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How is electrical energy measured, and how well does the Sun provide?

Electrical Units of Energy

In the so-called "International System of Units", which are based on metric units, and which form the basis for the electrical units we use, both work and energy have the same unit, called the "Joule". 

"Joule" sounds the same way as the word "jewel" (as in diamonds and emeralds). The Joule is named after the English physicist James Prescott Joule (pictured at right) who lived from 1818 to 1889.  Joule played an important role in generalizing the notions of mechanical energy that followed from Newton's Laws. In particular, he showed that heat is a type of energy. 

To understand the definition of a Joule, we first have to understand a definition of the unit of force used in the International System of units, which is called the "Newton", after the English physicist Isaac Newton. A Newton of force is defined to be the force that can accelerate a mass of 1 kilogram (about 2.205 lbs), such that it picks up 1 meter per second of velocity during each second that the force is exerted. Thus, after one second, the 1 kilogram mass is going 1 meter per second, after two seconds, 2 meters per second, and so on. 

Now recall that "work" is defined as force times distance (see the first section of this primer - "What is energy?"), and also that energy has the same units as work. A Joule is the amount of energy we expend as work if we exert a force of  1 Newton of Force over a distance of one meter. Intuitively, 1 Joule is about how much energy it takes to lift 1 lb about 9 inches.

When we talk about powering appliances in our home with electricity, we are not usually interested in how much energy an appliance uses per se, but rather the rate of energy use, or in other words, how much energy per unit time the appliance draws. This quantity is called the "power":

Power = Energy / Time

In particular, for electrical power we use the "Watt" (named after the scientist James Watt):

1 Watt = 1 Joule / Second.

It is important not to confuse power and energy, although they are closely related. Just remember that power is the rate at which energy is delivered, not an amount of energy itself. With simple algebra, can turn the formula above for power around to solve for energy instead, and write:

Energy = Power x Time.

For example, using the definition of the word watt given above, a 100 watt light bulb is a device that converts 100 joules of electrical energy into 100 joules of electromagnetic radiation (light) every second. If you leave a 100 watt light on for one hour, that is, 3600 seconds, then the total energy you used was:

Energy = Power x Time 

= (100 Joules/Second) x (3600 Seconds) 

= 360,000 Joules

Watts are a very convenient unit when working with appliances, for example, for specifying the power of light-bulbs. But there are also times when you are interested in the total energy use, for example, when you are calculating how much your utility bill is going to be. You can see that its not so convenient to work with Joules to specify total energy use in practical situations, because you get such large numbers, like the 360,000 Joules figure above. So, when it comes to working with total energy use (as opposed to the power you need to run something), people like work with another unit, called the "kilo-watt hour":

1 kilo-watt hour = the energy delivered by 1000 watts of power over a one hour time period.

This is the amount of energy you would use to run a typical hair dryer for one hour. To see how many Joules this is, we calculate:

Energy = Power x Time

 = (1000 Joules/Second) x (3600 Seconds) 

= 3,600,000 Joules = 3.6 million Joules!

That's alot of Joules! So you see that kilo-watt hours is a much better unit for large amounts of energy.

To give you a feeling for how much power the Sun provides, consider that on a sunny day, at solar noon, the sunlight at the surface of the Earth delivers about 1000 watts (one kilowatt) per square meter. A typical photovoltaic solar cell can convert about 15% of this to electricity, that is, about 150 watts (the best cells in the laboratory can go somewhat higher, up to about 34%, or 340 watts). 

Now lets ask how much power you would need to power your home. Assuming 15% percent efficient solar cells (so that we can capture 150 watts per square meter when the sun is shining), the total power will be given by:

   Power = (Area of solar panels) x 150 watts/m2

Plugging this into the formula above for energy, and the hours of sunlight for the time, we find:

Energy generated per day =  (Area of solar panels) x 150 watts/m2 x (hours of sunlight)

Assuming that the energy generated per day is equal to the energy used per day, and solving for the Area, we find:

Area of panels required = (Energy used per day)/(150 watts/m2 x (hours of sunlight))

US residences presently use about 14 kilo-watt-hours of electrical energy a day on average (which is probably unnecessarily high and could be easily lowered by switching to more efficient appliances). Suppose you have five good hours of sunlight during the day. Then, using the formula above, the area in solar panels you would need to obtain the average household draw of 14 kilo-watt-hours per day would be 

Area needed = 14,000 watt-hours / ( 150 watts/m2 x 5 hours ) 

= 18.6 square meters = 200 square feet

It can be seen that this figure is an area of 10 feet by 20 feet, much less than the roof area of a typical house. Therefore, the Sun provides ample power for household electricity!

Amps and Volts 

 Finally, some people may wonder about how amps and volts fit into all this. Voltage, measures how much electrical energy is delivered if a certain charge, that is, a certain number of electrons, are transmitted through a circuit. In other words, it tells you that such and such an amount of energy will be delivered if such and such a number of electrons pass through the circuit. The number of electrons is measured with the unit of a Coulomb, which consists of 1.6 x 1019 electrons. Amps are a measure of how many coulombs per second are being transmitted, which is call the current. Thus, a current of one amp in a wire means exactly 1.6 x 1019 electrons per second are flowing past any given point in the wire. 

A voltage of 1 volt means that 1 joule of energy will be delivered for each coulomb of charge that flows through the circuit. A voltage of 2 volts means that 2 joules of energy will be delivered for each coulomb, and so one. Since current is the number of coulombs per second, and power is the number of joules per second (watts), we see that

Power (in watts) =  Joules/Second

 = (Joules/Coulomb) x (Coulomb/Second)

 = volts x amps

 = number of Watts

Suppose now, for example, that we want to know how much current, in amps, that a hair dryer draws. Suppose that the hair dryer is rated to draw 1100 watts of power. In a typical house with alternating current (say, from a utility line) the power outlets in the wall supply 110 volts (at least in the USA). By turning the formula above around to solve for amps, we see that a 1100 watt hair dryer draws about:

amps = Power / volts = 1100 watts / 110 volts = 10 amps.

If the fuse for the outlet limits the amperage to about 15 amps (fuses are rated by the maximum current that can flow through them), then we see that if we plugged two of these hair dryers in at the same time, they would together draw 20 amps, and the fuse would blow!

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