A 2 kΩ resistor in series with a 0.015 µF capacitor is connected to a 15 kHz AC source. Determine the total impedance magnitude |Z| and the circuit phase angle θ (degrees).

Introduction / Context:
Series RC impedance problems combine frequency-dependent reactance with resistance via vector (phasor) addition. You must compute capacitive reactance, then form the magnitude and angle of the series impedance to understand current and voltage phase relations.

Given Data / Assumptions:

• R = 2 kΩ.
• C = 0.015 µF = 15 nF.
• f = 15 kHz (sinusoidal steady state).
• Ideal components; no stray inductance or ESR.

Concept / Approach:

Compute Xc = 1 / (2 * π * f * C). For a series RC, Z = R − jXc. The magnitude is |Z| = √(R^2 + Xc^2), and the phase angle is θ = arctan(−Xc / R) (negative for a capacitive circuit).

Step-by-Step Solution:

Verification / Alternative check:

Since Xc < R, |Z| should be slightly above R and angle modestly negative, matching 2121 Ω and −19.5°.

Why Other Options Are Wrong:

707 Ω is Xc, not |Z|. 734 Ω and −38.9° are inconsistent with the series values. 73.4 Ω is off by a factor-of-10 slip.

Common Pitfalls:

Mistaking Xc for |Z|; forgetting the negative sign of the capacitive angle; calculator in radians instead of degrees.

Final Answer:

2121 Ω and θ = –19.5°