正弦功率计算用到的公式

正弦功率计算用到的公式

正弦交流电路是最基本的交流电路形式。以下汇总正弦电路功率计算的核心公式。

一、瞬时功率

设 $u = U_m\sin\omega t$，$i = I_m\sin(\omega t - \varphi)$，瞬时功率为：文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

$p(t) = ui = U_m I_m\sin\omega t\cdot\sin(\omega t - \varphi)$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

二、有功功率（平均功率）

$P = UI\cos\varphi$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

其中 $U = \dfrac{U_m}{\sqrt{2}}$，$I = \dfrac{I_m}{\sqrt{2}}$ 为有效值，$\cos\varphi$ 为功率因数。文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

三、无功功率

$Q = UI\sin\varphi$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

四、视在功率

$S = UI$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

$S = \sqrt{P^2 + Q^2}$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

五、功率三角形

$\tan\varphi = \dfrac{Q}{P}$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html

$\varphi = \arctan\dfrac{Q}{P}$文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html 文章源自公式库网-https://www.gongshiku.com/html/201808/zhengxiangongshuaijisuanyongdaodegongshi.html