# Fermilab

## Inquiring Minds

Cost of Operating Light Bulbs

Dear Webmaster,

My wife and I are having a friendly dispute over the cost of operating electric light bulbs and I am hoping that perhaps a physicist might settle things for us. It is not lightly that I turn to such a prestidigious resource, but all other sources (ie. Com Ed customer relations - local electricians) have all demonstrated the recent phenomenon of the dimming down of America. I am pretty sure that in my high school physics class we were taught that starting friction is greater than moving friction. So far no problem, but these folks insist that there is no friction involved in electricity - "It just flows they say" - wouldn't it be nice if it did. Anyway if there is someone there who could help me with this dilemma I'd appreciate it. BTW I'm right here in Aurora if there is someone I could call or write I would be pleased to do that too.

Thanks for any help,
Rick Reynolds

Dear Mr. Reynolds:

Well, you have certainly asked an interesting and important question. Even more interesting is which one of you, you or your wife, will turn out to be right, and how friendly, exactly, is your argument. If she is right, I recommend the "You're right, I'm wrong, I'm sorry" approach. If you're right, I recommend exactly the same approach. It always keeps the peace.

All seriousness aside, here is what I know:

Electricity certainly exhibits the equivalent of friction. A metal is a bunch of uniformly spaced atoms more or less locked into position by a collection of "springs" that connect each atom to all its neighboring atoms. These springs are really the electric forces between the atoms, but they act like springs because when an atom is moved slightly, the electric force tries to move it back into its regular position; it acts as a restoring force. This array of atoms is called the lattice. The atoms always vibrate or oscillate a little on their "springs." The higher the temperature of the metal, the more the atoms oscillate.

All metals are conductors, and conductors have lots of electrons that are not very strongly attached to the atoms, moving about from atom to atom, sort of drifting around. These are called "free electrons," although they aren't completely free. When you put a voltage across a piece of metal, such as a wire, by attaching the poles of a battery to its opposite ends, for example, each free electron in the wire feels a force that accelerates it from the negative to the positive pole of the battery. But, before the electron can get up much speed, it hits an atom in the lattice, and slows down or comes to a stop, because some or all of its energy is transferred to the atom. But, it still feels the force due to the battery, so it starts to accelerate again. Then it hits another atom and stops again, and so forth. Sort of like Dodgem cars at the carnival. This is a phenomenon that is the equivalent of friction. If the metal is a good conductor, there are lots of free electrons and the number of collisions is small. At room temperature, silver, copper and aluminum are the best conductors. If the metal is a poor conductor, like tungsten or stainless steel, there are fewer free electrons and lots of collisions. The more collisions, the higher the friction, which in the case of conductors is called resistance: resistance to moving electrons. (Insulators don't have any free electrons so you can't move current in them, and semiconductors like silicon have some free electrons, but only a small fraction of what conductors have. One can make layers of semiconductors, and control the movement of the free electrons independent of the voltage across th semiconductor. This is the way transistors and integrated circuits are made.)

What happens to the energy transferred to the atoms? It moves the atoms a little bit. The restoring force tries to bring the atoms back, but they overshoot their normal positions (called the equilibrium position, where the restoring force is zero) so the atoms oscillate around their equilibrium positions. When the atoms of a material are moving a lot, it is as if the temperature of the material is very high. If enough of the atoms move, the material will be at a very high temperature, so high that the material will emit light, that is, glow like an incandescent light bulb. That is exactly what an incandescent bulb is: current passing through a poor conductor with so much friction (resistance) that the conductor glows white hot.

Some miraculous materials, when cooled to very low temperature, lose all their resistance to the flow of electrons. These are called superconductors. There are types that are made of metals and that are superconducting at 4 K, that is, four degrees (C) above absolute zero. (Absolute zero (0 K) is the temperature at which the natural oscillatory motion of atoms in the lattice ceases. It is about -460° F, which is pretty cold.) The magnets that guide the beams of protons around the Tevatron, the big ring at Fermilab, are made with such materials, and so they are very efficient, because we don't spend a lot of electrical energy heating up the wires in the magnet. There are recently discovered superconductors that are a type of ceramic that are superconducting at around 100 K, which is only about -280° F, which is still pretty cold. A lot of work is going on in industry and at national labs, including Fermilab, to try to develop practical superconductors of this type, and magnets that use them.

I hope this explanation wasn't too long and involved. If you have any more questions, you send them to our Webmaster at Public Affairs, and she will forward them to the appropriate people.

Peter Limon