What is power, exactly? Here is an all-encompassing definition: Power is the rate at which energy is expended, radiated, or dissipated. This definition can be applied to mechanical motion, chemical effects, dc and ac electricity, sound waves, radio waves, sound, heat, infrared (IR), visible light, ultraviolet (UV), X rays, gamma rays, and high-speed subatomic particles. In all cases, the energy is converted from one form into another form at a certain rate.

#### Units of Power

The standard unit of power is the watt, abbreviated W. A watt is equivalent to a joule per second ( J/s). Sometimes power is given as kilowatts (kW or thousands of watts), megawatts (MW or millions of watts), or gigawatts (GW or billions of watts). It is also sometimes expressed as milliwatts (mW or thousandths of watts), microwatts (μW or millionths of watts), or nanowatts (nW or billionths of watts).

#### Volt-Amperes

**When there is no reactance in an ac component, the power P is the product of the voltage E across the component and the current I through the component.**

In dc circuits, and also in ac circuits having no reactance, power can be defined this way: Power is the product of the voltage across a circuit or component and the current through that same circuit or component. Mathematically this is written P = EI. If E is in volts and I is in amperes, then P is in volt-amperes (VA). This translates into watts when there is no reactance in the circuit (above figure). The root-mean-square (rms) values for voltage and current are always used to derive the effective, or average, power. Volt-amperes, also called VA power or apparent power, can take various forms. A resistor converts electrical energy into heat energy, at a rate that depends on the value of the resistance and the current through it. A light bulb converts electricity into light and heat. A radio antenna converts high- frequency ac into radio waves. A speaker converts low-frequency ac into sound waves. The power in these forms is a measure of the intensity of the heat, light, radio waves, or sound waves.

#### Instantaneous Power

**Peak versus effective power for a sine wave. The left-hand vertical scale shows relative voltage. The righthand vertical scale shows relative power. The solid curve represents the voltage as a function of time. The light and heavy dashed waves show peak and effective power, respectively, as functions of time.**

Usually, but not always, engineers think of power based on the rms, or effective, ac value. But for VA power, peak values are sometimes used instead. If the ac is a sine wave, the peak current is 1.414 times the rms current, and the peak voltage is 1.414 times the rms voltage. If the current and the voltage are exactly in phase, the product of their peak values is twice the product of their rms values. There are instants in time when the VA power in a reactance-free, sine-wave ac circuit is twice the effective power. There are other instants in time when the VA power is zero; at still other moments, the VA power is somewhere between zero and twice the effective power level (above figure). This constantly changing power is called instantaneous power. In some situations, such as with a voice-modulated radio signal or a fast-scan television signal, the instantaneous power varies in an extremely complicated fashion. Have you ever seen the modulation envelope of such a signal displayed on an oscilloscope?

#### Imaginary Power

If an ac circuit contains reactance, things get interesting. In a pure resistance, the rate of energy expenditure per unit time (or true power) is the same as the VA power (also known as apparent power). But when inductance and/or capacitance exists in an ac circuit, the VA power is greater than the power actually manifested as heat, light, radio waves, or whatever. The apparent power is then greater than the true power! The extra power is called imaginary power, because it exists in the reactance, and reactance can be, as you have learned, rendered in mathematically imaginary numerical form. Imaginary power is also known as reactive power. Inductors and capacitors store energy and then release it a fraction of a cycle later. This phenomenon, like true power, is expressible as the rate at which energy is changed from one form to another. But rather than existing as a usable form of power, such as heat, light, radio waves, sound waves, or mechanical motion, imaginary power is stored up as a magnetic or electric field, and then released back into the circuit or system. This storage and release of power takes place over and over with each repeating ac cycle.

#### True Power Does Not Travel

**True power and imaginary power in a radio transmitter and antenna system.**

A common and usually harmless misconception about true power is the notion that it can travel. For example, if you connect a radio transmitter to a cable that runs outdoors to an antenna, you might say you’re “feeding power” through the cable to the antenna. Everybody says this, even engineers and technicians. But true power always involves a change in form, such as from electrical current and voltage into radio waves. It doesn’t go from place to place. It simply happens in a specific place. It’s the imaginary power that moves in situations like this, especially in transmission lines between power stations and power users, or between radio transmitters and radio antennas. In a real-life radio antenna system, some true power is dissipated as heat in the transmitter amplifiers and in the feed line (above figure). The useful dissipation of true power occurs when the imaginary power, in the form of electric and magnetic fields, gets to the antenna, where it is changed into electromagnetic waves.

You will often hear expressions such as “forward power” and “reflected power,” or “power is fed from this amplifier to these speakers.” It is all right to talk like this, but it can sometimes lead to wrong conclusions, especially concerning impedance and standing waves. Then, you need to be keenly aware of the distinction among true, imaginary, and apparent power.

#### Reactance Does Not Consume Power

**At A, current (I ) and voltage (E ) are in phase in a nonreactive ac circuit. At B, I and E are not in phase when reactance is present.**

A pure inductance or a pure capacitance cannot dissipate any power. The only thing that such a component can do is store energy and then give it back to the circuit a fraction of a cycle later. In real life, the dielectrics or wires in coils and capacitors dissipate some power as heat, but ideal components would not do this.

A capacitor, as you have learned, stores energy as an electric field. An inductor stores energy as a magnetic field. A component that contains reactance causes ac to shift in phase, so that the current is no longer exactly in step with the voltage. In a circuit with inductive reactance, the current lags the voltage by up to 90°, or one-quarter cycle. In a circuit with capacitive reactance, the current leads the voltage by up to 90°.

In a resistance-reactance circuit, true power is dissipated only in the resistive components. The reactive components exaggerate the VA power compared with the true power. Why, you ask, does reactance cause this discrepancy? In a circuit that is purely resistive, the voltage and current march right along in step with each other, and therefore, they combine in the most efficient possible way (above figure A). But in a circuit containing reactance, the voltage and current are out of step with each other (above figure B) because of their phase difference. Therefore, the actual energy expenditure, or true power, is not as great as the product of the voltage and the current.