Frequency effect in a series RC: When the frequency of a sinusoidal source applied to a series RC circuit is decreased, what happens to the circuit's impedance magnitude?

Introduction / Context:
The impedance of a capacitor depends on frequency through Xc = 1/(2πfC). In a series RC, the overall impedance magnitude is |Z| = √(R^2 + Xc^2). Understanding how |Z| varies with frequency is key to filter behavior and signal attenuation.

Given Data / Assumptions:

• Series RC network.
• Source frequency f is decreased.
• Component values fixed (R and C constant).

Concept / Approach:

As f decreases, Xc increases since Xc is inversely proportional to frequency. With a larger capacitive reactance vector, the magnitude of the vector sum with R increases or at least does not decrease if R stays fixed.

Step-by-Step Solution:

Verification / Alternative check:

Limiting cases: As f → 0, Xc → ∞, so |Z| → ∞ (open-circuit behavior). As f → ∞, Xc → 0, so |Z| → R (minimum).

Why Other Options Are Wrong:

'Decreases' contradicts Xc behavior. 'Remains the same' would require Xc constant. 'Doubles' is an arbitrary numeric claim without basis.

Common Pitfalls:

Mixing capacitor behavior with inductor behavior (which increases with frequency); forgetting the square-root relationship.

Final Answer:

increases