Final answer:
The current that flows through a 0.250 µF capacitor when connected to a 60 Hz, 480 V AC source is approximately 45.3 mA, which does not match any of the given multiple-choice options. At 25.0 kHz, the current would be approximately 7.53 A.
Step-by-step explanation:
The current that flows when a 60.0 Hz, 480 V AC source is connected to a 0.250 µF capacitor can be calculated using the formula for capacitive reactance (XC) and then using Ohm's law to find the current (I). The capacitive reactance is given by XC = 1 / (2πfC), where f is the frequency in hertz and C is the capacitance in farads. To find the current (I), use the formula I = V / XC, where V is the voltage in volts.
First, calculate the reactance for a frequency (f) of 60 Hz:
XC = 1 / (2π × 60 × 0.250 × 10-6) = 1 / (2π × 60 × 0.250 × 10-6) ≈ 1 / (0.000015) ≈ 10,600 Ω
Now, calculate the current I using the RMS voltage (Vrms) of 480 V:
I = Vrms / XC = 480 / 10600 ≈ 0.0453 A or 45.3 mA, which is not listed in the multiple-choice options provided.
For part (b) of your question, at a frequency of 25.0 kHz, the reactance would be:
XC = 1 / (2π × 25,000 × 0.250 × 10-6) ≈ 1 / (0.0157) ≈ 63.7 Ω
And the current I would be:
I = Vrms / XC = 480 / 63.7 ≈ 7.53 A