Power versus energy

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I.

If you investigate techniques for controlling power, it makes practical sense to know what is being manipulated. In the first place, although you interest centers on electrical or electronic control of power, the power actually being controlled can manifest itself electrically, mechanically, thermally, chemically, or in other ways.

Thus, power must have a common aspect applicable to diverse situations. It is often the case that a person who talks glibly about a powerful motor might not be altogether clear in defining this capability of the motor or other device. What, indeed, is power?

At the outset, realize that potter expresses a rate of doing something: specifically, power is the rate of using, transforming, or dissipating energy. What is energy? Energy, despite its many and varied manifestations, is the capacity or ability to do work. Finally, work in its elemental form always involves displacement of a force through a distance. Obviously, instead of providing a quick and easy definition of power, one entity has just been telescoped into another, resulting in complexity rather than simplicity. It turns out, however, that it is acceptable to say that energy is work, and that power is the rate of doing work, or the rate of utilizing energy. Thus, a powerful motor is one capable of doing much work in a given time.

Note the appearance of the quantity, time, in the above discussion. Because power is described as a rate, it is inevitable that time is always an implied aspect of power. For example, 1 horsepower is an energy or work rate of 33,000 foot-pounds per minute. Note that all is visible here - distance, force, and time. In as much as the product of distance and force represents work, or energy, 1 horsepower is a certain expenditure of energy per unit time. If you deal with other than mechanical manifestations of power, the factors making up energy might not be expressed in pounds or feet; but equivalent force, distance, or work units are involved. The net effect is that power expressed in electrical terms, such as watts, differs only from mechanical horsepower by a simple conversion factor.

Note that energy or work requires a force acting along a length, but torque requires the force to act at right angles to a length. The basic torque unit is the pound-foot. In contrast, the basic energy or work unit is the foot-pound. (2362)

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II.

From the previous discussion, you can see that the interchangeable use of the terms power and energy in the popular literature cannot be valid. You must always be aware that power is the rate given by energy per unit time. By the same token, if power is the known quantity, then energy is the product of that power and the time it is manifested. A practical example of this relationship is the watt-hour meter that obligingly provides the necessary billing information to the electric utility company. You are charged for the use of power over its relevant duration of time. The watt-hour m enter simply multiplies power by its time of use in order to compute energy. Faced with a choice of having the utility company make either high energy or high power available to you, which would be the better choice? Without certain assumptions, the answer is neither. High energy might only allow the burning of a small 25 W lamp continuously for a year. Thus, low power coupled with a long time could satisfy the promise of high energy. Conversely, high power could conceivably allow the operation of a refrigerator, washing machine, and dishwasher for a limited time, such as an hour.

You can appreciate that in most instances high power can be meaningless unless such a power level can be sustained. The high power you wish to enjoy from the utility company must be available around the clock. Although rarely stated, you generally assume this to be the case. In certain technologies, this obvious assumption might not hold. A rocket motor, for example, should generate high power within an acceptably short time. A reciprocal situation is a large storage battery that might require considerable energy to charge, but will do so from a low-power source if sufficient time is allowed. If the utility company is to impress you with its high energy claim, this must be accompanied by an acceptable rate of delivery of the energy, which means a power rating. As stated, you must be satisfied that the desired power capability is on a sustained basis. The essence of this discussion is that power and energy are not interchangeable terms despite their mutual involvement in producing forces, displacements, and work. (2208)

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