Final answer:
To calculate the power output of a sinusoidal voltage source in an RLC series circuit, the impedance of the circuit must be determined. The impedance is calculated using Ohm's law and the inductive and capacitive reactances of the circuit. Once the impedance is known, the current flowing through the load can be calculated, and the power output of the source can be found by multiplying the voltage across the load with the current.
Step-by-step explanation:
An RLC series circuit consists of a 10-ohm resistor, a 100-mH inductor, and a variable frequency sinusoidal voltage source. The voltage source supplies power to the circuit, and the load includes both the resistor and the inductor. The voltage across the load can be calculated using Ohm's law, and the power output of the source can be determined by multiplying the voltage across the load with the current flowing through it. To find the current, we need to calculate the impedance of the circuit.
The impedance of an RLC series circuit is given by Z = sqrt(R^2 + (Xl - Xc)^2), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. Since the inductor and capacitor are in parallel, their reactances subtract. The inductive reactance is given by Xl = 2pifL, where f is the frequency and L is the inductance. The capacitive reactance is given by Xc = 1/(2pifC), where C is the capacitance.
Once the impedance is determined, the current flowing through the load can be calculated using Ohm's law, I = V/Z. Finally, the power output of the source can be found by multiplying the voltage across the load with the current flowing through it, P = V * I.