Impedance of a series RC from given R and XC magnitudes A series RC circuit has resistance R = 120 kΩ and capacitive reactance magnitude |XC| = 160 kΩ at the operating frequency. What is the magnitude of the total impedance?

Introduction / Context:Combining resistance and reactance magnitudes correctly is crucial to predict current and voltage division in AC networks. For series RC, the total impedance magnitude follows a Pythagorean relationship due to the orthogonality of resistive and reactive components in the complex plane.

Given Data / Assumptions:

• R = 120 kΩ.
• |XC| = 160 kΩ.
• Series connection under sinusoidal excitation.
• We seek |Z|, not the phase angle (though it can be found as arctan(|XC|/R)).

Concept / Approach:The complex impedance is Z = R − j|XC|. The magnitude is |Z| = sqrt(R^2 + |XC|^2). The numbers 120 and 160 form a 3–4–5 multiple (since 12–16–20 scales to 3–4–5), which simplifies the square root.

Step-by-Step Solution:

Verification / Alternative check:Recognize 12–16–20 as the 3–4–5 family scaled by 4; multiply by 10 to reach 120–160–200. The Pythagorean identity confirms the result immediately without calculator use.

Why Other Options Are Wrong:

Common Pitfalls:Adding impedances as scalars; forgetting unit consistency (kΩ vs. Ω); ignoring that reactance contributes orthogonally to resistance.

Final Answer:200 kΩ