Fig. 251.—Diagram of cells connected in series.
272. Ohm's Law.—The relation between the electromotive force applied to a circuit, its resistance, and the current produced was discovered in 1827 by George Ohm. Ohm's law, one of the most important laws of electricity, states that, in any circuit, the current in amperes equals the electromotive force in volts divided by the resistance in ohms.
This principle is usually expressed thus:
Current intensity = electromotive force/resistance or
Amperes = volts/ohms or I = E/R
Fig. 252.—The street cars are connected in parallel with each other.
273. Resistance of Conductors in Series.—A study of the resistance of conductors when alone and when grouped in various ways is of importance since, the current flow through any circuit is dependent upon its resistance. The two most common methods of combining several conductors in a circuit are in series and in parallel. Conductors are in series when all of the current passes through each of the conductors in turn (Fig. 218), thus the cell, push-button, wires, and electric bell in an electric-bell circuit are in series. Conductors are in parallel when they are so connected that they are side by side and a part of the whole current goes through each. None of the current that passes through one conductor can go through the conductors in parallel with it. Thus the electric street cars are in parallel with each other. (See Fig. 252.) It is easily seen that none of the current passing through one car can go through any of the others. When the conductors are in series the combined resistance is the sum of the several resistances. Thus in an electric-bell circuit if the battery has a resistance of 1 ohm, the bell of 2 ohms, and the wire 1 ohm, the total resistance in the circuit is 4 ohms. When conductors are in parallel the combined resistance is always less than the separate resistances. Just as a crowd of people meets less resistance in leaving a building through several exits, so electricity finds less resistance in moving from one point to another along several parallel lines, than along one of the lines.
274. Resistance of Conductors in Parallel.—If three conductors of equal resistance are in parallel, the combined resistance is just one-third the resistance of each separately (Fig. 253). The rule that states the relation between the combined resistance of conductors in parallel and the separate resistances is as follows:The combined resistance of conductors in parallel is the reciprocal of the sum of the reciprocals of the several resistances. For example, find the combined resistance of three unequal resistances in parallel; the first being 4 ohms, the second, 6 ohms, and third 3 ohms. The reciprocals of the three resistances are 1/4, 1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 = 18/24. The reciprocal of this is 24/18 which equals 1-1/3 ohms, the combined resistance.