Final answer:
To calculate the rms voltmeter reading across a resistor in an AC circuit, one can use Ohm's law and formulas for impedance and capacitive reactance to determine the current in the circuit and then calculate the voltage across the resistor.
Step-by-step explanation:
The student is asking how to calculate the root mean square (rms) voltmeter reading across a resistor R in an alternating current (AC) series circuit that includes a resistor R and a capacitor C. Given the resistance value (20.0 Ω), the capacitance (31 μF), and an AC source with 80.0 V rms at 600 Hz, we must use the formula for the voltage across the resistor in an AC circuit, which basically is the product of the current through the circuit and the resistance R.
The rms current (√(Irms)) can be calculated using Ohm's law, √(Vrms) = √(Irms) × Z, where Z is the impedance of the series circuit. The impedance of the series circuit can be calculated using Z = √(R^2 + (X_L-X_C)^2), where X_L and X_C are the inductive and capacitive reactances respectively. However, since there is no inductance (L) provided in this scenario, X_L is zero, and we only calculate X_C using X_C = 1/(2πfC). Once we have Z, we calculate √(Irms) using the source voltage and impedance, and finally, we use √(Vrms)_R = √(Irms) × R to find the voltage across the resistor.