a given circuit a higher voltage will in general cause a proportionally greater current. Since it is the voltage which may cause electricity to pass from its proper path and seek other and perhaps dangerous paths, higher voltages require better insulation on wires and in all electrical appliances. The voltage used thus becomes an important factor in determining the protection necessary for safety.

Difference of Potential. Two points, as on conductors or between a conductor and the earth, are said to be at different potentials. When such an electrical condition exists on them a current tends to pass between them either along the conductor or across a gap between the points. Along the conductor such a current produces heat, while if the current "jumps the gap" or arcs, heat is produced in the spark or arc formed.

Resistance. Resistance is measured in ohms. All substances offer resistance to the passage of current. This is true of metals, liquids, and gases. A good conductor, such as copper, has comparatively little resistance. Other materials, such as slate, porcelain, and rubber, are very poor conductors and may generally be considered as insulators. Since heat is always produced, the conductors must be of suitable size and material to keep the temperatures below the dangerous values, or, in cases where the heat is the result desired, suitable protection must be provided. The resistance of conductors is thus a necessary but undesirable property in some ways and a usable and valuable property in others. In all cases the fact that current produces heat in conductors must be reckoned with in electrical problems.

The loss of power from the heat expended in a supply wire is an illustration of the undesired property of resistance. The electric flatiron is an appliance where the resistance produces a useful result.

Ohm's Law. For our purpose here the relation between current, voltage, and resistance in a direct-current circuit may be stated as follows: The current (amperes) in a circuit equals the voltage E This is true both

(volts) divided by the resistance (ohms), or I=

R

of entire circuits and parts of circuits, provided E and R are the voltage and resistance of the whole circuit or the part under consideration, respectively. For a. c. circuits a somewhat more elaborate formula must be used.

Power. Power is measured in watts. (A kilowatt is 1,000 watts.) In direct-current circuits the power expended in any portion of the circuit is obtained by multiplying the current in amperes by the

B

Fig. 2. Multiple Lamp Circuits

voltage across the portion of the circuit. Thus: If the current in an incandescent lamp is ampere and if a voltmeter shows that the voltage across the lamp terminals is 110 volts, the power is 55 watts.

The corresponding mechanical term is horse-power; 1 horse-power is equivalent to 746 watts and 1 kilowatt equals about 13 horsepower. With alternating current the power in watts is not always

A

SHUNT

Fig. 4. Diagram of Shunt Circuits

to be obtained by multiplying amperes by volts. With alternating currents, a third factor must be used, called the "power factor" of

the circuit. It is sufficient for our purpose here to remember that the power actually delivered and used with alternating current may be less than the simple product of amperes and volts. Thus,

Fig. 5. Single-Pole Switch and Double-Pole Fuses

if a current of 50 amperes as read by an ammeter, passes through a coil of wire, and the voltage across the terminals of the coil is 100 volts, the power consumed, if the current is direct, is 50X100=5,000 watts or 5 kilowatts. If, however, the coil surrounds an iron core (as in an electromagnet) and alternating current is used, the power consumed will not be 5 kilowatts. The power factor may be 60 per cent for this coil, and the power consumed will then be 50X100X .60=3,000 watts or 3 kilowatts, instead of 5 kilowatts. The following definitions will be useful to those unfamiliar with electrical terms.

Multiple Connection. When a number of devices such as lamps, motors, etc., are so connected that the current has a path through

Fig. 6. Short Circuit in the Floor Above Chandelier

each device separately from one supply wire to another, they are said to be connected in multiple. See Fig. 2. Incandescent lamps are almost always connected in multiple. In Fig. 2 if each of the 7 lamps shown takes 1 ampere of current the total current at A

and at B will be 7 amperes, while at C and at D it will be 2 amperes. Series Connection. When a number of devices are so connected that they come one after another, they are said to be connected "in series." In Fig. 3, the arc lamps are shown so connected. In this case the same current traverses all parts of the circuit and the

Fig. 7.

Effects of a Short-Circuit in Wires Under Floor

total current is no more and no less than the current in each connected series device.

Shunt. A shunt is a by-path between two points so connected that part of the current will traverse it. The division of the total current between the main path and the shunt will depend on the comparative resistances, the larger current going by the path of lower resistance. In Fig. 4 are shown the connections of a "shunt motor" and resistance box "shunted" by a wire.

Cut-Out. A cut-out is a device for automatically breaking a circuit, usually when the current reaches a predetermined value. Thus, a 60-ampere fuse is a cut-out designed to burn out when currents in excess of 60 amperes pass through it. A circuit breaker is an electro-mechanical switch which is also used as a cut-out.

Switches, fuses and other appliances are said to be single-pole if they are for but one wire of a circuit; double-pole if for two, triple-pole if for three. Fig. 5 shows a single-pole switch and a double-pole fuse.

Fig. 8. Arc Between Wires of 250-Volt Circuit

Ground. A ground is a connection either intentional or accidental between a part of an electric circuit and the carth, or any metal or other conducting substances which are in electrical connection with the earth, such as water and gas pipes, iron beams, etc.

Short-Circuit. A short-circuit is a connection which permits current to flow from one part of a circuit to another by any path which it is not intended it should take. Since such a connection is the result of accident or the failure of some insulation, and since it usually allows excessive currents to flow, a short-circuit may be very dangerous and liable to cause a fire, especially as the accidental connection may afford very poor contact and cause arcing and burning at the junction of the conductors. Fig. 6 illustrates a shortcircuit in a floor between the two supply wires to a chandelier in