In AC circuit theory, consider a parallel R–C (resistor–capacitor) network connected to a single AC source. Which statement best describes the voltage distribution and phase in such a parallel RC circuit?
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AThe voltage always has the same amplitude and phase at every parallel branch (same node voltage).
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BThe total source voltage equals the sum of the voltages across the resistor and the capacitor.
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CThe total voltage leads the total current by less than 90 degrees.
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DThe total voltage is less than the sum of the voltages across the resistor and the capacitor.
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ENone of the above
Answer
Correct Answer: The voltage always has the same amplitude and phase at every parallel branch (same node voltage).
Explanation
Introduction / Context:A key property of parallel AC networks is that all components connected across the same two nodes share exactly the same voltage waveform. In a parallel R–C circuit, the resistor current is in phase with the voltage, while the capacitor current leads the voltage by 90 degrees. This question probes whether you remember that voltage in parallel is common, whereas current divides with different phase angles.
Given Data / Assumptions:
- Ideal sinusoidal steady-state conditions.
- Ideal components (R and C) connected in parallel to a single AC source.
- No parasitic wiring impedance considered.
Concept / Approach:By definition of parallel circuits, each branch is connected to the same pair of nodes; therefore, the branch voltages are equal in amplitude and phase to the source voltage. The branch currents differ in amplitude and phase due to the elements’ impedances: I_R is in phase with V, and I_C leads V by 90 degrees. The vector sum of these branch currents gives the total current, which leads V by some angle between 0 and 90 degrees; however, the voltage itself does not lead the current in this case—rather, it lags the leading current.
Step-by-Step Solution:Identify topology: R and C in parallel across the same source nodes.Apply the parallel rule: V_R = V_C = V_source in both amplitude and phase.Determine currents: I_R in phase with V; I_C leads V by 90 degrees.Infer total current: I_total leads V by an angle between 0 and 90 degrees due to capacitive branch.Conclude: Voltage is common to branches; therefore option (a) is correct.
Verification / Alternative check:Use phasor analysis: V is the reference phasor. I_R = V/R (angle 0), I_C = V/X_C (angle +90). Since both currents derive from the same V phasor, branch voltages necessarily match the source exactly.
Why Other Options Are Wrong:(b) Summing voltages branch-wise is a series rule, not parallel. (c) Reverses the lead/lag: in RC parallel, current leads voltage, not the other way. (d) Implies a series-like relationship, which is inapplicable in parallel networks.
Common Pitfalls:Confusing series and parallel rules; assuming voltage division in parallel; mixing up whether voltage or current leads in capacitive circuits.
Final Answer:The voltage always has the same amplitude and phase at every parallel branch (same node voltage).