Final answer:
The frequency at which a 30.0 mH inductor has a reactance of 100 Ω is approximately 53.05 Hz. This is calculated using the inductive reactance formula and rearranging it to solve for the frequency.
Step-by-step explanation:
To determine at what frequency a 30.0 mH (millihenry) inductor will have a reactance of 100 Ω (ohms), we must use the formula for inductive reactance, which is XL = 2πfL, where XL is the reactance in ohms, π (pi) is approximately 3.14159, f is the frequency in hertz (Hz), and L is the inductance in henrys (H).
Rearranging the formula to solve for the frequency gives us f = XL / (2πL). Plugging in the values, we get f = 100 Ω / (2 * 3.14159 * 30.0 * 10-3 H), which when calculated gives us approximately 53.05 Hz. So, the correct answer is a) 53.05 Hz.