Energy and the Watt-Hour

Have you heard the terms “power” and “energy” used interchangeably, as if they mean the same thing? They don’t! Energy is power dissipated over a length of time. Power is the rate at which energy is expended. Physicists measure energy in units called joules. One joule (1 J) is the equivalent of a watt-second, which is the equivalent of 1 watt of power dissipated for 1 second of time (1 W  s or Ws). In electricity, you’ll more often encounter the watt-hour (symbolized W  h or Wh) or the kilowatt-hour (symbolized kW  h or kWh). As their names imply, a watt-hour is the equivalent of 1 W dissipated for 1 h, and 1 kWh is the equivalent of 1 kW of power dissipated for 1 h.

A watt-hour of energy can be dissipated in an infinite number of different ways. A 60-W bulb consumes 60 Wh in 1 h, the equivalent of a watt-hour per minute (1 Wh/min). A 100-W bulb consumes 1 Wh in 1/100 h, or 36 s. Besides these differences, the rate of power dissipation in real-life circuits often changes with time. This can make the determination of consumed energy complicated, indeed.

Following Figure illustrates two hypothetical devices that consume 1 Wh of energy. Device A uses its power at a constant rate of 60 W, so it consumes 1 Wh in 1 min. The power consumption rate of device B varies, starting at zero and ending up at quite a lot more than 60 W. How do you know that this second device really consumes 1 Wh of energy? You must determine the area under the curve in the graph. In this case, figuring out this area is easy, because the enclosed object is a triangle. The area of a triangle is equal to half the product of the base length and the height. Device B is powered up for 72 s, or 1.2 min; this is 1.2/60 = 0.02 h. Then the area under the curve is 1/2 × 100 × 0.02 = 1 Wh.

When calculating energy values, you must always remember the units you’re using. In this case the unit is the watt-hour, so you must multiply watts by hours. If you multiply watts by minutes, or watts by seconds, you’ll get the wrong kind of units in your answer.

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Two devices that burn 1 Wh of energy. Device A dissipates a constant amount of power. Device B dissipates a variable amount of power.

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Often, the curves in graphs like these are complicated. Consider the graph of power consumption in your home, versus time, for a day. It might look like the curve in above Figure. Finding the area under this curve is not easy. But there is another way to determine the total energy burned by your household over a period of time. That is by means of a meter that measures electrical energy in kilowatt- hours. Every month, without fail, the power company sends its representative to read your electric meter. This person takes down the number of kilowatt-hours displayed, subtracts the number from the reading taken the previous month, and a few days later you get a bill. This meter automatically keeps track of total consumed energy, without anybody having to go through high-level mathematical calculations to find the areas under irregular curves such as the graph of above Figure.