Capacitive reactance comparison at 60 Hz: given two capacitors, 10 µF and 20 µF, which one has the larger capacitive reactance magnitude Xc in a 60 Hz AC circuit?

Introduction / Context:
Capacitive reactance determines how strongly a capacitor opposes AC. Understanding how Xc depends on C and frequency helps in filter design and impedance matching.

Given Data / Assumptions:

• Frequency f = 60 Hz.
• Capacitances: 10 µF and 20 µF.
• Ideal components; ESR and ESL neglected.

Concept / Approach:
Capacitive reactance is Xc = 1 / (2 * pi * f * C). For fixed f, Xc is inversely proportional to C. Therefore, the smaller capacitor (10 µF) exhibits the larger reactance magnitude; the larger capacitor (20 µF) has half that reactance.

Step-by-Step Solution:

Verification / Alternative check:
Doubling C halves Xc at fixed frequency, consistent with the formula.

Why Other Options Are Wrong:
“20 µF larger / equal / independent of C / infinite at 60 Hz” each contradicts Xc = 1/(2*pi*f*C).

Common Pitfalls:
Mixing resistance with reactance; forgetting to convert microfarads to farads.

Final Answer:
10 µF has the larger reactance