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# Ohm's law and potential voltage

Thursday, October 3, 2013

Q. I am having a hard time understanding voltage. My lessons say it is electrical pressure. But it seems to be different from the kind of pressure in a water pipe. With that, the pressure is the same on all the walls of the pipe. If there is an opening in the pipe, water leaksout. But I know electrons don't leak out of wires. Also, I don't understand how there can be voltage without current. Ohm's law says that E = I times R. So if I is zero, how can there be any voltage?

A. The electric field around a charged object will attract or repel an electron, depending on its polarity. The electric field has the potential to move electrons, whether there are any electrons there or not. Voltage is basically the potential to move electrons in a circuit.

Suppose we we a long, thin length of wire and connect it across a battery. Let's say that the wire is so long and thin that it has a fair amount of electrical resistance. So when we connect it across the baterry, some current will flow, but now enough to "short" the battery and destroy it.

Along the whole length of the wire, electrons are constantly moving from the negative end of the battery toward the positive end. For every electron that leaves the negative terminal and enters the wire, another electron leaves the wire and enters the positive terminal.

Now think about what is happening inside the wire. If we pick any point along the length of the wire, electrons are flowing by. They are moving in response to a potential difference in the wire. To one side of the point we have chosen, the potential is slightly negative, and to the other side the potential is slightly positive. The electrons move in response to the difference in these potentials.

To put it another way, if we choose any segment of the wire, there is a voltage across the length of the segment. Current flows, in other words, electrons move, in response to this voltage. The electrons can't escape from the surface of the wire. This has to do with the physics of metals. Basically, electrons can easily move around inside the wire, but they don't have enough energy to leave the wire. The wire would have to be very hot, almost at the melting point, before electrons could be drawn off the surface. At ordinary envirionmental temperatures, the wire isn't nearly hot enough. So the wire acts like a pipe for the electrons.

Suppose we start making the wire thinner and thinner. Its electrical resistance will start to increase. The flow of electrons will decrease too. This is another way of saying that the current will decrease. The voltage between the ends of the wire is the same, since that is determined by the battery. This follows Ohm's law: I = E/R. We are making R larger, and E stays the same, so I must become smaller.

Eventuallywe will come to the point where the wire has become so "thin" it isn't there anymore. What will happen to R in this case? It will become infinite. We can't plug infinity into Ohm's law because we can't divide by infinity. But we can see what will happen as R becomes larger and larger and approaches infinity. As we use bigger adn bigger numbers for R, we get smaller and smaller numbers for I. So as R approaches infinity, I approaches zero. We basically have an open circuit, and no current can flow because there is no path through which the electrons can flow.

So what happens when we use E = I times R? The answer is that we can't use the formula in the case of an open circuit. Ohm's law only applies to a complete circuit, where there is a path for the flow of electrons. It can't be used where there is no such path.

The voltage is still there because the baterry still has the potential to move electrons, even though there is nothing connected to the battery. In other words, the voltage is there, although there is no current.