7.2 : 平均功率

For most practical applications, the time-varying instantaneous power is not a commonly used quantity.

Instead, the average power is used as the measurable quantity. It is calculated by integrating the instantaneous power over the period and dividing it by the period.

The expression for instantaneous power is substituted and further simplified to obtain a time domain expression for the average power.

The second term is the average value of the cosine function over a period and is zero.

The final expression of the average power is time-independent and is proportional to the phase difference between the voltage and current.

The term resulting from half the product of voltage and current in phasor form comprises both real and imaginary parts.

Comparing this phasor expression with the average power equation indicates that the real part corresponds to the average power.

In a purely resistive circuit, the in-phase voltage and current lead to a positive average power.

However, in purely reactive circuits, a ninety-degree phase shift between voltage and current results in zero average power.