In the last chapter the resistance offered by conductors to the passage of the electric current was considered. If we examine different points of a circuit by means of suitable instruments, we will discover that there is a gradual fall in the potential, proportionate to the distance from the source, where the potential is highest. This fall in potential is directly due to the resistance of the conductor. In an electric-light system, the lighting circuits are maintained at a substantially uniform potential by means of feed wires, which convey additional current to suitable points in the circuits, to restore the loss in potential due to the resistance of the circuit.

Fig. 22.

Fig. 23.

The fall in potential of a large current is usually measured with a voltmeter. With smaller currents, an instrument known as a wheatstone bridge is often used. A description of the construction of such an instrument will be given in the next number of this magazine, together with the method of using it.

The loss of potential due to resistance represents the amount of energy converted into heat. In addition to the resistance of. a conductor may be that of a counter E. M. F., such as is developed by the rotation of the armature of a motor. This opposing current reduces the available E. M. F., acting as so much additional resistance to the flow of the current, and is also converted into heat. Joule found the heat developed in a circuit to be propor-' tional to the resistance, to the square of the strength of the current, and to the time the current flows.

Many important uses are made of this property of developing heat by resistance. In blasting, a charge is ignited by heating a wire of high resistance, which is in contact with a fuse. Torpedoes may be exploded beneath the water, at any desired distance from the operator. In electric welding, a large current of low voltage is passed through the two pieces of metal to be welded. At the points of contact the resistance is very high, the current having but a very imperfect path. The heat developed at the point of contact soon brings the adjoining ends of the metal to a high heat, the increase in temperature increasing the resistance. Cooking by electricity is but another use of heat developed by the resistance of conductors arranged for that purpose.

In addition to a simple circuit, with but one path for the flow of the current, are those known as divided circuits, in which the current is divided between two or more paths. If an additional path serves simply as a by-pass for only a small portion of the whole current, it is termed a shunt. This is a device much used in motor construction and will be considered later. The resistance of each path of a divided circuit determines the current flowing through it, the relative strength of current in two branches being proportional to their separate conductances, or inversely proportional to their resistances. The joint resistance of a divided circuit will be less than that of either path alone, as the current has two paths through which to travel, in place of one. If the resistances of two paths are equal, then one-half of the whole current will pass through each path. If one path has twice the resistance of the other, then only one-half as much current will pass through the path of greater resistance as will pass through the path with the lesser, or one-third of the total current.

Fig. 24.

The joint resistance of a divided circuit is determined by dividing the product of the two separate resistances by their sum. This is known as the law of shunts, and should be studied until fully understood. To illustrate, suppose one branch of a divided circuit to have a resistance of 3 ohms, and the other a resistance of 6 ohms. The product of the two is 18, their sum 9; dividing, we find the joint resistance to be 2 ohms, or less than that of either branch singly. When the division is into more than two branches, the formula is a little more complicated, but a little study will make it plain. The joint resistance of any number of branches of a divided circuit is the reciprocal of the sum of the reciprocals of the separate resistances. The reciprocal of any number is the quotient obtained by dividing 1 by that number. To illustrate, assume a divided circuit of three branches of 10, 20 and 25 ohms resistance respectively, the problem would be as follows :

The reciprocal of 10 is .10 The reciprocal of 20 is .05 The reciprocal of 25 is .04

Sum of the reciprocals .19

Dividing 1 by .19 gives 5.26 ohms, the joint resistance. With battery circuits, the grouping of the cells differs with different uses. If a current of high E. M. F. or voltage is desired, the cells are arranged in series, as shown in Fig. 22. In this arrangement the current of each cell passes through those following, the positive terminal of one cell being connected to the negative of another. But while this arrangement increases the E. M. F., it also increases the internal resistance, as the current has to travel through the resistance of each cell following. So for that reason this arrangement is subject to limitations which have to be considered in ascertaining the most desirable way of grouping a battery. The usual method is to have the internal resistance of the cells equal the external resistance of the circuit. If the external resistance be small, however, the parallel grouping is employed. In this arrangement (Fig. 23) the positive poles are all connected with each other and the negative poles together. The internal resistance is thus much reduced, the current having several paths in place of one. The E. M. F. of this arrangement is but that of one cell.

It is sometimes necessary to make a combination of the two forms of grouping; one which will be partly in series and partly in parallel, as shown in Fig. 24, which represents two groups of cells in parallel with three cells in series in each group. In general, it may be said that the best grouping to secure economy is that in which the internal resistance is small compared with the external; to secure the greatest current, when the internal resistance equals the external; to secure the quickest action, when the internal resistance is higher than the external.