Phase relationship in a purely capacitive AC circuit: how does current relate to voltage?

Introduction:Understanding phase relationships is fundamental to AC circuit analysis. In purely reactive elements, voltage and current are out of phase. This question asks for the specific relationship in a purely capacitive circuit.

Given Data / Assumptions:

• Ideal capacitor (no resistance).
• Sinusoidal steady state.
• Single-frequency excitation.

Concept / Approach:The impedance of a capacitor is Zc = 1 / (j * 2 * pi * f * C) = −j * Xc. The negative imaginary sign indicates current leads voltage by 90 degrees. Equivalently, i(t) = C * dv/dt; the derivative emphasizes that current peaks when voltage crosses zero and vice versa, producing a +90° current lead.

Step-by-Step Solution:

Verification / Alternative check:Time-domain relation i(t) = C * dv/dt shows current is maximum at voltage zero crossings and zero at voltage peaks, consistent with a 90° lead.

Why Other Options Are Wrong:

• Voltage leads by 90° or current lags by 90°: These describe inductive, not capacitive, circuits.
• In phase: Requires resistive behavior; not applicable to ideal capacitors.

Common Pitfalls:Confusing the sign convention of j or mixing inductive and capacitive phase relations. Remember ‘‘ICE’’: in a Capacitor, Current leads Voltage.

Final Answer:Current leads voltage by 90°.