Final answer:
To calculate the power in an AC circuit with a specific voltage applied to a load of a resistor and inductor in parallel, instantaneous power for the resistor is computed from the square of the current times resistance, while for the inductor the instantaneous power absorbs averages to zero. Real and reactive powers for the load require RMS values and the phase angle, and the power factor is the cosine of the phase angle.
Step-by-step explanation:
The question pertains to the calculation of power in an AC circuit where a voltage v(t)=212·1cos(ωt) is applied to a load consisting of a 6-Ω resistor in parallel with an inductive reactance XL=ωL=3.77Ω. To find the instantaneous power absorbed by the resistor, we use PR(t) = i2*R. The current through the resistor i(t) = v(t) / R, which for the resistor is the same as the total circuit current because the voltage across elements in parallel is the same. For the inductor, PL(t) will be zero because the power absorbed by a pure inductor averages to zero over a cycle. Real power absorbed by the load (P) is calculated using P=VI*cos(ϕ), where ϕ is the phase difference between current and voltage, and V and I are the RMS values of voltage and current, respectively. Reactive power (Q) is Q=VI*sin(ϕ), and the power factor is the cosine of the phase angle (ϕ).