The concept of average power in AC circuits can indeed be applied to non-sinusoidal waveforms such as square or triangular waves, though the approach is somewhat different from that used for sinusoidal waves. For these types of waveforms, the average power calculation must consider the specific shape of the waveform. For instance, in a square wave, the voltage or current alternates between a fixed maximum and minimum value without the gradual rise and fall seen in sinusoidal waves. Consequently, the average power is calculated based on the duration these values are held and their respective magnitudes. In the case of a triangular wave, the linear rise and fall of the waveform need to be considered, which results in a different average value of the squared waveform compared to a sinusoidal one. Therefore, while the fundamental principle of averaging the instantaneous power over a cycle remains the same, the actual calculation must be adapted to the waveform's specific characteristics.

Using RMS (Root Mean Square) values rather than peak values in electrical systems is more convenient and practical for several reasons. Firstly, RMS values simplify the calculation of average power in AC circuits. RMS values provide a measure of the effective or equivalent DC value of an AC quantity (voltage or current) that would deliver the same power to a load. This simplification is extremely useful for designing and analysing electrical systems and appliances, as it allows for a direct comparison with DC systems. Secondly, RMS values are more representative of the actual energy transfer in an AC circuit over time, as opposed to peak values which only reflect the maximum instantaneous value. This is particularly important in real-world applications where understanding the energy consumption and heat dissipation is crucial for safety and efficiency. Lastly, most measuring instruments are calibrated to read RMS values because these are more relevant for assessing the practical implications of voltage and current in terms of power consumption and load handling.

The phase difference between voltage and current in an AC circuit significantly affects the calculation of average power. In a purely resistive circuit, the voltage and current are in phase, meaning they reach their maximum and zero values simultaneously. Under these conditions, the average power can be calculated using the RMS values of voltage and current directly. However, in circuits with inductive or capacitive components, the voltage and current are out of phase. This phase difference means that the peaks of voltage and current do not coincide, altering the waveform of the power and its average value over a cycle. To calculate average power in such cases, one must take into account the power factor, which is the cosine of the phase angle between voltage and current. The power factor adjusts the average power to reflect the actual effective power being used or dissipated in the circuit, which is less than or equal to the product of RMS voltage and current due to this phase difference.

The average power in an AC circuit does not equate to the arithmetic mean of the maximum and minimum power due to the sinusoidal nature of AC waveforms. In an AC circuit, especially a resistive one, power varies as the square of the current or voltage, which themselves vary sinusoidally. This squaring effect means that the power waveform is always positive and has a different form than the original sinusoidal current or voltage waveform. When calculating the average power, one must consider this squaring effect. As the average of the square of a sine function over a complete cycle is 1/2, the mean power in an AC circuit becomes half of the maximum power, rather than the arithmetic mean of maximum and minimum values. This distinction is crucial for understanding the energy transfer and consumption in AC systems, especially in scenarios where accurate power calculations are essential for the design and operation of electrical devices and systems.

Harmonic distortions in an AC circuit can significantly complicate the calculation of average power. Harmonics are essentially higher frequency components that are integer multiples of the fundamental frequency of the AC waveform. They can arise due to non-linear loads or devices within the circuit, such as transformers, motors, or electronic equipment. These harmonics alter the shape of the current and voltage waveforms from a pure sine wave to a more complex form. This change in waveform affects the power calculation because the average of the product of voltage and current over time – which is how average power is determined – will now include the effects of these additional frequency components. In circuits with significant harmonic content, the RMS values of voltage and current, and consequently the average power, can be higher than what would be predicted by considering only the fundamental frequency. Accurately calculating average power in such cases often requires sophisticated analysis methods, such as Fourier analysis, to decompose the waveform into its fundamental and harmonic components.