Final answer:
To achieve a 20.0 kΩ reactance at 500 Hz, the formula is XL = 2πfL. Solving for L gives us approximately 6.37 H, which does not match any of the provided options exactly, indicating that the answer would be none of the above.
Step-by-step explanation:
To determine the value of inductance required to achieve a 20.0 kΩ reactance at a frequency of 500 Hz, you can use the formula for inductive reactance: XL = 2πfL, where XL is the reactance in ohms, f is the frequency in hertz, and L is the inductance in henrys. By rearranging this formula to solve for L, you get L = XL / (2πf). Plugging in the given values, you have L = 20000 Ω / (2 * π * 500 Hz).
The calculation gives:
L = 20000 / (2 * π * 500)
L = 20000 / 3141.59
L = 6.3662 H which round to approximately 6.37 H .