# Electricity

People have a lot of confusion about electricity.  A few things you need to know:
• What  is electricity, and where does it go after it leaves the toaster?  (Apologies to Dave Barry)
• What's a watt?  What's a volt, ampere, etc?
• What about AC and DC?
Electricity is usually divided into `static' and `regular' electricity.  This is pretty much just plain wrong.  Forget all about that -- the electricity you use is really `electrical energy'.  This energy comes in over the utility wires and, at least in North America, is labelled `120 volt' (or `240 volt' for your air conditioner and electric dryer, and maybe a well pump and the like), `60 Hz AC'.  This electricity does have something to do with electrons, but the energy is really only pushed around via those electrons.  Like a long chain of springs, the electrons just have to push their neighbors, who then push their own neighbors, and so on.  (With `static electricity' you actually separate electrical charges, rather than just getting electrons to push on each other.  This is what makes it different, and why you should forget about it.)

### What's watt?

The `watt' is not the electricity.  The `watt' is how fast you are using the electricity.  Think of `watts' as `miles per hour'.  If you are driving down a road, you do not say `I have three mph to go before I get home'; that would make no sense.  Instead, you might say `I have three miles to go before I get home'.  If you are stuck in rush hour traffic and can only go 3 mph, those three miles will take an entire hour.  If you are zooming along at 60 mph, those three miles will take three minutes.  This means a 100-watt light bulb is really `going 100 watts down the electricity freeway'.  If it goes 100 watts for an hour, the `distance' it went is 100 watt-hours.  So the electricity you use is measured in watt-hours, or more typically, kilo-watt-hours or kWh.  Specifically, the watt-hour (or watt-minute or watt-second) measures energy.

Another name for a watt-second is a `Joule' (pronounced like `jewel', more or less).  A joule, or a kWh, measures energy -- real, actual stuff.  A watt measures only how fast you are using the real energy-stuff.  Saying you have a `watt' makes no sense; it is like saying you have a `mile per hour'.  When you have a 100 watt light bulb, you have a light-bulb with a normal speed of 100 watts.

In simple cases,  `watts' are exactly the same as `volts times amps'.  A good analogy here is water in a pipe.  The energy is a `real thing', much like water is a `real thing'.  If you could store energy in a bucket, you could almost say `I have a gallon of energy'.  Instead of gallons, though, you would have `kWh in a bucket'.  When you go to fill the bucket, you can fill it at whatever speed you like.  To fill the `energy bucket' quickly, you could use a great big hose that only has a little water pressure, so that lots of water just sort of dribbles out, or a little teeny hose that has lots of water pressure, so that a thin stream squirts out really fast.  Either way the bucket will fill pretty fast.

The volts are like the water pressure, and the amperes (`amps') are like the width (cross-section) of the hose.  The watts are like the gallons-per-minute that comes out of the hose.  Crank up the water pressure, keeping the hose the same size, and you get more water out every second -- this is the same as cranking up the voltage and keeping the amperage the same, and getting more watts.  Use a skinnier hose, keeping the water pressure the same, and you get less water per second.  Crank the pressure back down on the hose and you also get less water per second.

If you have one guy drinking water out of a hose at a speed of `3 watts', and you add another guy who wants to drink at a speed of `2 watts' from that same hose, you have to run at least `5 watts' continuously through the hose.  Here `3 watts' tells you how fast the first guy is drinking, and `2 watts' tell you how fast the second guy is drinking.  If you do not supply `5 watts', at least one of them will go thirsty.

Unlike water, however, electrical power is difficult to store effectively.  Thus, electricity has to be generated as needed.  Even a battery does not really store electricity.  Instead, it is a very small chemical-powered generator that operates whenever you connect it to a `load'.  When you `charge up' a battery, you just run the chemistry backwards.  That is, it stores the energy, not the raw electricity.  The battery is `full' when it can no longer store more energy -- its chemicals are all as ready to generate as they can ever get.  The battery is `empty' when the chemicals have had all their energy squeezed out [1].

The bigger the load, the bigger the generator needed.  Generation and load is measured in those same `watts', or often in kilowatts or megawatts.  Again, these measure how fast the energy is coming out of the generator, or how fast the load is `using up' the generation.  The total energy is `how fast' times `how long' -- watts times hours, or watt-hours.

(Actually, you never `use up' electrical energy.  You just `use' it to do work: shine a light, run a motor, work a TV or computer, or whatever.  The `Law of Entropy' says that eventually, all energy turns into heat.  If you did not really want heat, then the less heat you get while using some energy, the more effectively you are using that energy.  If you did want heat, great -- but if not, any heat you get amounts to `waste' [2].  As long as electricity is cheap, you might not really care anyway.  When electricity gets expensive is when you should care how effectively you are using it.)

So, generation has to match load.  Whenever someone flips on a light switch somewhere, some generator, somewhere, has to work a little harder to make up the extra load.  That has to happen more or less instantaneously.  Luckily, when you take millions of users and collect them up, it turns out you can predict closely enough how many of them will turn on switches, and when.  This is called `scheduling' the load and generation: timing things so that they match.

### AC, DC, esoterica

AC stands for `alternating current' and DC stands for `direct current'.  People sometimes talk about these as if they were also different kinds of electricity, but they are not.  Remember that the whole point is not to move electrons, but rather to push electrical energy around.  If the electrons work like springs, pushing on each other, and if you set up a `circuit' -- a loop of wire -- you can get the electrons to push (say) clockwise, and just keep on pushing clockwise.  It does not matter if any electrons actually move along inside the wire, round and round; as long as they keep pushing clockwise, you can tap energy off that push.  This is like DC.  It is simple and straightforward, and in DC circuits, the `volts times amps equals watts' always works.

Sometimes, though, it is easier to push the electrons back and forth.  First you push them clockwise, then you relax.  Then, you push those little electrons counter-clockwise, then you relax again.  This is like pumping a swing.  The swing itself never really moves very far, but there is still plenty of energy available.  This is how AC works.  In the early days of electricity, people thought AC would never work, because the electrons never go anywhere, just like that swing never goes far.  But in fact it works fine; it is just a bit more complicated.  When dealing with AC power, the voltage starts at 0, goes up for a while, reaches a peak, goes down for a while, and then actually goes negative.  The whole thing forms a sine wave (insert graphic here).  The energy flow (in watts) is no longer `volts times amps' -- now we have to use calculus.  Luckily, someone else has already done the work, and the wattage for a simple circuit, like a light bulb, in a pure sine wave AC system uses the `RMS' (root-mean-square) of the voltage curve.  The voltage number on an AC circuit -- the `120 volts' for your household current -- is given in RMS, and for most cases, `RMS volts' times amps gives watts again.  At 120 volts RMS, a 120-watt bulb draws one amp, and a 5/6ths-amp bulb uses energy at a speed of 100 watts (100 * 5 / 6).

In an AC system, it is easy to swap volts for amps or vice versa using a transformer.  Transformers are those big lumpy things you plug into a wall socket, that then have a small wire coming out of them to go to the computer modem, the cordless phone, or whatever.  (Sometimes the transformer is a big lumpy thing in the wire, which is nice because then the lumpy thing does not block the other outlet.  Sometimes it is at the device end, instead of the plug.  Most of the cheap ones seem to be at the plug end though.)  These are what people sometimes call `wall warts', because when you plug them in, they look like big warts clinging to the wall.

A simple transformer consists of a square iron `core' with some wire wrapped around each of two sides [insert graphic here].  Each side has some number of turns (loops of wire) going around the core.  If there are ten turns on one side, and 100 on the other, the transformer will do a one-to-ten -- or ten-to-one -- conversion.  Put in 120 volts RMS at 1 amp on the 10-turn side, and you will get 1200 volts RMS at 0.1 amp on the 100-turn side.  Turn it around, and the 120 volts RMS 1 amp input will become 12 volts RMS at 10 amps output.  The transformer acts like a pipe fitting in a hydraulic (water-power) system, turning pressure into volume or vice versa.  The wattage in and out is always the same -- 120 watts in gives 120 watts out -- but the `water pressure' (voltage) and `pipe width' (current) change.  No transformer is perfect though: they all `leak' some of the `water', or in this case, leak some of the electrical energy by getting hot.  This `leakage' can be minimized by careful design, although that tends to make the transformers more expensive -- the cheap `wall warts' tend to be pretty leaky.  If you touch one and it feels warm, that warmth is due to this leakage.

The ease of transforming from `fat pipes at low water pressure' (high current at low voltages like 120 volts) to `really skinny pipes at high water pressure' (low current at high `transmission' voltages like 500,000 volts) makes long-distance power transmission practical.  It costs a lot less to run a `skinny' pipe (small wire) for 30 miles than to run a really big, hefty wire with lots and lots of metal in it for the same 30 miles.  Of course, the high pressure means the electricity is very ready to `squirt out', so high voltage transmission lines are not something to play with.

When running things like refrigerator motors or even computers, AC systems sometimes need something called a `power factor' to account for not using the pure sine wave `properly'.  The power factor number is some fraction that is always less than or equal to 1.  One way to visualize this is to imagine a computer power supply that needs to provide 12 volts instead of 120.  How do you get 1/10th the voltage?  One way is to use a transformer, but transformers are relatively big and heavy, so another way is to use a `switching' power supply.  In effect, the switching power supply watches the incoming voltage, which of course swings from 0 up to about 170 volts, down through 0 again to about -170 volts, and on back up to 0.  Whenever the voltage hits 12 the switcher `turns on' and sucks in the power that the computer needs.  Then it `turns off' and lets the computer run off some stored-up 12-volt power.  The effect is as if the computer drew all its load at 12 volts instead of 120 volts.  If a 120-watt computer would need 1 amp at 120 volts, that means it might really need 10 amps, because it only takes its `amps' when the voltage is right at 12.  That would give it a power factor of 0.1 (1/10th).  Real computer power supplies are not anywhere near this bad, but they are below 1.0.  As a rule of thumb, if you are building a generator, you can use a power factor of about 0.9 or so and probably be `good enough' for most ordinary household uses.

Power factors are the reason that AC generators (like home backup generators, or the ones used on construction sites) are rated in `VA' -- volt-amperes -- instead of watts.  Suppose you buy one that will put out 120 volts RMS and 30 amps, or 3600 `VA'.  If you had a really low power factor of 0.1, by pulling the full 30 amps `out of phase' or `at 12 volts',  you could only use 360 watts -- 12V x 30A -- instead of the full 3600 watts that the generator could deliver.  Its power `speed limit' is 3600 watts, but unless you get your power factor up to 1.0, you will never get it to go that fast.

### Review

AC or DC, a 100 watt bulb uses 100 watt-seconds of real, actual `energy stuff' every second.  In other words, it uses 100 joules per second.  If you leave it on for one minute, it uses 6000 joules.  Leave it on for an hour and it uses 360,000 joules -- 360 kilojoules -- of energy.  Leave it on for a full day and you need 8.64 megajoules (MJ).  You might prefer the other, more usual unit, the `watt-hour', because that 100 watt bulb uses 100 watt-hours in an hour, or 2400 watt-hours (2.4 kWh) in a day.  2.4 kWh sounds less than 8.64 MJ, but actually they are exactly the same.

Watts are, in effect, a `speed limit'.  Turn on a 100-watt bulb and it cruises down the electron highway at a speed of 100 watts.  Turn on your 1500-watt hair dryer and you really put the pedal to the metal, zooming along at 1500 watts.  Add 100 for the light bulb and your generator needs to `speed up' to 1600 watts to keep up with you.

[1] Big batteries like car batteries are often rated in `amp-hours'.  If you know the voltage is always 12 volts, and you know the battery can crank out 100 amps when needed, then it can supply 12 x 100 = 1200 watts.  But since watts are just how fast the energy comes out, that does not say how much energy the battery can store in its chemicals.  This is where the `hours' come in.  If the battery holds 500 `amp-hours', at 12 volts, then it stores 12 volts x 500 amp-hours = 6000 volt-amp-hours = 6000 watt-hours = 6 kWh.

[2] When you charge a battery, it gets hot.  This is some of that `waste'.  They can also get hot when discharging.  You have to be careful when using some kinds of batteries that they do not get too hot.  Always heed any printed warnings on the battery, so that you do not accidentally start a fire.