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The average power is the time average of the instantaneous power. In the case you describe, the instantaneous power is a 1W peak square wave and, as you point out, the average over a period is zero. But, consider the case of (in phase) sinusoidal voltage and current:
It is the average amount of work done or energy converted per unit of time. Average power is often called "power" when the context makes it clear. Instantaneous power is the limiting value of the average power as the time interval Δt approaches zero.
Mathematically, the average value of a periodic function is defined as the time integral of the function over a complete period, divided by the period. Therefore, the average power P for a periodic instantaneous power p is given by.
The average power is more convenient to measure. In fact, the wattmeter, the instrument for measuring power, responds to average power. The average power, in watts, is the average of the instantaneous power over one period. Thus, the average power is given by
Electrical power can be time-varying either as a DC quantity or as an AC quantity. The amount of power in a circuit at any instant of time is called the instantaneous power and is given by the well-known relationship of power equals volts times amps (P = V*I).
Average Power. The average power is defined as the average of instantaneous power over one cycle and is denoted by upper case letter P. It is also measured in watts. Avergae Power, p = Avg. of p over one cycle $$\mathrm{p=\frac{1}{2\pi}\int_{0}^{2\pi}p\:d\omega\:t\:\:\:\:...(4)}$$ Average Power Formula. Case 1 – Pure Resistive Circuit
What we’re almost always concerned with is the power averaged over time, which we refer to as the average power. It is defined by the time average of the instantaneous power over one cycle: Pave = 1 T∫T 0p(t)dt, where T = 2π / ω is the period of the oscillations.
Almost always the desired power in an AC circuit is the average power, which is given by P avg = VI cosφ where φ is the phase angle between the current and the voltage and where V and I are understood to be the effective or rms values of the voltage and current.
Calculating average power is essential and relatively simple using the relevant formulas. The key is understanding the concepts of work, force, and time, then applying them correctly. With some practice, you’ll be able to master the art of calculating average power and apply it whenever necessary.
Describe how average power from an ac circuit can be written in terms of peak current and voltage and of rms current and voltage; Determine the relationship between the phase angle of the current and voltage and the average power, known as the power factor