AC resistor behavior — phase relationship: Which statement correctly describes current and voltage across a pure resistor in an AC circuit?

Introduction / Context:In AC analysis, the phase relationships between voltage and current depend on the element type. For resistors, the relationship is simplest: there is no phase shift. This concept underpins power factor, phasor diagrams, and impedance calculations.

Given Data / Assumptions:

• Ideal, linear resistor with no reactive effects.
• Sinusoidal steady-state conditions.
• No additional reactive components present.

Concept / Approach:Ohm’s law in phasor form for a resistor is V = I * R, where R is real (no imaginary component). Therefore, voltage and current share the same phase angle; neither leads nor lags.

Step-by-Step Solution:Represent the impedance: Z_R = R (angle 0 degrees).Phasor relationship: V = I * R with angle(V) − angle(I) = 0.Conclude that current and voltage are in phase across the resistor.

Verification / Alternative check:Instantaneous power p(t) = v(t) * i(t) has positive average value with no reactive oscillation, consistent with zero phase shift.

Why Other Options Are Wrong:(b) and (c) describe capacitive or inductive phase shifts, not resistive behavior. (d) cannot be correct because options are mutually exclusive.

Common Pitfalls:Confusing resistor behavior with that of capacitors (current leads voltage) and inductors (current lags voltage).

Final Answer:Current and voltages are in phase through a resistor.