Final answer:
The average power delivered to a 40 ohm resistor in an RLC circuit can be found using the formula Pave = Vrms squared over the resistance. At resonance the phase angle is zero, and cos(θ) equals 1, simplifying the calculations. For the provided Vrms of 120 V at resonance, the average power is 360 W.
Step-by-step explanation:
To find the average power delivered to a 40 ohm resistor in an RLC circuit, we use the formula Pave = Irms × Vrms × cos(θ), where Pave is the average power, Irms is the root mean square of the current, Vrms is the root mean square of the voltage, and θ is the phase angle between current and voltage.
In the scenario where Vrms is 120 V and Pave is 60.0 W at resonance, we can deduce that θ = 0° because an RLC circuit at resonance behaves like a purely resistive circuit. Therefore, cos(θ) = 1. To calculate the average power at any other frequency, we need to consider the phase angle and calculate the new power factor.
For the given example, at resonance, the average power delivered can be calculated by simply squaring the Vrms divided by the resistance, as follows: Pave = (Vrms²/R) = (120 V)²/(40 Ω) = 360 W. However, at frequencies other than the resonant frequency, the power calculations require the power factor, which is not provided in the excerpt.