Frequency through series RC: A 6 kHz sinusoidal voltage is applied to a series RC circuit. What is the frequency of the voltage appearing across the resistor?

Introduction / Context:
Linear time-invariant (LTI) circuits do not change the input frequency; they only alter amplitude and phase of each sinusoidal component. Therefore, the frequency across any element in a simple series RC equals the source frequency.

Given Data / Assumptions:

• Source frequency f_in = 6 kHz.
• Series RC—linear, time-invariant.
• No nonlinearities or modulation effects.

Concept / Approach:

An LTI circuit acts as a filter characterized by a transfer function. It scales and phase-shifts sinusoidal inputs at the same frequency; it does not generate new frequencies under linear operation.

Step-by-Step Solution:

Verification / Alternative check:

Measure in the lab: oscilloscope FFT will show a single line at 6 kHz for an ideal RC driven by a single-tone sinusoid.

Why Other Options Are Wrong:

12 kHz and 18 kHz imply frequency doubling or tripling, which does not occur in LTI elements. 0 Hz would require rectification or averaging, not present here.

Common Pitfalls:

Confusing time constant effects (amplitude/phase) with frequency conversion; mixing with nonlinear device behavior.

Final Answer:

6 kHz