Series RC circuits — phase relationship clarification: Which statement about a series RC (resistor–capacitor) AC circuit is true regarding the phase of current and the source voltage?

Introduction / Context:
In AC network analysis, understanding the phase relationship of current and voltage in a series RC circuit is fundamental. Because capacitors store and release energy in an electric field, they cause current to lead voltage. Recognizing which quantity leads or lags helps with phasor diagrams, impedance calculations, and power factor correction in electronics and electrical engineering.

Given Data / Assumptions:

• Series circuit containing a single resistor R and capacitor C.
• Sinusoidal source voltage applied (steady-state AC).
• Ideal components (no parasitic inductance or resistance in C beyond R).

Concept / Approach:

For a capacitor, current i leads capacitor voltage v_C by 90 degrees because i = C * dv/dt. In a series RC, the same current flows through both R and C. The resistor voltage v_R is in phase with current, while the capacitor voltage v_C lags current by 90 degrees. The source voltage is the phasor sum v_S = v_R + v_C, which therefore lags the current by an angle 0 < phi < 90 degrees. Thus, current leads the source voltage by phi in a series RC circuit.

Step-by-Step Solution:

Verification / Alternative check:

Create a phasor diagram: draw I on the positive real axis; v_R along I; v_C straight downward (−j axis). The source voltage is the diagonal from the origin to the tip of the v_R + v_C vector, clearly lagging I. Therefore, I leads v_S.

Why Other Options Are Wrong:

• The capacitor's voltage and the resistor's voltage are not in phase; they differ by 90°.
• The current lags the source voltage: incorrect for RC (that would be RL where current lags).
• The resistor voltage lags the current: v_R is in phase with current, not lagging.
• Source leading resistor voltage by 90°: the phase shift is less than 90° and depends on R and X_C.

Common Pitfalls:

• Confusing RC and RL behavior; in RC, current leads, in RL, current lags.
• Assuming the phase shift is always 90°; it is between 0° and 90° for series RC.

Final Answer:

The current leads the source voltage.