What is the capacitive reactance Xc for a 100 μF capacitor at 50 Hz?

What is the capacitive reactance Xc for a 100 μF capacitor at 50 Hz?

• A. Approximately 3.18 Ω
• B. Approximately 31.8 Ω
• C. Approximately 63.7 Ω
• D. Approximately 9.0 Ω

Answer: (B)

Capacitive reactance tells us how much a capacitor impedes AC, and it follows the formula Xc = 1 / (2π f C). So it gets smaller when frequency or capacitance increases, and larger when either decreases. For this problem, C is 100 μF, which is 0.0001 F, and f is 50 Hz. Compute the denominator: 2π f C = 2π × 50 × 0.0001 ≈ 0.0314159. Invert that to get Xc ≈ 1 / 0.0314159 ≈ 31.83 Ω. So the capacitive reactance is about 31.8 Ω, which matches the option listing roughly 31.8 Ω. This reinforces that higher frequency or a larger capacitor lowers Xc, whereas a smaller C or lower f raises Xc.

Capacitive reactance tells us how much a capacitor impedes AC, and it follows the formula Xc = 1 / (2π f C). So it gets smaller when frequency or capacitance increases, and larger when either decreases.

For this problem, C is 100 μF, which is 0.0001 F, and f is 50 Hz. Compute the denominator: 2π f C = 2π × 50 × 0.0001 ≈ 0.0314159. Invert that to get Xc ≈ 1 / 0.0314159 ≈ 31.83 Ω.

So the capacitive reactance is about 31.8 Ω, which matches the option listing roughly 31.8 Ω. This reinforces that higher frequency or a larger capacitor lowers Xc, whereas a smaller C or lower f raises Xc.