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?
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A6 kHz
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B12 kHz
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C0 Hz
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D18 kHz
Answer
Correct Answer: 6 kHz
Explanation
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:
Input: v_in(t) = Vp sin(2π * 6k * t).Output across R: v_R(t) = |H_R(jω)| * Vp * sin(2π * 6k * t + φ_R), where ω = 2π * 6k.Frequency component is unchanged at 6 kHz; only magnitude and phase are modified by H_R(jω).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