Final answer:
The RMS current in the circuit can be calculated by first determining the capacitive reactance, then finding the total impedance of the circuit which includes the resistance and capacitive reactance, and finally using Ohm's law to find the RMS current by dividing the RMS voltage by the total impedance.
Step-by-step explanation:
To calculate the RMS current in the circuit with a given capacitor, resistor, and AC generator, we need to use the concept of capacitive reactance and Ohm's law. First, we find the capacitive reactance (XC) using the formula XC = 1/(2πfC), where f is the frequency and C is the capacitance. Then we use Ohm's law, where the RMS current (IRMS) is the RMS voltage (VRMS) divided by the total impedance (Z) of the circuit. The impedance in this case is just the combination of the resistance R and capacitive reactance in series: Z = √(R^2 + XC^2).
Given values:
Calculations:
XC = 1/(2π × 51.0 × 30.9 × 10^-6) Ω
Z = √((50.2²) + (XC²)) Ω
IRMS = VRMS / Z A