Series RL impedance magnitude: A 1.2 kΩ resistor is in series with a 15 mH inductor across a 10 kHz AC source. What is the total impedance magnitude?

Introduction / Context:
Here we compute the magnitude of series RL impedance by combining resistance and inductive reactance via the root-sum-square relationship, a routine but essential AC task.

Given Data / Assumptions:

• R = 1.2 kΩ = 1200 Ω.
• L = 15 mH; f = 10 kHz.
• Ideal components, sinusoidal steady state.

Concept / Approach:
XL = 2 * pi * f * L. Total impedance magnitude is |Z| = sqrt(R^2 + XL^2).

Step-by-Step Solution:

Verification / Alternative check:
Angle check: θ = arctan(XL / R) ≈ arctan(942.5 / 1200) ≈ 38.9°, reasonable for RL with R slightly dominant. This supports the computed magnitude.

Why Other Options Are Wrong:

• 152.6 Ω and 942 Ω: Confuse steps (either divide by 10 or use XL alone).
• 1,200 Ω: Ignores inductive reactance contribution.
• 1,920 Ω: Overestimates by summing instead of using root-sum-square.

Common Pitfalls:

• Adding R and XL directly instead of vectorially.

Final Answer:
1,526 Ω