes voltages and currents in a parallel RLC circuit driven by an AC source?

Introduction / Context:In a parallel RLC circuit, the resistor, inductor, and capacitor are each connected across the same two nodes. Understanding how voltage and current distribute among the branches is essential for analyzing impedance, resonance, and power factor in AC circuits.

Given Data / Assumptions:

• Parallel configuration of R, L, and C across a single AC source.
• Linear, time-invariant components; sinusoidal steady state.
• Ideal elements unless otherwise noted.

Concept / Approach:

• In parallel, the voltage across each branch equals the source voltage. Therefore the voltage amplitude and phase are identical for all branches relative to the source.
• Branch currents depend on each element's admittance; they typically differ in amplitude and phase from one another and from the source current.
• Source (applied) current equals the phasor sum of branch currents, not simply their arithmetic sum in magnitude.

Step-by-Step Reasoning:

Verification / Alternative check:

Why Other Options Are Wrong:

• The sum of the current is always less than the applied current: Applied (source) current equals the phasor sum of branch currents; magnitudes do not obey a simple 'less than' rule.
• The current waveform for each component… same amplitude/phase as applied current: False; branch currents have different magnitudes/phases based on R, L, and C.
• All of the above: Cannot be true because the preceding statements are not both correct.
• None of the above: Incorrect because the voltage statement is correct.

Common Pitfalls:

• Confusing series and parallel properties: in series, current is common; in parallel, voltage is common.
• Adding current magnitudes instead of phasors, leading to wrong totals.

Final Answer: