# 電壓

（重定向自電勢差

V , V , U , U

Voltage = 能量 / 電荷

## 定義

### 以電位能定義

{\displaystyle {\begin{aligned}\Delta V_{AB}&=V(x_{B})-V(x_{A})\\&=-\int _{r_{0}}^{x_{B}}{\vec {E}}\cdot d{\vec {l}}-\left(-\int _{r_{0}}^{x_{A}}{\vec {E}}\cdot d{\vec {l}}\right)\\&=-\int _{x_{A}}^{x_{B}}{\vec {E}}\cdot d{\vec {l}}\end{aligned}}}

${\displaystyle U=\Delta V=-L{\frac {dI}{dt}}}$

### 以電場的分解定義

${\displaystyle {\vec {E}}=-\nabla V-{\frac {\partial {\vec {A}}}{\partial t}}}$

{\displaystyle {\begin{aligned}\Delta V_{AB}&=-\int _{x_{A}}^{x_{B}}{\vec {E}}_{\mathrm {conservative} }\cdot d{\vec {l}}\\&=-\int _{x_{A}}^{x_{B}}\left({\vec {E}}+{\frac {\partial {\vec {A}}}{\partial t}}\right)\cdot d{\vec {l}}\\&=-\int _{x_{A}}^{x_{B}}({\vec {E}}-{\vec {E}}_{\mathrm {induced} })\cdot d{\vec {l}}\end{aligned}}}

### 在電路分析的電壓

${\displaystyle \int \mathrm {\vec {E}} \cdot d{\vec {l}}=-L{\frac {dI}{dt}}}$

## 應用

### 電壓的相加

A,C之間的電壓會是A,B之間的電壓加上B,C之間的電壓。各種電路中的電壓可以用克希荷夫電路定律計算。

## 參考資料

1. ^
2. ^
3. ^ IEV: voltage
4. ^ Demetrius T. Paris and F. Kenneth Hurd, Basic Electromagnetic Theory, McGraw-Hill, New York 1969, ISBN 0-07-048470-8, pp. 512, 546
5. ^ P. Hammond, Electromagnetism for Engineers, p. 135, Pergamon Press 1969 OCLC 854336.
6. ^ Introduction to Electrodynamics. ISBN 1108420419.
7. ^ Bagotskii, Vladimir Sergeevich. Fundamentals of electrochemistry. 2006: 22. ISBN 978-0-471-70058-6.
8. Robert N. Varney, Leon H. Fisher, "Electromotive force: Volta's forgotten concept", American Journal of Physics, vol. 48, iss. 5, pp. 405–408, May 1980.
9. ^ C. J. Brockman, "The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed", Journal of Chemical Education, vol. 5, no. 5, pp. 549–555, May 1928