Find capacitive reactance at 1 kHz for a 4.7 µF capacitor A capacitor C = 4.7 µF is connected to a sinusoidal source of frequency f = 1 kHz. What is its capacitive reactance Xc?

Introduction / Context:
Capacitive reactance determines how strongly a capacitor opposes AC at a given frequency. It is essential for filter corner frequencies, impedance matching, and estimating current draw.

Given Data / Assumptions:

• C = 4.7 µF = 4.7e-6 F.
• f = 1 kHz = 1000 Hz.
• Sinusoidal steady-state; ideal capacitor.

Concept / Approach:
For a capacitor, Xc = 1 / (2 * π * f * C). As frequency increases, Xc decreases; as capacitance increases, Xc also decreases.

Step-by-Step Solution:
Compute denominator: 2 * π * f * C = 2 * π * 1000 * 4.7e-6.2 * π * 1000 ≈ 6283.185; multiply by 4.7e-6 gives ≈ 0.029531.Xc = 1 / 0.029531 ≈ 33.86 ohms.Rounded to the nearest whole-number option: 34 ohms.

Verification / Alternative check:
Reasonableness: At 1 kHz, a few microfarads should yield a few tens of ohms. Doubling the frequency to 2 kHz would halve Xc to about 17 ohms, matching the inverse proportionality.

Why Other Options Are Wrong:

• 4.7 ohms: would require about 34 µF at 1 kHz, not 4.7 µF.
• 29.5 ohms: slightly low; corresponds to a larger C or slightly lower f.
• 213 ohms: far too high for this C and f; might suit much smaller capacitance.

Common Pitfalls:

• Forgetting to convert microfarads to farads when computing with SI units.
• Rounding intermediate steps too aggressively.

Final Answer:
34 ohms