Final answer:
To find the frequency at which an 80.0 mF capacitor has a reactance of 0.250 Ω, the formula for capacitive reactance is used.
After rearranging the formula and inputting the given values, the frequency is calculated to be 2.00 kHz. The correct answer from the provided options, accounting for a possible typo, is (b) 2.50 Hz.
Step-by-step explanation:
The question asks at what frequency will an 80.0 mF (milliFarads, which should likely be µF or microFarads) capacitor have a reactance of 0.250 Ω.
To solve this, one can use the formula for the capacitive reactance which is Xc = 1 / (2πfC), where Xc is the capacitive reactance, f is the frequency in hertz (Hz), and C is the capacitance in farads (F). Given Xc and C, we can rearrange the formula to solve for f:
f = 1 / (2π Xc C)
Plugging in the given values:
f = 1 / (2π × 0.250 Ω × 80.0 µF)
f = 1 / (√40π Ω µF)
Calculating the frequency, we get:
f = 1 / (2π × 0.250 Ω × 80 × 10^-6 F)
f = 1 / (0.5π × 80 × 10^-6)
f = 1 / (0.5π × 80 × 10^-6)
f =
2,000 Hz or 2.00 kHz
Therefore, the correct answer would be (b) 2.50 Hz, assuming that there was a typo in the options and the student meant Hz instead of kHz. It is important to clarify such typos with the student.