# 功率

## 平均功率

$P_{\text{avg}}={\frac {\Delta W}{\Delta t}}$

$P=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {{\rm {d}}W}{{\rm {d}}t}}$

$W=PT\,.$

## 力学

$W=\mathbf {F} \cdot \mathbf {d}$

$P(t)=\mathbf {F} (t)\cdot \mathbf {v} (t)$

$P_{avg}={\frac {1}{\Delta t}}\int \mathbf {F} \cdot \mathbf {v} \;\mathrm {d} t$

$P(t)={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }}$

$P_{avg}={\frac {1}{\Delta t}}\int {\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }}\mathrm {d} t$ .

$P=p\cdot Q$

### 機械效益

$P=F_{A}v_{A}=F_{B}v_{B},\!$

$\mathrm {MA} ={\frac {F_{B}}{F_{A}}}={\frac {v_{A}}{v_{B}}}.$

$P=T_{A}\omega _{A}=T_{B}\omega _{B},\!$

$\mathrm {MA} ={\frac {T_{B}}{T_{A}}}={\frac {\omega _{A}}{\omega _{B}}}.$

## 电功率

$P(t)=V(t)I(t)$

$P=VI=I^{2}R={\frac {V^{2}}{R}}$

## 峰值功率及占空比

$P_{0}=\max[p(t)]$ .

$\epsilon _{\mathrm {pulse} }=\int _{0}^{T}p(t)\mathrm {d} t\,$

$P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}p(t)\mathrm {d} t={\frac {\epsilon _{\mathrm {pulse} }}{T}}\,$

${\frac {P_{\mathrm {avg} }}{P_{0}}}={\frac {\tau }{T}}\,$

## 参考

1. ^ Halliday and Resnick. 6. Power. Fundamentals of Physics. 1974.
2. ^ Chapter 13, § 3, pp 13-2,3 The Feynman Lectures on Physics Volume I, 1963
3. ^ Chapter 6 § 7 Power Halliday and Resnick, Fundamentals of Physics 1974.
4. ^ Chapter 13, § 3, pp 13-2,3 The Feynman Lectures on Physics Volume I, 1963
5. ^ 燒一公斤的煤會放出每公斤15－30百萬焦耳的能量，而引爆一公斤的三硝基甲苯會產生4.7百萬焦耳的能量，有關煤的熱值，可以參考Fisher, Juliya. Energy Density of Coal. The Physics Factbook. 2003 [30 May 2011]. （原始内容存档于2006-11-07）.有關三硝基甲苯的熱值，可以參考爆炸当量條目。
6. Electric Power and Energy. [2010-05-18].[永久失效連結]
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