AC PowerAs in the case with DC power, the instantaneous electric power in an AC circuit is given by P = VI, but these quantities are continuously varying. Almost always the desired power in an AC circuit is the average power, which is given by 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. The term cos φ is called the "power factor" for the circuit. Default values will be entered for unspecified parameters, but all component values can be changed. Click outside the box after entering data to initiate the calculation. 
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Instantaneous PowerAs in DC circuits, the instantaneous electric power in an AC circuit is given by P=VI where V and I are the instantaneous voltage and current.
and using the trig identity the power becomes: Averaging this power over a complete cycle gives the average power. 
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Average PowerNormally the average power is the power of interest in AC circuits. Since the expression for the instantaneous power is a continuously varying one with time, the average must be obtained by integration. Averaging over one period T of the sinusoidal function will give the average power. The second term in the power expression above averages to zero since it is an odd function of t. The average of the first term is given by

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Average Power IntegralFinding the value of the average power for sinusoidal voltages involves the integral The period T of the sinusoid is related to the angular frequency ω and angle θ by Using these relationships, the integral above can be recast in the form:

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