|MadSci Network: Science History|
NOTE: I tried to send this answer several weeks ago, but I don't believe you got it. I've been having trouble with my email. The short (and not so interesting) answer to your questions is this: the voltage and frequency chosen for commercial and residential power distribution are somewhat arbitrary. But once they're chosen, standardization for a geographic region (country, continent, etc.) is very important. It's kind of like having everyone drive on the right or left hand side of the road. The choice doesn't matter very much, but agreeing on the choice matters a lot! That said, would any frequency and any voltage be as good as any other? And the answer is no. Let's consider the reasons for this by looking at what's good and bad about high and low voltage. From there we can zero in on a voltage range that's low enough to avoid the bad things about being high and high enough to avoid the bad things about being low. Then we'll do the same thing for frequency. As most everyone knows, really high voltage is dangerous--deadly dangerous! So for safety reasons in a home, you want voltage to be as low as possible. Well then why not make it really low, say a volt or two, like a battery? The reason involves the relationships between electric voltage, current, resistance and power, so let's review them. When current flows through a wire, the wire heats up as electrical energy is turned into heat. This is how electric stoves, toasters, hairdryers etc. work. If enough current flows, the wire can even glow, giving off energy in the form of light. That's how light bulbs work. The rate that electrical energy is being turned into heat and/or light is called power and is given by: P = I*V where P (power) is in units of watts, I (current through the wire) is in amps, and V (voltage difference between one end of the wire and the other) is in volts. So a watt is equal to a volt*amp. A 100 watt light bulb could be designed to be lit with 50 volts and 2 amps or 110 volts and 0.9 amps or 220 volts and 0.45 amps, and so on. But they would be different bulbs; a 220 volt bulb would be very dim if connected to a 110 volt outlet. The equation relating the current flowing through a wire (or any object with resistance) to the voltage applied across its ends is called Ohm's law: V = I*R where V and I are the same as above and R is electrical resistance in units of ohms. Ohm's law says that for a wire of given resistance, the more voltage applied across its ends, the more current will flow. Now if you substitute Ohm's law into the equation for power you get: P = (I^2)*R (that's, "p equals i squared times r" in plain English). Having eliminated voltage, we can now see that as current increases in a wire, the power dissipated (that is, the rate that electrical energy is converted to heat and light) goes up very fast, namely as the square of the current. That's all the physics we need for now; let's see what it's telling us. Suppose in your house there's a 10,000 watt electric stove. The equation for power, P = I*V, says you'll get just as much heat with high current and low voltage as with low current and proportionally higher voltage. So the stove could be designed for, say, 10 volts and 1000 amps or 1000 volts and 10 amps; it should get just as hot, just as fast either way. But it doesn't; the 1000volt*10amp stove gets a lot hotter a lot faster than the 10volt*1000amp stove. The reason is that the stove isn't the only thing heating up; the cord from the stove that plugs into the wall is getting hot too, and that uses some of the power. And even a big fat copper (in other words, low resistance) cord will get hot when a lot of current flows through it. That's what the other equation for power, P = (I^2)*R is telling us. Even with a small resistance, high current means lots of heat because the current is getting squared! So to keep from wasting all your power in the cord you want current to be low. But that means voltage has to be high, which is dangerous. And that's how residential voltage standards were arrived at; 1000 volts is too dangerous, and 10 volts is too inefficient for high-power appliances. The balance was struck around 220 volts, low enough to be safe and high enough to be efficient with high-power appliances (like stoves). Nearly all countries (including the US) use 220 volts as the basic service into the house. In the US we also use 110 for low power applications, such as light bulbs and electronic equipment, where current is low enough for power loss in the cord to be negligible. It turns out that these products can be made a little cheaper, if designed to use lower voltage. For example, the filament in a 220V/100W light bulb would have to be thinner and longer (therefore more expensive to fabricate) than the filament in a 110V/100W bulb of equal life expectancy. This was a bigger issue in the early days of light bulb manufacturing than it is now, but Americans are used to 110V outlets, and changing everything to 220V would (for no good reason) scare the heck out of us! What about frequency! You'll be glad to know that you've just learned most of what you need in order to see where the frequency standards came from. Let's follow our same approach and ask: What's wrong with real low frequency? What's wrong with real high frequency? Then we'll try to see what a good compromise would be. The lowest possible frequency is 0Hz or direct current (DC). What's wrong with that? Why not 110 or 220 volts DC? The answer begins with the same reason we found for using higher voltage with the stove. You just need to think on a bigger scale. Imagine a big city. It uses lots of electric power, so it's kind of like a high-power (VERY high-power) appliance! It gets that electric power from a huge power plant (usually several huge power plants) located tens or even hundreds of miles away. The power is delivered through wires from the plants to the city. So think of the city as a big stove, the power lines as a cord, and the power plants as the wall socket. Our real stove needed 10,000 watts; a big city might use 10,000 million watts (10,000 megawatts). That's a million times as much power as the stove. If that much power were delivered at 220volts, the current would be more than 45 million amps (I = P/V), and we know that when electric power is delivered along a wire, high current means lots of power being wasted in the wire (because P = I^2*R) Now 45 million squared is over 2000 trillion! And remember, we're trying to get 10,000 million watts to the city. So even if we could keep R down to a millionth of an ohm (a micro-ohm) efficiency would be only a littled over 80%: efficiency = (power to the city)/(power to the city + power wasted) = 10,000 megawatts/(12,000 megawatts) What would a 100 mile long, 1 micro-ohm, copper wire look like? The equation for resistance of a copper wire is: R (ohms) = (1.5E-6)*Length /(pi*Radius^2) where the length and radius are in centimeters. I'll let you figure out the radius. But it's way too big to be practical! Fortunately there's a better way, and we know what it is: deliver the power (P=I*V) at high voltage and low current instead of low voltage and high current. If we increase the voltage by a factor of a hundred, the current could be reduced by a factor of 100 for the same 10,000 megawatts of generated power. But that reduces the power lost in the lines by a factor of 10,000 (because power varies with current SQUARED) so most of the 10,000 megawatts could actually get to the city! That seems too easy! And you've probably figured out the catch: multiplying 220 volts by 100 means 22,000 volts. We don't want that on the utility pole in front of our house--to say nothing of letting it inside! So here's how it works. For most of the distance from the plant to your house, power is delivered at tens of thousands of volts. That would be dangerous if people could get close to it, so the power lines are suspended on those huge towers that hold them way up in the air. When the lines get to your house, the voltage is reduced (stepped down) to 220 and the current is increased (stepped up) from what ever it was to whatever you need. Actually it's a little more complicated than that because your house isn't the only place the power is going. So the voltage gets stepped down a couple of times, first at a sub station, to around a few thousand volts, then at the utility pole in front of your house to 220. There's only one cost effective way to "step down" a voltage without wasting power and that's with a transformer. These are placed on utility poles close to your house. The input to the transformer is high voltage/low current (from the power station), and the output is low voltage/high current (to your house). There's just one last catch; transformers have no moving parts, and use electromagnetic induction. Without moving parts, there's no such thing as electromagnetic induction with constant (direct) current! It has to be AC, which rules out 0Hz! Ok, how about 1Hz? Just kidding! Actually transformers do get more efficient with increasing frequency, but around 20Hz they can be made very efficient. By the way "efficient" here means that the power out of the transformer (to your house) is very nearly equal to power in (from the power station). The reason for higher frequency has to do with lightbulbs. At 20Hz, oscillations in brightness are noticable (and annoying!) even with incandescent light bulbs. Flourescent bulbs actually go completely on and off with AC, and at 20Hz this flickering would be extremely annoying! Flickering goes away around 50Hz, the standard used in many countries. The 60Hz standard adopted in the US comes from the use of the periodic voltage as a timing mechanism for electric clocks (60 minutes in an hour, 60 seconds in a minute, so 60 cycles in a second). There doesn't seem to be any advantage to frequencies above 60Hz, and there are several disadvantages. They would require that generators turn faster, or have more parts. In other words, they'd be more expensive. Also, wires with alternating current flowing through them emit electromagnetic radiation, and it turns out that the power radiated away (that is, wasted) through this process increases with increasing frequency (this is exactly the same physics that makes transformers only work with AC). Well, I bet you never thought the answer to your question could be so long! And since you posted it in the "Science History" area, I should finish with a reference to the history of these standards. It's a very interesting story of American industry involving perhaps two of the greatest inventors of all time, Thomas Edison and Nicola Tesla. You can get started learning about it right here at the MadSci Network in the answer to question #910978615Sh.
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