AC Power

As 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.

RLC series circuit details RLC串联电路细节 平均功率 P_avg = VI cosφ

For C = μF 对于 C = μF 中文译文中的待填/计算数值依次对应：1：cm。实际数值以上方原输入框为准。 and 并且 L = mH L = mH（专名或术语） 中文译文中的待填/计算数值依次对应：1：lm。实际数值以上方原输入框为准。 and resistance R = ohms 并有电阻 R = 欧姆 中文译文中的待填/计算数值依次对应：1：r。实际数值以上方原输入框为准。

at angular frequency ω = x10^ rad/s, 在角频率 ω = x10^ rad/s， 中文译文中的待填/计算数值依次对应：1：wb 2：wp。实际数值以上方原输入框为准。

frequency f = x10^ Hz = kHz = MHz 频率 f = x10^ Hz = kHz = MHz 中文译文中的待填/计算数值依次对应：1：fb 2：fp 3：fk 4：fm。实际数值以上方原输入框为准。

the impedance is

阻抗是

Z = x10^ ohms at phase φ = degrees. Z = x10^欧姆在相位φ =度。 中文译文中的待填/计算数值依次对应：1：zb 2：zp 3：ph。实际数值以上方原输入框为准。

For an applied rms voltage V = volts,

对于施加的均方根电压 V = 伏特，

中文译文中的待填/计算数值依次对应：1：vapp。实际数值以上方原输入框为准。

the rms current will be I = x 10^ amperes.

均方根电流将为 I = x 10^ 安培。

中文译文中的待填/计算数值依次对应：1：ib 2：ip。实际数值以上方原输入框为准。

and the AC power is given by Pavg = VI cosφ = watts 交流电的功率由 P_avg = VI cosφ = 瓦特给出 中文译文中的待填/计算数值依次对应：1：p。实际数值以上方原输入框为准。

The power factor is cos φ = 功率因数是cos φ = 中文译文中的待填/计算数值依次对应：1：powf。实际数值以上方原输入框为准。

so the power is reduced to that fraction of what it would be in a DC circuit with the same voltage and current.

因此，功率降到了在相同电压和电流的直流电路中应有的那部分分数。

Instantaneous Power

As 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.

Since then the instantaneous power at any time t can be expressed as 则在任意时间t的瞬时功率可以表示为 由于

and using the trig identity

the power becomes:

Averaging this power over a complete cycle gives the average power.

Average Power

Normally 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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Since the rms voltage and current are given by 由于有效值电压和电流由		and 并且	,

Average Power Integral

Finding 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:

	Which can be shown using the trig identity: which reduces the integral to the value 1/2 since the second term on the right has an integral of zero over the full period. 这可以通过三角恒等式证明：这将积分简化为1/2，因为右边的第二项在整个周期内积分值为零。