Series RC circuits — does the total impedance vary directly with frequency?

Introduction / Context:
This statement probes how the magnitude of impedance in a series RC circuit changes with frequency. Understanding this relationship is fundamental for filter design, Bode plots, and time-constant intuition in electronics.

Given Data / Assumptions:

• Series RC network driven by a sinusoidal source of angular frequency ω = 2 * π * f.
• Impedance of resistor R is R (independent of frequency).
• Impedance of capacitor C is Zc = 1 / (j * ω * C).

Concept / Approach:
The total series impedance is the vector sum of R and the capacitive reactance magnitude Xc = 1 / (ω * C). As frequency increases, Xc decreases. The impedance magnitude therefore decreases toward R, not increases “directly with frequency.”

Step-by-Step Solution:

Verification / Alternative check:
Sketch a Bode magnitude plot for |Z|. The curve slopes downward with a corner near ω = 1 / (R * C), confirming inverse dependence on frequency due to the 1 / (ω * C) term.

Why Other Options Are Wrong:

• Choosing “True” implies |Z| grows with f, contradicting |Z| = sqrt( R^2 + (1 / (ω * C))^2 ).

Common Pitfalls:
Confusing impedance of a capacitor (inversely proportional to frequency) with that of an inductor (directly proportional to frequency). Only inductive reactance Xl = ω * L increases with frequency.

Final Answer:
False