In a single-phase sinusoidal AC circuit, the instantaneous voltage and current vary as sinusoidal functions over time. The amplitude, fundamental frequency, and average value of the instantaneous power can be described as follows:
Amplitude: The amplitude refers to the peak value of the voltage or current waveform. It represents the maximum magnitude reached by the sinusoidal function. The amplitude is typically denoted by "Vmax" for voltage or "Imax" for current.
Fundamental Frequency: The fundamental frequency of an AC circuit is the frequency at which the sinusoidal waveform repeats itself. It is denoted by "f" and is usually measured in Hertz (Hz). In most countries, the standard frequency for AC power systems is 50 Hz or 60 Hz.
Average Value of Instantaneous Power: The instantaneous power in an AC circuit is given by the product of the instantaneous voltage and current at any given time. However, since the voltage and current waveforms are sinusoidal, the power varies over time. The average value of the instantaneous power can be calculated using the concept of RMS (Root Mean Square) values.
The RMS values of voltage and current, denoted as Vrms and Irms respectively, are related to the amplitude values by the following equations:
Vrms = Vmax / √2 Irms = Imax / √2
The average value of the instantaneous power, denoted as Pavg, can be calculated using the following formula:
Pavg = Vrms * Irms * cos(θ)
where θ represents the phase angle between the voltage and current waveforms.
It's worth mentioning that in an ideal single-phase sinusoidal AC circuit with a purely resistive load, the phase angle between voltage and current is zero (θ = 0), resulting in a purely real power. In this case, the average value of the instantaneous power simplifies to:
Pavg = Vrms * Irms
However, in circuits with reactive components (such as inductive or capacitive loads), the phase angle will differ from zero, leading to a power factor that affects the average power value.