Final answer:
Given a series RLC circuit with a resistance of 23 ohms, a capacitance of 0.79 µF, an inductance of 280 mH, and a fixed root mean square (rms) voltage output of 12 volts, further specific calculations or conclusions require additional information or a defined frequency value from the variable-frequency source.
Step-by-step explanation:
In a series RLC circuit, the combination of resistance (R), inductance (L), and capacitance (C) affects the impedance and behavior of the circuit when connected to an alternating current (AC) source. The impedance (Z) in such a circuit is given by the formula Z = √(R² + (Xl - Xc)²), where Xl represents the inductive reactance (Xl = 2πfL) and Xc denotes the capacitive reactance (Xc = 1/(2πfC)).
However, to precisely determine the impedance and other circuit properties like resonant frequency, current, or power, a specific frequency value from the variable-frequency source is required. At the resonant frequency, the inductive and capacitive reactances become equal, resulting in the minimum impedance.
Given the root mean square (rms) voltage output of 12 volts, it's crucial to determine the frequency of the AC source to calculate the current flowing through the circuit (I = V/Z) and analyze other circuit characteristics. Without the frequency value, specific calculations concerning current, resonant frequency, or power cannot be accurately determined. Hence, to comprehensively assess the circuit's behavior and response to the applied voltage, the specific frequency value from the variable-frequency source is necessary to perform precise calculations and draw conclusions regarding the series RLC circuit's performance.