## 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·Ior

P = I^{ }^{2 }·Ror

P = V^{ }^{2}/RP 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}cosφ

Pis 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]

φis theimpedance 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}sinφ

Qis 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]

φis theimpedance 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}

Sis 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}

Pis the real power in watts [W]

Qis the reactive power in volt-ampere-reactive [VAR]

Sis the apparent power in Volt-amper [VA]

## See also