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There are two ways to transmit the same amount of power, 1 amp at 1 million volts or 1 million amps at 1 volt. Conceptually what is the difference?

How can I think about it conceptually?

I would prefer it if an analogy were made.

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up vote 23 down vote accepted

Suppose you are using a waterwheel to do some form of work (e.g. grind corn). You need a head of water to make the wheel move, and you could use either 1kg of water at a height of a million metres or you could use a million kg of water at a height of one metre. In both cases the water would do the same amount of work as it flowed through your wheel.

The pressure of the water (i.e. the height) is analogous to the voltage, so the water at a height of a million metres (OK, OK, that would be above Earth's atmosphere but it's just an analogy :-) has a voltage a million times greater than the water at a height of one metre. The current is analogous to the water flow rate. If all the water flows through the wheel in the same time then obviously the million kg of water at 1 metre has a flow rate a million times as great as the one kg of water at a million metres.

Although in both cases the total energy of the water is the same, they would behave very differently in practice. Your water wheel probably has an ideal flow rate (i.e. current) at which it's most efficient. So in practice the two cases almost certainly wouldn't grind the same amount of corn. You'd choose whichever was best suited to your purpose. The same is true of electricity. For example, resistive losses scale with current, so for transmission across the country you want a high voltage and low current. In the home a high voltage would lead to lots of fried customers, so you want a low voltage and correspondingly higher current.

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+1 for considering the fried customers... – woliveirajr Jul 2 '13 at 14:39

Theoretically no difference but the real world comes into play and it's all about power loss (generated as heat) in the transmitting cable which will have a resistance. Power=volts*amps but recall that Ohms law says volts/amps=Ohms. Therefore we can express power loss in the transmitting cable as amps^2 * Ohms.

Transmission companies like to keep the current as low as possible which means making voltage as high as is practically possible.

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I think it is a bit more complicated as the power loss is also as volt^2/ohms. But this is to be seen as a serial (rather than parallel) structure. The point is then that, for a given cable, the loss of voltage on the line is also lower with low current, so that most of the voltage is left available for actual use. In a serial structure, the current is a fixed flow for the whole circuit, while the repartition of voltage determines the repartition of energy. – babou Jul 2 '13 at 21:02
John Rennie mentioned this in his answer. – Larry Harson Jul 2 '13 at 22:05

The ampere is just the unit measuring the number of charges passing a given point per second. So 1 million amps means 1 million times more charges passing a given point in a second than 1 amp.

A separate issue is the amount of energy that each of those charges carries -- or more precisely, the amount of energy each charge loses as it goes through the circuit. That's what the voltage measures. $1\,000\,000\, \mathrm{volts}$ means $1\,000\,000$ times as much energy per charge.

Now, power is just the amount of energy transferred to the "circuit" per second, so you multiply the number of charges times the amount of energy they've given up. $(1\, \mathrm{amp}) \times (1\,000\,000\, \mathrm{volts})$ is, as you point out, the same amount of power as $(1\,000\,000\, \mathrm{amp}) \times (1\, \mathrm{volts})$. But in the first case, each individual charge is giving up $1\,000\,000$ times as much energy, so you just don't need as many of them per second to give up the same amount of energy.

The usual analogy is to water flowing through a pipe, but that's a little less useful here. So let's think of pushing a log up a hill instead. You can get together with a million of your closest friends, and everyone can push just a little bit to get that log up the hill. Or, you could just get Superman to do it, because he can exert a million times as much power as each of your one million friends. But that's just for each of your individual puny friends; in total, you and your friends exert the same amount of power, so you can get the log up the hill just as fast as Superman.

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These couple of answers have already given a couple of good analogies, but I will try to provide you with another analogy. This one is one that my physics professor gave in class: fish in a stream. Say you have a given period of time - 1 second, and a given volume of water in the stream, say 1 cubic meter. The power relates to the number of fish that will flow through this volume in the time period. Either way it will be the same, but the way the fish move through the stream is much different at the level that would be analogous to the number of electrons flowing through the material. In the case of 1 million volts/1 amp, the million fish would be flowing through the one meter volume in one second, but only one fish would populate the volume at a given time. In the case of 1 volt/1 million amps, the same million fish would pass through the volume in a second; however, instead of there only being 1 fish in the volume at a given time, there are a million fish in the volume, but those million are only moving at a rate that the million fish take a second to get through the volume. Of course this isn't entirely accurate, as electrons don't move that slowly and 1 volt is not equivalent to one electron per second, but hopefully you get what I am trying to explain.

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The reason both are not suitable for a real use are strictly practical. To transfer 1M amp, you can't create a copper wire as big as the needed current requires and to sustain itself at the same time, and consider the fact that copper is expensive, so it does not make sense even in term of money. 1Mv is not so far from the reality: big power lines are at about 300Kv. Here comes insulation problems: to imagine such a line take the biggest power line you see and multiply four times the distance between wires, the distance between the wires and the trellis, and the entire height: the result would be probably no suitable as well. So engineer choose the two term in order to minimize the cost due to copper with the constraints the line can be reasonably insulated and safe. Of course when engineer has to connect to regular houses they would prefer safety ( trust me having 1Kv at home would be quite dangerous, imagine 1Mv :) ) and they actually don't need too much copper anyway since 3-6 kW is generally enough for a family ).

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