Question

The capacitive reactance offered by a capacitance of 10 microfarads to an alternating current of \( i = I_m \sin(100\pi t - \frac{\pi}{6}) \) amperes is

• A. 318.31 ohms
• B. 0.31831 ohm
• C. 31.831 ohms
• D. 3183.1 ohms

Hint:

To calculate capacitive reactance, use the formula \( X_C = \frac{1}{2\pi f C} \), where \( f \) is the frequency and \( C \) is the capacitance.

Answer 1

The Correct Option is A

Step 1: Use the formula for capacitive reactance.
The capacitive reactance \( X_C \) is given by the formula: \[ X_C = \frac{1}{2\pi f C}, \] where \( f \) is the frequency and \( C \) is the capacitance.
Step 2: Extract the frequency from the current equation.
The current equation is \( i = I_m \sin(100\pi t - \frac{\pi}{6}) \), so the frequency \( f \) is: \[ f = \frac{100\pi}{2\pi} = 50 \, \text{Hz}. \]
Step 3: Calculate the capacitive reactance.
Substitute \( f = 50 \, \text{Hz} \) and \( C = 10 \times 10^{-6} \, \text{F} \): \[ X_C = \frac{1}{2\pi \times 50 \times 10 \times 10^{-6}} = 318.31 \, \text{ohms}. \]
Step 4: Conclusion.
Thus, the capacitive reactance is 318.31 ohms, which corresponds to option (A).