For an ideal pure capacitor excited with a sinusoidal AC source, what is the phase relationship between current and voltage?

Introduction / Context:Phase relationships in reactive elements are fundamental to AC analysis, filter design, and power factor correction. A pure capacitor exhibits a characteristic lead of current relative to voltage.

Given Data / Assumptions:

• Ideal capacitor with no series resistance.
• Sinusoidal steady state.
• No other components in series or parallel affecting the phase.

Concept / Approach:The current through a capacitor is i = C * dv/dt. Differentiation causes a +90 degree phase shift of current relative to voltage. In phasor terms, I = j * ω * C * V, showing that current leads voltage by 90 degree for a purely capacitive impedance.

Step-by-Step Solution:Step 1: Use i = C * dv/dt.Step 2: For sinusoidal v, differentiation advances phase by 90 degree.Step 3: Conclude current leads voltage by 90 degree for an ideal capacitor.

Verification / Alternative check:Impedance of a capacitor is Z_C = 1 / (j * ω * C). The negative imaginary nature indicates current lead of 90 degree relative to voltage.

Why Other Options Are Wrong:

• In phase: True for a pure resistor, not a capacitor.
• Converted to DC: A capacitor does not convert AC to DC by itself.
• Current lags by 90 degree: That is the behavior of an inductor, not a capacitor.
• None of the above: Incorrect because the 90 degree lead is correct.

Common Pitfalls:Confusing capacitor and inductor phase rules is common. Remember: in a capacitor, current leads; in an inductor, current lags.

Final Answer:ac current leads the voltage by 90 degree.