Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 54 of 127
A \(10\ \mu\text{F}\) capacitor is connected to a \(50\text{ Hz}\) AC source. What is the approximate capacitive reactance \(X_C\)?
A
\(159\ \Omega\)
B
\(318\ \Omega\)
C
\(636\ \Omega\)
D
\(500\ \Omega\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \(318\ \Omega\)
Concept:

Capacitive reactance is calculated from the formula \(X_C = \frac{1}{2\pi f C}\).

Formula / Reaction:

$$X_C = \frac{1}{2\pi f C}$$

Solution:

  • Given: \(f = 50\text{ Hz}\), \(C = 10 \times 10^{-6}\text{ F}\).


  • \(2\pi f C = 2 \times 3.1416 \times 50 \times 10^{-5} = 314.16 \times 10^{-5} = 3.1416 \times 10^{-3}\).


  • \(X_C = \frac{1}{3.1416 \times 10^{-3}} = \frac{1000}{3.1416} \approx 318.3\ \Omega\).


Why other options are incorrect:

  • Opt_A: \(159\ \Omega\) corresponds to \(C = 20\ \mu\text{F}\).


  • Opt_C: \(636\ \Omega\) corresponds to \(C = 5\ \mu\text{F}\).


  • Opt_D: \(500\ \Omega\) is an incorrect estimate.

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