A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the

A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?

A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?

Correct Answer: 318.31 Hz

Step 1: Understand the formula for capacitive reactance, which is X_C = 1 / (2πfC).
Step 2: Identify the values given in the problem: X_C = 50 ohms and C = 10 microfarads (which is 10 x 10^-6 farads).
Step 3: Rearrange the formula to solve for frequency (f): f = 1 / (2πX_CC).
Step 4: Substitute the values into the rearranged formula: f = 1 / (2π * 50 * 10 x 10^-6).
Step 5: Calculate the denominator: 2π * 50 * 10 x 10^-6 = 0.00314.
Step 6: Calculate the frequency: f = 1 / 0.00314 = 318.31 Hz.
Step 7: Round the answer to the nearest kilohertz: approximately 1 kHz.

Capacitive Reactance – Capacitive reactance (X_C) is the opposition that a capacitor offers to the flow of alternating current, calculated using the formula X_C = 1 / (2πfC).
Frequency Calculation – The frequency (f) of an AC circuit can be determined by rearranging the capacitive reactance formula to f = 1 / (2πX_CC).
Capacitance Units – Understanding the unit of capacitance (farads) and converting microfarads to farads is essential for accurate calculations.