Final answer:
The required capacitance to produce a 2.00 MΩ reactance at 60.0 Hz is approximately 0.00133 μF (1.33 nF), which is not listed among the provided options. This value was calculated using the formula C = 1/(2πfΩ) and plugging in the given frequency and reactance.
Step-by-step explanation:
The student asked what capacitance is necessary to produce a 2.00 MΩ reactance at 60.0 Hz. To find the answer, we can use the formula for capacitive reactance, which is Ω = 1/(2πfC), where Ω is the reactance in ohms, f is the frequency in hertz, and C is the capacitance in farads. Solving for C, we get C = 1/(2πfΩ).
By plugging in the values, we obtain C = 1/(2π × 60.0 Hz × 2.00 MΩ). Calculating this gives us a capacitance value of approximately 1.33 × 10^-9 farads, or 1.33 nF (nanofarads), which is 0.00133 μF. Therefore, none of the options provided (a) 2.12 μF, (b) 4.24 μF, (c) 6.36 μF, or (d) 8.48 μF would produce the required reactance.
It is important to note that in practical engineering applications, standard values of components are used, and an exact value may need to be accomplished through component combinations or an adjustable capacitor.