in which C = the current; R=the resistance of the conductor; and t = the time.
It is obvious that a protective device, such as an overload circuit-breaker for a motor, or a protector for telephone apparatus, needs to operate more quickly for a large current than for a small one, and this is just what all well-designed protective devices are intended to do. The general problem which these heating hazards present with relation to telephone apparatus and circuits is: To cause all parts of the telephone system to be made so as to carry successfully all currents which may flow in them because of any internal or external pressure, or to supplement them by devices which will stop or divert currents which could overheat them.
Electrolytic hazards depend not on the heating effects of currents but on their chemical effects. The same natural law which enables primary and secondary batteries to be useful provides a hazard which menaces telephone-cable sheaths and other conductors. When a current leaves a metal in contact with an electrolyte, the metal tends to dissolve into the electrolyte. In the processes of electroplating and electrotyping, current enters the bath at the anode, passes from the anode through the solution to the cathode, removing metal from the former and depositing it upon the latter. In a primary battery using zinc as the positive element and the negative terminal, current is caused to pass, within the cell, from the zinc to the negative element and zinc is dissolved. Following the same law, any pipe buried in the earth may serve to carry current from one region to another. As single-trolley traction systems with positive trolley wires constantly are sending large currents through the earth toward their power stations, such a pipe may be of positive potential with relation to moist earth at some point in its length. Current leaving it at such a point may cause its metal to dissolve enough to destroy the usefulness of the pipe for its intended purpose.
Lead-sheathed telephone cables in the earth are particularly exposed to such damage by electrolysis. The reasons are that such cables often are long, have a good conductor as the sheath-metal, and that metal dissolves readily in the presence of most aqueous solutions when electrolytic differences of potential exist. The length of the cables enables them to connect between points of considerable difference of potential. It is lack of this length which prevents electrolytic damage to masses of structural metal in the earth.
Electrical power is supplied to single-trolley railroads principally in the form of direct current. Usually all the trolley wires of a city are so connected to the generating units as to be positive to the rails. This causes current to flow from the cars toward the power stations, the return path being made up jointly of the rails, the earth itself, actual return wires which may supplement the rails, and also all other conducting things in the earth, these being principally lead-covered cables and other pipes. These conditions establish definite areas in which the currents tend to leave the cables and pipes, i.e., in which the latter are positive to other things. These positive areas usually are much smaller than the negative areas, that is, the regions in which currents tend to enter the cables form a larger total than the regions in which the currents tend to leave the cables. These facts simplify the ways in which the cables may be protected against damage by direct currents leaving them and also they reduce the amount, complication, and cost of applying the corrective and preventive measures.
All electric roads do not use direct current. Certain simplifications in the use of single-phase alternating currents in traction motors have increased the number of roads using a system of alternating-current power supply. Where alternating current is used, the electrolytic conditions are different and a new problem is set, for, as the current flows in recurrently different directions, an area which at one instant is positive to others, is changed the next instant into a negative area. The protective means, therefore, must be adapted to the changed requirements.