Series RC phase dependence In a series RC circuit driven by a sinusoidal source, the phase difference between the total source voltage and the current is determined by which factor?

Introduction / Context:
The phase relationship between voltage and current in reactive circuits shapes filter characteristics, stability margins, and timing. In a series RC, the resistor and capacitor share the same current but their voltage drops are out of phase. The net phase between the source voltage and current is not constant; it varies with component values and frequency.

Given Data / Assumptions:

• Topology: series RC.
• Sinusoidal steady-state excitation.
• Ideal components for clarity.
• Phase defined between total source voltage and circuit current.

Concept / Approach:
The series RC impedance is Z = R − j|XC| with |XC| = 1/(ωC). The phase angle φ between total voltage and current satisfies tan(φ) = −|XC|/R. Therefore the magnitude |φ| = arctan(|XC|/R). Changing R, C, or the frequency (which changes |XC|) alters |XC|/R and hence the phase.

Step-by-Step Solution:

Verification / Alternative check:
Limit cases support the conclusion: if R ≫ |XC|, φ ≈ 0° (almost resistive). If |XC| ≫ R, |φ| approaches 90° (dominantly capacitive). Continuous variation between these limits confirms dependence on R and C (via |XC|).

Why Other Options Are Wrong:

Common Pitfalls:
Confusing individual component voltage phases with the overall source-to-current phase; assuming linear circuits exhibit amplitude-dependent phase shift (they do not).

Final Answer:
depends on the values of R and C