Series RC circuit fundamentals: Which statement correctly describes the current behavior throughout a series RC circuit driven by a single source?

Introduction / Context:Series and parallel circuit behaviors differ fundamentally. In series networks, the same current flows through each element because there is a single path. This question checks recognition of that principle in the context of a resistor-capacitor (RC) series circuit.

Given Data / Assumptions:

• One source drives a series connection of R and C.
• Steady-state sinusoidal operation is implied.
• Ideal components (no parasitic branching).

Concept / Approach:In a series circuit, Kirchhoff’s Current Law (KCL) implies the same current at every point along the single path. Voltages across R and C differ in amplitude and phase (V_R in phase with current, V_C lags current by 90 degrees), but the current itself is identical through each element.

Step-by-Step Solution:Identify topology: series → single current path.Apply KCL: the current entering a series element equals the current leaving it.Conclude: I_R = I_C = I_total in amplitude and phase at any instant.Note: Only voltages split and phase-shift across elements.

Verification / Alternative check:Phasor analysis: I is common, while V_R = I * R (in phase with I), and V_C = I * X_C (lags I by 90 degrees). Their vector sum equals the source voltage, confirming series behavior.

Why Other Options Are Wrong:(b), (c), (d) all imply separate branch currents being summed, which describes parallel circuits, not series.

Common Pitfalls:Mixing series and parallel concepts; assuming different instantaneous currents in reactive elements due to phase, which is incorrect in a single-path series network.

Final Answer:The current always has the same amplitude and phase for every part of the circuit.