## Electric Power

Electric power is the rate of energy consumption in an electrical circuit.

The electric power is measured in units of watts.

- Electric power definition
- Electric power calculation
- Power of AC circuits
- Power factor
- Power calculator

### Electric power definition

The electric power P is equal to the energy consumption E divided by the consumption time t:

P is the electric power in watt (W).

E is the energy consumption in joule (J).

t is the time in seconds (s).

#### Example

Find the electric power of an electrical circuit that consumes 120 joules for 20 seconds.

Solution:

*E* = 120J

*t* = 20s

*P* = *E* / *t* = 120J / 20s = 6W

### Electric power calculation

*P* = *V *⋅* I *

or

*P = I ^{ }*

^{2 }⋅

*R*

or

*P = V ^{ }*

^{2}

*/*

*R*

P is the electric power in watt (W).

V is the voltage in volts (V).

I is the current in amps (A).

R is the resistance in ohms (Ω).

### Power of AC circuits

The formulas are for single phase AC power.

For 3 phase AC power:

When line to line voltage (V_{L-L}) is used in the formula, multiply the single phase power by square root of 3 (√3=1.73).

When line to zero voltage (V_{L-0}) is used in the formula, multiply the single phase power by 3.

#### Real power

Real or true power is the power that is used to do the work on the load.

*P* = *V _{rms}*

*I*

_{rms}*cos*

*φ*

*P *is the real power in watts [W]

V_{rms} is the rms voltage = V_{peak}/√2 in Volts [V]

I_{rms} is the rms current = I_{peak}/√2 in Amperes [A]

*φ * is the* *impedance phase angle = phase difference between voltage and current.

#### Reactive power

Reactive power is the power that is wasted and not used to do work on the load.

*Q* = *V _{rms}*

*I*

_{rms}*sin*

*φ*

*Q *is the reactive power in volt-ampere-reactive [VAR]

V_{rms} is the rms voltage = V_{peak}/√2 in Volts [V]

I_{rms} is the rms current = I_{peak}/√2 in Amperes [A]

*φ * is the* *impedance phase angle = phase difference between voltage and current.

#### Apparent power

The apparent power is the power that is supplied to the circuit.

*S* = *V _{rms}*

*I*

_{rms}

*S *is the apparent power in Volt-amper [VA]

V_{rms} is the rms voltage = V_{peak}/√2 in Volts [V]

I_{rms} is the rms current = I_{peak}/√2 in Amperes [A]

#### Real / reactive / apparent powers relation

The real power P and reactive power Q give together the apparent power S:

*P*^{2} + *Q*^{2} = *S*^{2}

*P *is the real power in watts [W]

*Q *is the reactive power in volt-ampere-reactive [VAR]

*S *is the apparent power in Volt-amper [VA]