3. Two parallel resistances, of 5 and 10 ohms respectively, are connected in series with a resistance of 15 ohms. What is the current in each branch of the circuit when the total fall of potential is 10 volts?

4. Twenty similar lamps, in parallel, are supplied with 0.5 ampere each, with a difference of potential of 110 volts at the lamps. If 2.2 volts are lost on the line which connects them to the generator, what is (a) the voltage at the terminals of the generator? (b) the resistance of the line ? (c) the power loss in the line ?

1.5

5. A battery with an internal resistance of 2 ohms is connected, by wires with a resistance of 0.8 ohm, to an instrument which has a resistance of 2.2 ohms. If the current is 4 amperes, (a) find for each part of the circuit the loss of voltage produced by resistance. (b) What is the total 4 loss? (c) What is the E. M. F. of the battery?

6. Two resistances, of 6 and 12 ohms respectively, are connected in parallel. To the combination is connected a cell with an E.M.F. of 1.5 volts and with an internal resistance of 1 ohm. (a) Compute the value of the current in the battery. (b) Find the current in each branch.

7. Two resistances, of 20 and 40 ohms, are connected in parallel. This group is in series with 10 ohms and with a battery the internal resistance of which is 5 ohms. If the E. M. F. of the battery is 10 volts, compute the current in the battery.

8. Two cells, each having an internal resistance of 3 ohms and an electromotive force of 1.5 volts, are connected in parallel. Find the total current when the circuit is completed through a resistance of 4 ohms.

9. A cell having a resistance of 2 ohms and an E. M. F. of 1.4 volts is connected to a coil with a resistance of 5 ohms. Compute (a) the current, and (b) the difference of potential between the terminals of the cell.

10. 5 amperes are to be supplied for house-lighting. The lamps, which are near together and in parallel, are connected to a storage battery by 250 ft. of wire which runs 1.6 ohms per 1000 ft. What must be the difference of 1 potential of the battery terminals in order to have 30 volts across the lamps ?

11. A dry cell with an E. M. F. of 1,5 volts and an internal resistance of 0.2 ohm is connected in series with a gravity cell having an E.M.F. of 1 volt and an internal resistance of 2 ohms. The circuit is completed by wires having a resistance of 2.8 ohms. (a) What is the current? (b) Compute the difference of potential at the terminals of each cell.

12. The connections of the circuit of Problem 11 are changed so that the two electromotive forces are opposing each other. What is (a) the current ? (b) the difference of potential at the terminals of each cell ?

! 13. A dynamo having an internal resistance of 0.2 ohm sends a current of 20 amperes through wires having a resistance of 1.3 ohms to a distant building, where the difference of potential of line is 105 volts. (a) What is the E. M. F. of the dynamo? (b) How much power is lost in the dynamo and the connecting wires ?

14. A storage battery of a home-lighting plant has an E. M. F. of 32 volts and an internal resistance of 0.2 ohm. It is connected by wires having a resistance of 0.2 ohm to a group of 5 lamps which are in parallel. (a) If each lamp has a resistance of 30 ohms, what is the current supplied ? (b) What is the difference of potential at the lamp terminals ?

15. A current of 12 amperes divides, flowing through two parallel resistances of 1.5 ohms and 0.5 ohm. Find the current through the branch having a resistance of 0.5 ohm.

16. The moving coil of an ammeter has a resistance of 1.998 ohms, while the shunt has a resistance of .002 ohm. What is the current through each part when the total current is 20 amperes?

17. A certain ammeter has a resistance of 0.1 ohm. It is desired to add a shunt to it so that the ammeter proper and the shunt will together carry a current a hundred times greater than that indicated on the ammeter scale. What must be the resistance of the shunt?

18. Five lamps in parallel, each having a resistance of 30 ohms, are connected by wires with a resistance of 0.5 ohm to a dynamo which has a resistance of 0.2 ohm. What must be the E. M. F. in order that each lamp may have a current of 1 ampere ?

19. A dynamo, the voltage across the terminals of which is 220 volts, is connected to a distant motor by wires having a resistance of 0.5 ohm. The loss of voltage in the wires is 20 volts. (a) How much current is supplied to১ the motor? (b) What is the difference of potential of the motor terminals ?

20. The voltage across the terminals of a direct-current motor is 205 volts, and the current is 20 amperes. If the internal resistance is 0.5 ohm, what is the counter E. M. F. of the motor?

21. A dynamo having an internal resistance of 0.5 ohm is connected, by wires with a resistance of 1.5 ohms, to a place where the power is used. At this place a voltmeter shows 114 volts, and an ammeter 25 amperes. What is the E. M. F. of the dynamo?

22. A storage cell has a resistance of 0.1 ohm and an E. M. F. of 2.2 volts. (a) What resistance must be connected in series with the cell so that it can be charged on a 20-volt circuit with a current of 5 amperes? (b) What will be the difference of potential of the terminals of the cell during charging? (The E. M. F. of a storage cell is a counter E. M. F. when on charge.)

23. A dynamo, the internal resistance of which is 0.4 ohm and the E. M. F. 120 volts, is charging a series of 50 storage cells, each having an E. M. F. of 2.1 volts. The resistance of each cell is 0.01 ohm, and that of all connecting wires used is 0.6 ohm. What is (a) the current? (b) the difference of potential at the terminals of the dynamo? (c) the difference of potential at the terminals of the battery?

24. A storage battery is charged by a dynamo circuit with a current of 10 amperes. In order to get this current, a resistance of 3 ohms is in series with the battery. The resistance of the dynamo and the connecting wires is 1.5 ohms. A voltmeter connected to the battery terminals reads 60 volts. (a) How much power is supplied to the battery? (b) How much power is wasted in heat in the 3 ohms, the dynamo, and the connecting wires ? (c) What is the E. M. F. of the dynamo?

25. The E. M. F. of a storage battery is 100 volts. When producing 10 amperes, the difference of potential at its terminals is 98 volts. What is its internal resistance ?

CHAPTER XXXI

CONDUCTION OF ELECTRICITY THROUGH ELECTROLYTES

Introduction, 448. Electrolysis, 449. Historical note, 450. The electrolysis of water, 451. Electroplating, 452. Ions, 453. Faraday's laws of electrolysis, 454. A theoretical derivation of Faraday's laws; the absolute mass of a hydrogen atom, 455. The voltameter, or coulometer, 456. The theory of the simple cell, 457. Types of cells, 458. Storage cells, 459.

448. Introduction. In the conduction of electricity through metals there is no evidence of any transfer of the material of the conductor. Hence there is no reason for believing that the current is carried by atoms or molecules of these metallic conductors. It is now generally believed that current in solid conductors is carried solely by the migration of electrons the very small, negatively charged particles which are far smaller than the atoms of any element.

But in the conduction of electricity through liquids the facts are quite different. Material is carried by the current. A familiar instance is that of electroplating: in the plating of silver, for example, silver atoms migrate through the liquid and are deposited on one of the plates which dips into the liquid. A great many illustrations could be cited, and some of these will be given later. The evidence shows that electricity is carried through most liquids in an entirely different way from that by which it is carried in solid conductors. The difference between the two is so great that the subject of the conduction of electricity through liquids is often treated as a separate branch of electricity.

449. Electrolysis. When a current flows through a liquid, not only is there a transport of material, but usually there are chemical changes in the liquid. For example, if a current flows through a solution of common salt (sodium chloride), entering and leaving the liquid by means of platinum terminals which dip into the liquid, sodium hydroxide, or caustic soda, is formed in the liquid near one terminal, and hydrochloric acid near the other. Liquids in which such changes are produced by electric currents are called electrolytes, and the whole process is called electrolysis. Faraday, who introduced these names, suggested also the names now commonly used for the terminals conducting the current into and from the liquid. These he called electrodes: the one which conducts the current into the liquid he called the anode, and the one which leads the current out, the cathode.

Mercury and other molten metals conduct in a manner similar to that of solid metals.

450. Historical note. On March 20, 1800, Volta wrote a letter to Joseph Banks, the president of the Royal Society of London, describing a method of making a battery with plates of zinc and copper and with pieces of cloth wet with a salt solution. These were laid one on top of another in the following order: zinc, cloth, copper, zinc, cloth, copper, zinc, cloth, copper, and so on. The zinccloth-copper forms a complete cell, and stacking up a large number of pieces forms a battery of many cells in series. Within six weeks after Volta's letter was received, a battery-the first in Englandhad been constructed; and by means of it the decomposition of water had been discovered by Nicholson and Carlisle. This discovery aroused great interest and led others to take up the work. Soon Cruickshank precipitated silver and copper from their solutions, a discovery which led to electroplating. In 1807 Davy decomposed soda and potash, proving that they were not elements, as had been supposed, but chemical compounds. After this, progress was rapid.

Before the voltaic cell was discovered, there were no sources known that would give currents large enough to produce electrolytic effects which could be readily observed. Forms of the electrostatic machine were in use, but they were of little service in producing continuous currents. The discovery of the voltaic cell opened up a new era in electricity: the discoveries in electrolysis were only a part of the great discoveries that took place in the years from 1800 to 1830.