Question

An 7.70-mF capacitor is connected across an AC source with an rms voltage of 66.0 V oscillating with a frequency of 25.0 Hz. What are the following for this circuit?

(a) capacitive reactance_____Ω
(b) rms current_____A
(c) maximum current_____A

Answer 1

To find the capacitive reactance, rms current, and maximum current for the given AC circuit, use the formulas X_C = 1/(2πfC), I_rms = V_rms / X_C, and I_max = √2 x I_rms, respectively.

Step-by-step explanation:

The question is asking to calculate the capacitive reactance and currents (rms and maximum) in an AC circuit with a given capacitance, voltage, and frequency. Capacitive reactance (XC) in an AC circuit can be calculated using the formula XC = 1/(2πfC), where f is the frequency and C is the capacitance. The rms current (Irms) can be found using Ohm's Law for AC circuits, Irms = Vrms / XC, and the maximum current (Imax) is Imax = √2 x Irms. To solve for these values:

1. First calculate the capacitive reactance: XC = 1/(2π(25.0Hz)(7.70×10-3F)), which will give you the reactance in ohms (Ω).
2. Then, calculate the rms current: Irms = 66.0V / XC, which will give you the rms current in amperes (A).
3. Finally, find the maximum current: Imax = √2 x Irms.