Question

A capacitor of capacitance \(50\ \mu\text{F}\) is connected to an AC source of frequency \(50\ \text{Hz}\). The capacitive reactance is approximately:

• A. \(31.8\ \Omega\)
• B. \(63.7\ \Omega\)
• C. \(95.5\ \Omega\)
• D. \(127.4\ \Omega\)

Hint:

Capacitive reactance: \[ X_C=\frac1{2\pi fC} \] It decreases when: \[ f \text{ or } C \] increases.

Answer 1

The Correct Option is B

Capacitive reactance is given by: \[ X_C=\frac1{2\pi fC} \] where:
• \(f=50\ \text{Hz}\)
• \(C=50\ \mu\text{F}=50\times10^{-6}\ \text{F}\)
Step 1: Substitute the values \[ X_C= \frac1{2\pi(50)(50\times10^{-6})} \]
Step 2: Simplify \[ X_C= \frac1{2\times3.14\times50\times50\times10^{-6}} \] \[ X_C\approx63.7\ \Omega \] Thus: \[ \boxed{X_C\approx63.7\ \Omega} \] Option analysis:
• Option (A): Incorrect
• Option (B): Correct
• Option (C): Incorrect
• Option (D): Incorrect Therefore: \[ \boxed{\text{(B)}} \]