Question

Let vₛ(t) = 1cos(2t)V, R₁ = 8Ω, R₂ = 6Ω, C₁ = 500mF and C₂ = 550mF.

a). If Zₗ is a purely resistive load chosen to maximize the average power it receives, the resistor value is Zₗ = ____ and resulting average power is P = ____ W

Answer 1

The given information is not enough to calculate the load resistor value, ZL, or the average power without additional context on the circuit configuration. For maximum power transfer, the load impedance should match the complex conjugate of the circuit's total impedance without the load.

Step-by-step explanation:

The question asks for the optimal value of a load resistor, ZL, that maximizes the average power received by it in an AC circuit that also includes resistors, inductor, and capacitors. To find the value of ZL that maximizes average power, we would need to ensure that the load resistor is matched to the equivalent resistance of the circuit. However, the given circuit values (R1, R2, C1, C2, and the source voltage vs(t)) are not enough to calculate ZL without additional context such as the configuration of the components (series or parallel), and whether the load resistor is in series or parallel with the rest of the circuit.

In general, for maximum power transfer in an AC circuit, ZL should be equal to the complex conjugate of the total impedance of the circuit without the load (Zth). The maximum average power can then be computed using the formula P = V2/(4Zth), where V is the RMS voltage across the load resistor.