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

Introduction / Context:
Understanding the phase relationship between current and voltage in ideal reactive elements is core to AC circuit analysis, power factor correction, and resonance. A pure inductor exhibits a characteristic quadrature phase shift that drives many design choices in filters and power systems.

Given Data / Assumptions:

• Inductor is ideal: zero resistance and no core losses.
• Source is sinusoidal steady state.
• No other components are in series with the inductor.

Concept / Approach:
Voltage across an inductor is v = L * di/dt in time domain. For a sinusoidal current, the derivative shifts phase by +90 degree. Equivalently, with current as reference, voltage leads current by 90 degree. Therefore, current lags voltage by 90 degree in an ideal inductor. This is captured by the inductive reactance X_L = 2 * pi * f * L, which is purely imaginary and positive in phasor form, representing a +90 degree voltage lead.

Step-by-Step Solution:
1) Write v = L * di/dt for an inductor.2) For sinusoidal steady state, differentiation introduces a 90 degree phase lead in voltage relative to current.3) Hence, with voltage as the reference, the current must lag by 90 degree.

Verification / Alternative check:
Using phasors: V = j * X_L * I where j denotes +90 degree. This shows V leads I by 90 degree, so I lags V by 90 degree.

Why Other Options Are Wrong:

• Option A: Reverses the correct lead-lag relation.
• Option B: In-phase behavior is for resistors, not ideal inductors.
• Option D: AC is not converted to DC by a pure inductor.
• Option E: Incorrect because Option C is correct.

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

Final Answer:
AC current lags the voltage by 90 degree.