Resistance versus impedance — in AC analysis of an RC network, is resistance the same as impedance? Choose the most accurate statement.

Introduction / Context:
In AC circuits, impedance generalizes resistance to include the effects of reactance from capacitors and inductors. Confusing resistance with impedance leads to incorrect magnitudes and phase angles. This question checks basic vocabulary and the mathematical form of impedance for an RC network.

Given Data / Assumptions:

• Sinusoidal steady-state analysis.
• Components are ideal, with a resistor R and capacitor C.
• Capacitive reactance Xc = 1 / (omega * C).

Concept / Approach:
Resistance is a real scalar measured in ohms and relates voltage and current without phase shift: V = I * R. Impedance is a complex quantity, Z = R + jX, that relates phasor voltage and current: V = I * Z. For a capacitor, the reactance is negative imaginary (Xc is treated as -|Xc|), so in series RC we write Z = R - jXc. The magnitude is |Z| = sqrt(R^2 + Xc^2), and the phase angle is phi = arctan(Xc / R), with current leading voltage in a capacitive circuit.

Step-by-Step Solution:

Verification / Alternative check:
At extremely high frequencies Xc approaches 0, so Z approaches R (still not literally equal except in the ideal limit). At DC, Xc tends to infinity, the circuit blocks current, and Z is not equal to R.

Why Other Options Are Wrong:

• “Correct — interchangeable” ignores the imaginary component from reactance.
• “Valid only at resonance” does not apply to a lone RC branch; resonance requires both L and C.
• “Valid only at high frequency” is an approximation, not an identity.

Common Pitfalls:
Using R instead of |Z| in current calculations or neglecting phase when combining AC voltages.

Final Answer:
Incorrect — impedance includes both R and Xc and is not the same as resistance.