Final answer:
The frequency at which the generator will produce an mms current of 8.00 mA in the capacitor is approximately 11.9 kHz.
Step-by-step explanation:
To find the frequency at which the generator will produce an mms (milliampere meter square) current of 8.00 mA in the capacitor, we need to use the formula:
f = 1 / (2 * pi * sqrt(LC))
Where f is the frequency, L is the inductance, and C is the capacitance.
From the given information, the capacitance (C) is 0.0130 μF. We can rearrange the formula to solve for frequency:
f = 1 / (2 * pi * sqrt(L * C))
Given that the voltage across the capacitor (V) is 464 V and the current (I) is 8.00 mA, we can use Ohm's law to find the impedance (Z) of the capacitor: Z = V / I. The impedance of a capacitor is given by: Z = 1 / (2 * pi * f * C). Rearranging the formula, we get: f = 1 / (2 * pi * Z * C).
Substituting the values, we get:
f = 1 / (2 * pi * 464 V / (8.00 mA * 0.0130 μF))
Simplifying this expression, we find that the frequency is approximately 11.9 kHz.