Electrical Formulas

Overview

Fundamental formulas for DC and single-phase and three-phase AC electrical circuits, covering Ohm's Law, power, impedance, and motor calculations.

Key Formulas

Ohm's Law

The relationship between voltage, current, and resistance in any electrical circuit.

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

DC Power

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

Energy

$W = P \cdot t$

where t is time in seconds (J) or hours (Wh).

AC Single-Phase Power

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

AC Three-Phase Power

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

Impedance (Series RLC)

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

Inductive Reactance

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

Capacitive Reactance

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

Variables

Electrical Units

Calculators

Ohm's Law

DC Power & Energy

Unit Converter

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.

Restored Original Source Tables

The following tables are restored from the original source page to preserve the complete reference data.

Original Source Images

The following original source images are preserved to avoid losing visual reference material. When an image contains chart or tabular data, its extracted values are represented in the page tables, calculators, or interactive charts; remaining images are retained as visual source references.

ohms law

Engineering Notes

• 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.

References

• Original Source — Engineering ToolBox: Electrical Formulas