In an AC series RLC circuit, under which operating condition does the circuit's voltage lag the circuit's current (i.e., current leads and the net reactance is negative/capacitive)?

Introduction:
Understanding phase relationships between voltage and current is fundamental in AC circuit analysis. In a series RLC circuit, whether voltage leads or lags current depends on the net reactance (inductive or capacitive). This question asks you to identify the operating condition under which the voltage lags the current, meaning the current leads by a positive phase angle.

Given Data / Assumptions:

• Series RLC circuit driven by a sinusoidal source.
• Ideal components used for conceptual clarity.
• We are comparing qualitative operating conditions: inductive, capacitive, resistive, and resonant.

Concept / Approach:
The total reactance of a series RLC circuit is X = XL − XC, where XL = 2 * pi * f * L and XC = 1 / (2 * pi * f * C). The phase angle phi between source voltage and current is given by tan(phi) = X / R. If X is positive (inductive), voltage leads current; if X is negative (capacitive), voltage lags current (equivalently, current leads). At resonance, X = 0 and voltage and current are in phase.

Step-by-Step Solution:

Verification / Alternative check:
Using i(t) and v(t) phasors: for capacitive behavior, i(t) = C * dv/dt implies current peaks occur before voltage peaks (lead), confirming that the circuit voltage lags the current when the circuit acts capacitively.

Why Other Options Are Wrong:

• Resistively: With purely resistive behavior, voltage and current are in phase; neither leads nor lags.
• Inductively: Inductive dominance makes voltage lead current, the opposite of what is asked.
• Resonantly: At resonance, phase angle is approximately 0 degrees; there is no lead/lag.

Common Pitfalls:
Students often reverse the sign of X or confuse “current leads” with “voltage leads.” A quick rule is “ICE”: in a Capacitor, current (I) leads voltage (V); in an Inductor (L), voltage leads current. Always check XL − XC to determine the sign of X.

Final Answer:
Capacitively.