---
tags:
  - destiny/fleeting
  - topic/construction/electrical
  - type/encyclopedia
title: Alternating Current
---
# Alternating Current

> [!quote] [Alternating current (AC)](https://en.wikipedia.org/wiki/AC_power)
> is electric current that reverses direction periodically.
> The voltage and current in an AC circuit
> oscillate in a sinusoidal manner.
> The frequency of the oscillation
> is the number of complete cycles per second measured in hertz (Hz).
> The frequency of the AC power grid in the United States is 60 Hz.

* Ungrounded conductor - "Hot"
* Grounded conductor - "Neutral"

## Impedance

[resistance](https://en.wikipedia.org/wiki/Electrical_resistance)
[reactance](https://en.wikipedia.org/wiki/Electrical_reactance)
[impedance](https://en.wikipedia.org/wiki/Electrical_impedance)

## 3-Phase Power

The conductors between a voltage source and a load are called lines,
and the voltage between any two lines is called **line voltage**.
The voltage measured between any line and neutral is called **phase voltage**.

* Poles vs Phases vs Wires

* 3Ø = 3PH 3W
* 3ØY = 3PH 4W

> [!info] Phase Abbreviations
> * PH
> * Φ (capital phi)
> * Ø (latin O with stroke)

### Formula

#### Active Power

The formula for active power in a three phase system is given by

$$
P = \sqrt{3} \times V_{L} \times I_{L} \times \text{PF}
$$

where:

* $P$ is the active power,
* $V_{L}​$ is the line voltage,
* $I_{L}$ is the line current,
* $\text{PF}$ is the power factor.

#### Apparent Power

The formula for apparent power in a three phase system is given by

$$
S = \sqrt{3} \times V_{L} \times I_{L}
$$

$$
I_{L} = \frac{S}{\sqrt{3} \times V_{L}}
$$

where:

* $S$ is the apparent power,
* $V_{L}​$ is the line voltage,
* $I_{L}$ is the line current.

### Voltage Systems

120/240V 1-Phase 3-Wire:
* 120V 1-Phase 2-Wire --- Line to Neutral
* 240V 1-Phase 2-Wire --- Line to Line

208Y/120V 3-Phase 4-Wire:
* 120V 1-Phase 2-Wire --- Line to Neutral
* 208V 1-Phase 2-Wire --- Line to Line
* 208V 3-Phase 3-Wire --- Line to Lines

480Y/277V 3-Phase 4-Wire:
* 277V 1-Phase 2-Wire --- Line to Neutral
* 480V 1-Phase 2-Wire --- Line to Line
* 480V 3-Phase 3-Wire --- Line to Lines

Wiring Configurations

* 1-Phase 2-Wire --- Line to Line (2-Pole) or Line to Neutral (1-Pole)
* 1-Phase 3-Wire --- Line to Line and Line to Neutral (2-Pole)
* 3-Phase 3-Wire --- Line to Lines (3-Pole)
* 3-Phase 4-Wire --- Line to Lines and Line to Neutral (3-Pole)

## Active and Reactive Power

As a consequence of the periodic nature of AC,
and the electromagnetic "inertia" of inductance and capacitance,
inherent of all matter,
the power in an AC circuit is divided into two components:

* **Active Power**
  (abbreviated $P$, measured in watts)
  also known as real power, is power that _does work_.

* **Reactive Power**
  (abbreviated $Q$, measured in volt-amperes reactive (VAR))
  transfers no net energy to the load.

derived from these components are others:

* **Complex Power**
  (abbreviated $S$, measured in volt-amperes (VA))
  is the vector sum of the active and reactive components.
  It is "complex" because it exists on the real and imaginary axes
  of active and reactive power respectively.

* **Apparent Power**
  (abbreviated $|S|$, measured in volt-amperes (VA))
  is the magnitude of the complex power vector.

* **Power Factor**
  (abbreviated $\text{PF}$, unitless)
  is the ratio of active power to apparent power.

$$
P = S \times \text{PF}, \quad S = \frac{P}{\text{PF}}, \quad \text{PF} = \frac{P}{\text{S}}
$$

### Power Factor Correction

Capacitance and inductance can both be measured in VAR,
but their effects cancel each other out rather than add.

## Ferroelectric Hysteresis

The Venn Diagram of ferroelectric and ferromagnetic materials
has a large but not complete intersection.
