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In an alternating current circuit, power is defined as the amount of energy delivered by the circuit per unit of time. It is used to determine the total power needed to run a load. In the case of a DC circuit, voltage and current become constant. However, in an alternating current circuit, the instantaneous values of current and voltage flows are not constant; thus, the power of the supply varies with time. As a result, different methods are used to measure the power of an alternating current.
As a general concept, power describes the rate at which a particular amount of energy is released/transmitted by a system. This energy can take various forms, such as kinetic, magnetic, electric, etc. Power is thus expressed in any domain as an amount of energy per unit of time. Joule/second (J/s) or Watt (W) is the SI unit of power.
An AC signal is taken with V(t) = Vmax × sin (ωt + Φv) being the voltage and I(t) = Imax sin × (ωt + ΦI) being the current where,
Vmax, Imax are the max values,
ω is the angular frequency,
Φv, ΦI are the phases of voltage and current signal.
Therefore, ΔΦ = Φv – ΦI
Along with V(t), I(t), sin(X)sin(Y) = 1/2(cos(X-Y)-cos(X+Y)) and (Vrms × Irms)/2 = Vrms × Irms is combined and gives:
P(t) = Vrms × Irms (cos(ΔΦ)-cos(2ωt + ΔΦ))
Therefore,
P = 1/T T∫oP(t)dt =Vrms × Irmscos(ΔΦ)
Power factor
The ratio of the actual power running across the circuit to an apparent power existing in the circuit is known as the power factor of the alternating current. True power is the power dissipated in a circuit’s resistance or the power used in the circuit. In an alternating current circuit, a voltmeter measures the effective voltage and an ammeter measures the effective current. The apparent power is the product of these two readings. That power appears to be available in an alternating current circuit with a reactive component. It is determined by the product of RMS voltage and RMS current, and its unit is volt-amps. To obtain the true available power, it is multiplied by the power factor.
The apparent power is equal to the true power only when the AC circuit is made up of pure resistance.
PF = [(true power)(W)] / [(apparent power)(V/A)]
Power triangle
A power triangle is a correlation between active power, reactive power and apparent power that can be clarified by defining numbers in geometrical forms, such as the vector. The amount of power that is dissipated or does useful work in the circuit is referred to as active, genuine or real power.
The power that travels back and forth between the source and the load is referred to as reactive power. The complicated combination of true and reactive powers is referred to as apparent power. Regardless of phase angle, the perceived power equals the multiplication of voltage and current.
Conclusion
As a general concept, power describes the rate at which a particular amount of energy is released/transmitted by a system. The ratio of the true power running across the circuit to an apparent power existing in the circuit is known as the power factor of the alternating current. Every electrical and electronic device and gadget has an electrical power limit it can safely handle. An AC circuit has three abilities: reactive power, active power, and apparent power. Active power is denoted by the letter P and is measured in watts. Reactive power is represented by the letter Q and is measured in volt-ampere. The letter S represents apparent power, measured in volt-amperes.
