7.2:
Average Power
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.
7.2:
Average Power
In practical electrical applications, the concept of time-varying instantaneous power is not frequently utilized. Instead, focus shifts to the more practical quantity known as average power. Average power is determined by integrating the instantaneous power over a specified time period and subsequently dividing it by that duration.
The equation for instantaneous power is simplified to arrive at a time-domain expression for average power. Notably, the second term, involving a cosine function, averages out to zero over a complete cycle.
As a result, the final expression for average power is independent of time and contingent upon the phase difference between voltage and current.
Upon comparing this expression with the phasor representation of the product of voltage and current, it becomes evident that the real part of the phasor corresponds to the average power.
In purely resistive circuits, where voltage and current are perfectly in phase, the average power is positive, signifying continuous power consumption. Conversely, the average power dwindles to zero in purely reactive circuits characterized by a ninety-degree phase shift between voltage and current. This phenomenon is attributed to the cyclic storage and release of energy, where, on average, no net power is consumed.
It's important to recognize that while instantaneous power varies with respect to time, average power remains constant. Calculating instantaneous power requires voltage and current in the time domain, but average power can also be determined when voltage and current are represented in the frequency domain using phasors.
Understanding average power is vital in practical applications, as it facilitates the assessment of power consumption and efficiency, especially in circuits featuring diverse combinations of resistive and reactive components.