Question

An AC source with an output rms voltage of 27.0 V at a frequency of 60.0 Hz is connected across a 12.2-µF capacitor. (a) Find the capacitive reactance. Ω (b) Find the rms current. A (c) Find the maximum current in the circuit. A (d) Does the capacitor have its maximum charge when the current has its maximum value? Yes No Explain. This answer has not been graded yet.

Answer 1

Step-by-step explanation:

a) capacitive reactance Xc = 1/2πfC

f is the frequency of the AC source

C is the capacitance of thw capacitor

Given f = 60.0Hz

C = 12.2-µF

C = 12.2 × 10^-6Farads

Xc = 1/2π×60×12.2×10^-6

Xc = 1/0.004599

Xc = 217.44ohms

b) Using the formula Vrms = IrmsXc Vrms

Irms = Vrms/Xc

Irms = 27.0/217.44

Irms = 0.124Amperes

c) Since Irms = Im/√2

Where Im is the maximum current

Im = Irms×√2

Im = 0.124× √2

Im = 0.088A

d) No, the capacitor has no charge when the current is at maximum.