A capacitor of 10μF is connected to an AC source of frequency 60Hz. What is the

A capacitor of 10μF is connected to an AC source of frequency 60Hz. What is the capacitive reactance? (2020)

A capacitor of 10μF is connected to an AC source of frequency 60Hz. What is the capacitive reactance? (2020)

Step 1: Identify the values given in the problem. We have a capacitor value C = 10μF (microfarads) and a frequency f = 60Hz.
Step 2: Convert the capacitor value from microfarads to farads. 10μF = 10 x 10^-6 F = 0.00001 F.
Step 3: Calculate the angular frequency (ω) using the formula ω = 2πf. Substitute f = 60Hz: ω = 2π(60).
Step 4: Calculate ω. First, find 2π ≈ 6.2832, then multiply by 60: ω ≈ 6.2832 x 60 ≈ 376.99 rad/s.
Step 5: Use the formula for capacitive reactance: Xc = 1/(ωC). Substitute ω ≈ 376.99 and C = 0.00001 F.
Step 6: Calculate Xc. Xc = 1/(376.99 x 0.00001) = 1/(0.0037699) ≈ 265.2 ohms.

Capacitive Reactance – Capacitive reactance (Xc) is the opposition that a capacitor offers to the flow of alternating current (AC) and is calculated using the formula Xc = 1/(ωC), where ω is the angular frequency and C is the capacitance.
Angular Frequency – Angular frequency (ω) is related to the frequency (f) of the AC source by the formula ω = 2πf, which converts frequency in hertz to radians per second.