Electric power is the rate of energy consumption in an electrical circuit.
The electric power is measured in units of watts.
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).
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
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).
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 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 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.
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]
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]
