Series RLC behavior: which statement best characterizes currents and voltages in a series R–L–C circuit under sinusoidal steady state?

Introduction / Context:
Understanding series RLC circuits is essential for analyzing filters, resonance, and power factor correction. In a series connection, the same current must pass through each element because there is only one path for charge flow.

Given Data / Assumptions:

• Elements R, L, and C are connected in strict series.
• Sinusoidal steady state (phasor analysis applies).
• No mutual coupling or nonidealities significant enough to change the qualitative rule.

Concept / Approach:
In series circuits, current continuity dictates that the branch current is identical everywhere: I_R = I_L = I_C = I_total (same amplitude and phase). Voltages, however, differ in amplitude and phase across R, L, and C because each element’s impedance is different: Z_R = R (in phase), Z_L = jX_L (leads voltage), Z_C = −jX_C (lags voltage). Thus, while current is the same, individual component voltages add vectorially to the source voltage.

Step-by-Step Solution:
Recognize series topology implies one current path.Apply phasors: I is common; V_R = I * R, V_L = I * jX_L, V_C = I * (−jX_C).Note voltage phases differ; only currents are identical in amplitude and phase.Select the statement: the current waveform is the same through all components.

Verification / Alternative check:
KCL at any series node gives identical current; KVL around the loop shows the vector sum of voltages equals the source, confirming voltage differences but current equality.

Why Other Options Are Wrong:
Voltages same in amplitude/phase: false; each element’s voltage depends on its impedance.All of the above: cannot be true because (a) is incorrect.Sum of currents less than applied: makes no sense in series (only one current exists).

Common Pitfalls:
Confusing series with parallel rules; assuming voltages “share” equally; mixing up lead/lag relationships.

Final Answer:
The current waveform for each component always has the same amplitude and phase as the applied current