Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# AC - Active, Reactive and Apparent Power

## Real, imaginary and apparent power consumption in AC circuits

The required power supply to an electric circuit depends on the

• active power - real electrical resistance power consumption in circuit
• reactive power - imaginary inductive and capacitive power consumption in circuit

The required power supply is called the apparent power and is a complex value that can be expressed in a Pythagorean triangle relationship as indicated in the figure below.

### Apparent Power - S

The apparent power is the power supplied to the electric circuit - typical from a power supplier to the grid - to cover the real and reactive power consumption in the loads.

Apparent power can be calculated as

S = (Q2 + P2)1/2                     (1)

where

S = apparent power supply to the circuit (volt ampere, VA)

Q = reactive power consumption in load (volt ampere reactive, VAR)

P = active power consumption in load (watts, W)

Apparent power is measured in volt-amperes (VA) - the AC system voltage multiplied with flowing current. Apparent power is a complex value and the vector sum of the active and reactive power as indicated in the figure above.

#### Single Phase Current

S = U I                  (2a)

where

U = electric potential (V)

I = current (A)

#### Three Phase Current

S = 31/2 U I

= 1.732 U I                 (2b)

### Active Power - P

Active - or real or true - power do the actual work in the load. Active power is measured in watts (W) and is the power consumed by electrical resistance.

#### Single Phase Current

P = U I cos φ

= U I PF                   (3a)

where

φ = phase angle between the electrical potential (voltage) and the current

PF = cos φ

=  Power Factor

#### Three Phase Current

P = 31/2 U I cos φ

= 1.732 U I PF                     (3b)

#### Direct Current

P = U I                         (3c)

### Reactive Power - Q

Reactive power is the imaginary or complex power in a capacitive or inductive load. Reactive power represents an energy exchange between the power source and the reactive loads where no net power is gained or lost. The net average reactive power is zero. Reactive power is stored in and discharged by inductive motors, transformers, solenoids and capacitors.

Reactive power should be minimized because it increases the overall current flowing in an electric circuit without providing any work to the load. Increased reactive currents only provides unrecoverable power loss due to power line resistance.

Increased reactive and apparent power will devrease the power factor - PF.

Reactive inductive power is measured in volt-amperes reactive (VAR).

#### Single Phase Current

Q = U I sin φ

= U I PF                    (4a)

where

φ = phase angle

#### Three Phase Current

Q = 31/2 U I sin φ

=  1.732 UI PF                   (4b)

## Related Topics

• Electrical - Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

11 29