The same thing is true of electrical circuits. If the current through an electrical circuit at a certain voltage is measured, and then the voltage is doubled, the current reading will also be doubled. It can also be observed that, provided the pressure is kept constant, and, instead, the size of the conductor is varied either in length or in cross section, the current will change also. Increasing the length of the conductor or decreasing its cross-sectional area will decrease the current, since this will increase the resistance. All other things being equal, if the resistance of a circuit is cut in half, the current will be doubled; and if the resistance is cut to one-third of its original value the current will be trebled, and vice versa; that is, three times the resistance will result in one-third of the current, etc. These facts were first presented as a definite rule by a man named Ohm, which resulted in the use of his name as applied to the unit of resistance. The unit of current is known as the ampere. The value of an ohm of resistance was so chosen that it would require an electrical pressure of one volt to force an electric current of one ampere through it.

If any two of the three factors mentioned above (voltage, current, and resistance) are known, the third factor may be found from one of the following equations :

where E represents the voltage, R the resistance in ohms, and I the current in amperes.

If a valve is placed in the pipe line, the flow of water can be restricted. In the same manner the flow of electricity can be restricted by placing a resistance in the circuit. If the resistance is made variable, the current can be changed at will. A variable resistance of this type is known as a rheostat.

If the water pipe is tapped at various points at different distances from the pump, and the water pressure is measured between these points while water is flowing through the pipe, the pressure of the water will be found to vary in proportion to the distance of these points from the pump measured along the pipe. A resistor carrying an electric current and tapped at various intervals has a similar effect, that is, if the voltage is measured between one end and the different taps, the voltage will vary from one point to another. A resistor used in such a manner is known as a potentiometer. Potentiometers of the simplest variety are usually made of "resistance wire" wound on a form, and are provided with a sliding arm which permits contact with the resistor at any point throughout its length. With such a device any desired fraction of the impressed voltage can be "tapped off" by simply moving the sliding arm.

6