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:
Use the parallel rule: V_R = V_L = V_C = V_source (same amplitude and phase).Determine branch currents: I_R = V/R (in phase with V); I_L = V / jX_L (lags V by 90° as current lags voltage in an inductor); I_C = V * jωC (leads V by 90°).Compute total current: I_source is the vector (phasor) sum of I_R, I_L, and I_C.
Verification / Alternative check:
At resonance (ωL = 1/ωC), I_L and I_C can be large and cancel in phasor sense, while the voltage across every branch remains equal to the source voltage.
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:
The voltage waveform for each component always has the same amplitude and phase as the applied voltage
Discussion & Comments