Electric Power

 

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

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

P=\frac{E}{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 (VL-L) is used in the formula, multiply the single phase power by square root of 3 (√3=1.73).

When line to zero voltage (VL-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 = Vrms Irms cos φ

 

P      is the real power in watts [W]

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√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 = Vrms Irms sin φ

 

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

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√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 = Vrms Irms

 

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

Vrms  is the rms voltage = Vpeak/√2 in Volts [V]

Irms   is the rms current = Ipeak/√2 in Amperes [A]

 

Real / reactive / apparent powers relation

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

P2 + Q2 = S2

 

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]

 

Power factor ►

 

See also

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