




Because of the shell arrangements of electrons in various atoms and molecules, some substances are quite good at allowing a few electrons to move about freely (e.g., copper, silver, gold, aluminum), and some not (e.g., sulfur, rubber, quartz). Materials that fall into the first group are conductors; those in the second insulators. To some degree, greater or less, all materials offer resistance to the passage of an electrical current. The unit of electrical resistance is the ohm; it was arrived at by way of a mathematical construction, the most basic of electrical relationships, called Ohm's Law.
Stated in words, Ohm's Law says that how much current (amps) a given voltage can push through a circuit is affected by how much resistance it must act against. Higher resistance, fewer amps; lower resistance, more amps. Mathematically it all boils down to this:


E = IR (where E is voltage, I is current, and R resistance)


The product of current and resistance is voltage. If you start with a certain voltage—from a battery, or from a wall outlet—the current that will flow is limited by resistance in the circuit. With, say, 100 volts at the outlet and 100 ohms in the circuit, one amp will flow (100 = 1 X 100); pushing current through 1,000 ohms, a hundred volts will cause a tenth of an amp to flow (100 = 0.1 X 1000). And so forth.
Having established for a particular circuit its voltage and the current that will flow, these two quantities may be combined as a measure of the power, in watts, used. That is:


P = IE (where P is power)


This formalizes the idea that if lots of electrons are propelled with great electrical force the result is more power than if fewer are moved and with less force. Note, though, that the same given power can be achieved by juggling current and voltage. One amp delivered at a thousand volts makes a thousand watts of power, but so would a thousand amps delivered at one volt. In a practical sense—because wires may melt and insulators break down—it can make a great deal of difference how the current and voltage values are manipulated. Fifty amps at twenty volts might work, for example, as an efficient welding circuit but a dangerous hair dryer, whose identical power requirement would more safely run to about eight amps at 125 volts.
More importantly, the ability to generate and send electrical power over long transmission lines and then to use it efficiently at the other end depends crucially on the practical possibility of swapping large currents into high voltages and back again in the basic power equation. In this the modern electrified world owes its largest debt to Tesla, who designed essentially the system and all its parts.


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