Magnitude of impedance in a specified series RC case A series RC circuit has R = 50 Ω and capacitive reactance magnitude |XC| = 50 Ω at the operating frequency. What is the magnitude of the total impedance?

Introduction / Context:
Impedance magnitude in a series RC circuit combines resistance and reactance vectorially, not arithmetically. This magnitude determines current for a given applied RMS voltage and therefore influences power and filter behavior.

Given Data / Assumptions:

• R = 50 Ω.
• |XC| = 50 Ω (capacitive).
• Series connection, sinusoidal steady-state.
• Seek |Z|, the magnitude of total impedance.

Concept / Approach:
For series RC, Z = R − j|XC|. The magnitude is |Z| = sqrt(R^2 + |XC|^2). Equal magnitudes of resistance and reactance form a 45° impedance triangle (since opposite and adjacent legs are equal).

Step-by-Step Solution:

Verification / Alternative check:
Use the 1–1–√2 triangle analogy: equal legs imply the hypotenuse is leg × √2 → 50 × 1.414 ≈ 70.7 Ω, matching the calculation and the chosen option.

Why Other Options Are Wrong:

Common Pitfalls:
Adding R and |XC| directly; forgetting to take the square root; mixing magnitudes with signed reactance values.

Final Answer:
70 Ω