Angular frequency of an alternating voltage:

The angular frequency of an alternating voltage is denoted by ω. It represents the rate at which the voltage changes over time in an alternating current (AC) circuit. The angular frequency is given by the equation:

ω = 2πf

where f is the frequency of the alternating voltage in hertz (Hz).

Angular frequency of instantaneous real power absorbed:

The instantaneous real power absorbed in an AC circuit is given by the equation:

P(t) = V(t) * I(t) * cos(θ)

where P(t) is the instantaneous real power, V(t) is the instantaneous voltage, I(t) is the instantaneous current, and θ is the phase angle between the voltage and current waveforms.

The angular frequency of the instantaneous real power absorbed is denoted by ω'. It represents the rate at which the real power changes over time in the AC circuit. The angular frequency is related to the frequency of the voltage and current waveforms by the equation:

ω' = 2πf'

where f' is the frequency of the instantaneous real power in hertz (Hz).

Explanation of the answer:

The angular frequency of the instantaneous real power absorbed in an AC circuit is related to the angular frequency of the alternating voltage by the equation:

ω' = 2ω

This means that the angular frequency of the instantaneous real power is twice the angular frequency of the alternating voltage. Therefore, the correct answer is option A, 2ω.

This relationship can be understood by considering the nature of the real power waveform in an AC circuit. The real power waveform is a product of the voltage and current waveforms, and it varies with time due to the phase difference between the voltage and current. The angular frequency of the real power waveform is determined by the rate at which the voltage and current waveforms change, which is twice the angular frequency of the voltage waveform. Hence, the answer is option A, 2ω.