Final answer:
To find the load Z that maximizes average power at ab terminals, we need to consider the power factor and phase angle of the circuit. However, without additional information about the circuit configuration and values of other components, we cannot provide a specific answer.
Step-by-step explanation:
To find the load Z that receives the maximum average power at ab terminals, we need to consider the power factor and phase angle of the circuit. At resonance or in a purely resistive circuit, Z = R and the power factor is 1, meaning voltage and current are in phase. At other frequencies or in an RLC circuit, the average power is affected by the phase angle and the power factor.
Therefore, to solve for ZL that maximizes average power, we need more information about the circuit configuration and the values of other components in the circuit.
The load Z that receives maximum average power in an AC circuit is achieved at the resonant frequency, where the load impedance equals the circuit's resistive part and the reactive components cancel out, resulting in a power factor of 1.
The question deals with finding the load Z that receives the maximum average power at ab terminals in an AC circuit containing a resistor (R), an inductor (L), and a capacitor (C). According to maximum power transfer theorem, a load receives maximum power when the load resistance is equal to the source (Thevenin's) resistance looking from the load terminals when all energy sources are deactivated. In an AC circuit at resonant frequency, the impedance of the inductor and capacitor cancel each other out, leaving only the resistive part, which implies that the phase angle between the voltage and current is zero.
To achieve maximum average power transfer, the circuit should be at resonance where the reactive components of the impedance (inductive and capacitive reactances) cancel each other out, and the power factor is 1 (cos φ = 1). The average power (Pave) delivered to an RLC circuit can be calculated using the formula Pave = Irms Vrms cos φ, where Irms and Vrms are the root-mean-square values of the current and voltage respectively, and φ is the phase angle. At resonance, the power factor is at its maximum, cos φ = 1, hence maximizing Pave.