电气工程公式

概述

直流、单相和三相交流电路的基本公式，涵盖欧姆定律、功率、阻抗和电机计算。

关键公式

欧姆定律

任何电路中电压、电流和电阻之间的关系。

$V = I \cdot R \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}$

直流功率

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

能量

$W = P \cdot t$

其中 t 为时间，以秒 (J) 或小时 (Wh) 为单位。

交流单相功率

$P = V \cdot I \cdot \cos\phi$

交流三相功率

$P = \sqrt{3}\; V_{L} \; I_{L} \; \cos\phi$

阻抗（串联 RLC）

$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$

感抗

$X_{L} = 2\pi f L$

容抗

$X_{C} = \frac{1}{2\pi f C}$

变量

Electrical Units

计算器

欧姆定律

直流功率与能量

单位换算器

The source page included a Unit Converter section. This calculator preserves common electrical unit conversions used with the formulas above.

Motor Formulas

For three-phase AC motors the following relationships apply.

Motor Efficiency

$\eta = \frac{746 \cdot P_{hp}}{P_{in}}$

where P_hp is shaft horsepower and P_in is electrical input in watts.

For a three-phase supply:

$\eta = \frac{746 \cdot P_{hp}}{\sqrt{3}\; V_{L}\; I_{L}\; \cos\phi}$

Motor Current (3-Phase)

$I = \frac{746 \cdot P_{hp}}{\sqrt{3}\; V_{L}\; \eta\; \cos\phi}$

Motor Input Power (3-Phase)

$P_{in} = \frac{\sqrt{3}\; V_{L}\; I_{L}\; \cos\phi}{1000} \quad \text{(kW)}$

Worked Examples

Battery & resistor — A 12 V battery drives an 18 Ω load:

$I = \frac{12}{18} = 0.67 \; \text{A}$

Resistor dissipation — 12 V across 50 Ω for 60 s:

$P = \frac{12^{2}}{50} = 2.88 \; \text{W} \qquad W = 2.88 \times 60 = 173 \; \text{J}$

Stove — 5 MJ consumed from 230 V in 60 min:

$P = \frac{5 \times 10^{6}}{3600} = 1389 \; \text{W} \qquad I = \frac{1389}{230} = 6.0 \; \text{A}$

Interactive Ohm's Law Charts

The source page includes Ohm's Law and power nomogram images. The charts below convert their relationships into interactive datasets.

还原的原始源表

以下表格还原自原始来源页面，以保留完整的参考数据。

原始源图

以下原始来源图像予以保留，以免丢失视觉参考资料。当图像包含图表或表格数据时，其提取值已呈现在页面的表格、计算器或交互式图表中；其余图像保留为视觉来源参考。

ohms law

工程要点

• DC vs. AC power: In DC circuits volt-amperes equal watts. In AC circuits the power factor causes apparent power (VA) to exceed real power (W). Always specify whether a rating is in W or VA.
• Power factor correction: Industrial facilities often install capacitor banks to bring the power factor closer to unity, reducing demand charges and line losses.
• Three-phase convention: The √3 factor assumes a balanced three-phase system. Unbalanced loads require per-phase analysis.
• Motor efficiency (η): The constant 746 converts horsepower to watts (1 hp = 746 W). Typical motor efficiencies range from 80 % to 96 % depending on size and class.
• Thermal limits: Formulas assume steady-state conditions. Actual conductor and component ratings must account for ambient temperature, insulation class, and duty cycle per NEC / IEC standards.
• Reactive power: Inductive and capacitive reactance cause current and voltage to be out of phase. The impedance formula combines resistive and reactive components in series.

参考资料

• Original Source — Engineering ToolBox: Electrical Formulas