Final answer:
The power absorbed by the load in the presence of a sinusoidal voltage and a nonsinusoidal current is calculated using the RMS values of the fundamental components of voltage and current, along with the cosine of the phase difference between them.
Step-by-step explanation:
The power absorbed by a load in an AC circuit with a sinusoidal voltage source and a nonsinusoidal current can be calculated using the product of the voltage and the current at each harmonic followed by averaging over time. Since real power is absorbed only when voltage and current are in phase, we consider the fundamental frequency at which current and voltage have the same frequency (60 Hz in this case) for the power calculation.
The sinusoidal voltage source is given by v(t) = 120cos(2ω60t) V, and the Fourier series formed current is given as i(t) = 10cos(2ω60t + 30°) + terms at higher harmonics which we ignore for the power calculation. The power absorbed at the fundamental frequency is the product of the RMS values of the voltage and the fundamental component of the current, along with the cosine of the phase angle difference, Φ, between them.
The RMS value of the voltage is 120V/√2, and the RMS value of the fundamental component of the current is 10 A/√2. The phase difference is 30°. Therefore, the power absorbed by the load, P, is calculated as P = (VRMS)(IRMS)cos(Φ), which yields P = (120/√2)(10/√2)cos(30°) W.