3 Real, Reactive, and Active Power
DC Circuit
In a DC circuit, all the derivations of the power formula combined with ohms law can be used such as Power = V*I, Power = I2R, and Power = V2/R. The units of DC power are Watts [named after James Watt (1736-1819)]. DC power can be thought of as power consumed by a resistor.
AC Circuit
In an AC circuit power becomes much more complicated. In the US the AC power is generated for a 60 Hz, 120-volt standard. Hz means cycles per second. Hence 60 times a second a sine wave with a peak amplitude of approximately 170 volts is generated. This cycling sine wave in AC can create three types of power: 1) real power, 2) reactive power, and 3) apparent power.
- Real, Active, or Average Power is the power consumed by a resistor. It is denoted with a ‘P’. As in DC circuits, real power has units of watts. Only two power formulas can be used to calculate real power:
P = I2R or P = V2/R.
Examples
#1 Calculate the power consumed by a 1 kΩ resistor with 5 mA flowing through it.
P = I2R = (5mA)2*1kΩ = 25 mW
#2 Calculate the power consumed by a 1 kΩ resistor with a 15 volt drop across it.
P = V2/R = (15v)2/1 kΩ = 225 mW
Examples of electrical devices that only consume real power are electric stoves, hairdryers, electric water heaters, and toasters. - Reactive Power is the power that is consumed by inductors and capacitors. It is denoted with a ‘Q’. Reactive power has units of VAR (Volt-Amps Reactive). Hence, 60 times the second energy is stored and released in inductors and capacitors. The inductive reactance of pure inductors +jXL. This means that an inductor is +90 degrees out of phase with a resistor (which is at 0 degrees). The capacitive reactance of a pure capacitor -jXC. This means that a capacitor is -90 degrees out of phase with a resistor (which is at 0 degrees). The net reactance in a circuit is X = +jXL-jXC. Hence, the reactance will always be either net capacitive or net inductive. Only two power formulas can be used to calculate reactive power:
Q = I2X or Q = V2/X. If the net reactance is inductive Q is positive and if the net reactance is capacitive, Q is negative.
Examples
#1 Calculate the power consumed by a 2 kΩ inductive reactance with 4 mA flowing through it.
Q = I2R = (4mA)2*2kΩ = 32 mVAR
#2 Calculate the power consumed by a 1 kΩ inductor with a 15 volt drop across it.
P = V2/XL = (15v)2/1 kΩ = 225 mVAR
Examples of electrical devices that generate some reactive power are microwaves, washing machines, fans, and air conditioners. - Apparent Power is the hypotenuse of real and reactive power (see figure below). It is denoted with an ‘S’. Apparent power has units of VA (Volt-Amps). Apparent power is useful since it reveals the total current used by a combination of resistive, inductive, and capacitive components. Apparent Power = V*I. S = sqrt(R2 + Q2).
- Power Factor
The power factor is defined to be Fp = cos Θ. Where Θ is the angle in the power triangle shown above (the angle between the Apparent Power an