RC high-pass filter design: For a 0.2 µF capacitor in series with a 220 Ω resistor (output taken across the resistor), what is the critical (cutoff) frequency fc of the circuit?

Introduction / Context:This problem checks fundamental filter theory for an RC high-pass network. In a simple series RC high-pass filter with output across the resistor, the critical (cutoff) frequency fc is the frequency at which the output voltage equals the input divided by √2, corresponding to a −3 dB point and a 45° phase shift.

Given Data / Assumptions:

• Capacitance C = 0.2 µF.
• Resistance R = 220 Ω.
• Output is taken across R (standard RC high-pass).
• Ideal components and sinusoidal steady-state conditions.

Concept / Approach:For an RC high-pass filter, the cutoff frequency is defined by fc = 1 / (2 * pi * R * C). At fc, the magnitudes of the capacitive reactance and the resistance are equal, so the output is at −3 dB relative to the high-frequency passband.

Step-by-Step Solution:

Verification / Alternative check:As a quick check, note that for R ≈ 220 Ω and C ≈ 0.2 µF, the time constant τ = RC ≈ 44 µs. Using the shortcut fc ≈ 1 / (6.283 * 44 µs) gives ≈ 3.6 kHz, confirming the precise calculation.

Why Other Options Are Wrong:

• 723 Hz and 362 Hz: These come from using incorrect R or C values, or mixing milli/µ prefixes.
• 7,234 Hz: Roughly twice the correct value (e.g., missing the 2 * pi factor).

Common Pitfalls:

• Forgetting to convert µF to F before calculation.
• Using fc = 1 / (pi * RC) instead of fc = 1 / (2 * pi * RC).

Final Answer:3,617 Hz