## Watts Up With Your Electric Bill?

Your local utilities company charges you for how much electricity you use, usually listed in units of kWh. Let’s wonder a bit about what this energy-related unit means and how it can make your utility bill understandable.

When it comes to electrical things, energy is the coin of the realm. It takes energy to make the bulb in your flashlight glow, energy to power your cell phone, energy to turn bread that perfect shade of brown in your toaster. James Joule, the 19th-century English scientist (and brewer!), was one of the first to understand the nature of energy. Physicists use the unit “joule” to quantify energy.

A glance at your utility bill, however, reveals no “J” and no joules. Where is energy, then?

Although energy is fundamental, a more useful concept in our daily lives is power, the rate at which we use energy.

Although energy is fundamental, a more useful concept in our daily lives is power, the rate at which we use energy. Power is measured in watts, the “W” in kWh. Light bulbs are measured in watts; the higher the wattage, the brighter the bulb. Audio amplifiers are measured in watts; the higher the number of watts, the louder the maximum sound. You might have a hair dryer or a microwave oven characterized by the power it delivers. Same idea.

Watt is a what? Sorry—what is a watt? (Nerd alert; physics humor!) Watts, as a measure of the rate of energy delivery, are equivalent to the number of joules of energy that flow into or out of a device every second. For example, when you turn on a 100 W incandescent light bulb, it uses 100 joules of energy every second. Most of that energy is given off as heat. So the warmth you feel when you put your hand near a 100 W bulb is about 100 watts of power.

A cell phone charger consumes 5 watts of power. The most efficient large-screen televisions draw around 100 watts. It takes about 1,000 watts to run a medium-size room air conditioner. And the average toaster needs around 1,200 watts to make the toasting magic happen.

Wait! An air conditioner runs at lower power than a toaster? Aren’t air conditioners supposed to be energy expensive?

The key to squaring the energy cost of a toaster with that of an air conditioner is hidden in the way we quantify energy and power. The toaster runs at 1,200 watts, that is, it requires 1,200 joules of energy every second. Making the perfect piece of toast takes 216 seconds (according to researchers at the University of Leeds in Great Britain). So the total energy required for your morning’s toast? That would be 1,200 joules per second times 216 seconds, or about 260,000 joules.

On a hot summer’s day you might run that air conditioner for seven hours, or about 25,000 seconds. At 1,000 watts—1,000 joules per second—this requires 1,000 times 25,000, or 25 million joules. That’s about a hundred times more energy than the toaster. Oh, yes, your air conditioner is an energy hog!

So let’s look back at that electrical bill on which you are charged by the kWh. The “k” is kilo, shorthand for 1,000. A “kW” is a kilowatt, or 1,000 watts. The “h” is hours, an amount of time. Multiply kW (energy per time) by an amount of time, that’s energy. The number of kWh, or kilowatt-hours, gives the amount of energy you use.

Running your 1,200 W toaster for 0.06 hours (216 seconds) requires 0.07 kWh (1.2 kW times 0.06 hours) of energy. At 15 cents per kWh (for most of the U.S., the base rate for electricity is between 10 and 20 cents per kWh) the cost to make toast is about a penny. A year’s worth of toaster use is about \$3.50.

How about your air conditioner at 1 kW for 7 hours? Multiply 1 kW times 7 h, that’s 7 kWh. At 15 cents per kWh, running the air conditioner costs \$1.05 each day. It adds up quickly—for just a summer’s worth of AC, the cost is more than \$100!

What’s the energy bottom line? Find the electricity cost to run a device by multiplying your utility company’s rate—it’s right on your bill – by the power of the device in kW and the number of hours the device is running. Easy!

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Questions to ponder:

Oops! You accidently left the light on in the garage overnight. About how much did that cost?

Oops! You accidently left the light on in the garage before you left for a two-week vacation. About how much did that cost?

Your phone charger draws about 0.1 W when it’s plugged in but not charging anything. How much does it cost per year to leave it plugged in 24x7?

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