2. MAGNETISM AND E.M.F. 11. In an electric conductor moving relatively to a magnetic field, an e.m.f. is generated proportional to the rate of cutting of the lines of magnetic force by the conductor. Unit e.m.f. is the e.m.f. generated in a conductor cutting one line of magnetic force per second. 108 times unit e.m.f. is the practical unit, called the volt. Coiling the conductor n fold increases the e.m.f. n fold, by cutting each line of magnetic force n times. In a closed electric circuit the e.m.f. produces an electric current. The ratio of e.m.f. to electric current produced thereby is called the resistance of the electric circuit. Unit resistance is the resistance of a circuit in which unit e.m.f. produces unit current. 109 times unit resistance is the practical unit, called the ohm. 10 ELEMENTS OF ELECTRICAL ENGINEERING The ohm is the resistance of a circuit, in which 1 volt produces 1 amp. The resistance per unit length and unit section of a conductor is called its resistivity, p. The resistivity p is a constant of the material, varying with the temperature. The resistance r of a conductor of length I, area or section A, ... lp and resistivity p is r = -7" 12. If the current in the electric circuit changes, starts, or stops, the corresponding change of the magnetic field of the current generates an e.m.f in the conductor carrying the current, which is called the e.m.f. of self-induction. If the e.m.f. in an electric circuit moving relatively to a magnetic field produces a current in the circuit, the magnetic field produced by this current is called its magnetic reaction. The fundamental law of self-induction and magnetic reaction is that these effects take place in such a direction as to oppose their cause (Lentz's law). Thus the e.m.f. of self-induction during an increase of current is in the opposite direction, during a decrease of current in the same direction as the e.m.f. producing the current. The magnetic reaction of the current produced in a circuit moving out of a magnetic field is in the same direction, in a circuit moving into a magnetic field in opposite direction to the magnetic field. Essentially, this law is nothing but a conclusion from the law of conservation of energy. EXAMPLES 13. (1) An electromagnet is placed so that one pole sur- rounds the other pole cylindrically as shown in section in Fig. 4, and a copper cylinder revolves between these poles at 3000 rev. per min. What is the e.m.f. generated between the ends of this cylinder, if the magnetic flux of the electromagnet is <£ = 25 megalines? During each revolution the copper cylinder cuts 25 mega- lines. It makes 50 rev. per sec. Thus it cuts 50 X 25 X 106 = 12.5 X 108 lines of magnetic flux per second. Hence the gener- ated e.m.f. is E = 12.5 volts. GENERATION OF E.M.F. 11 Such a machine is called a " unipolar," or more properly a " non-polar" or an "acyclic," generator. 14. (2) The field spools of the 20-pole alternator in Section 1, Example 4, are wound each with 616 turns of wire No. 7 (B. & S.), 0.106 sq. cm. in cross section and 160 cm. mean length of turn. The 20 spools are connected in series. How many amperes and how many volts are required for the excitation of this alternator field, if the resistivity of copper is 1.8 X 10~6 ohms per cm.3 1 FIG. 4. — Unipolar generator. Since 616 turns on each field spool are used, and 4280 ampere- 4280 turns required, the current is fi1fi = 6.95 amp. The resistance of 20 spools of 616 turns of 160 cm. length, 0.106 sq. cm. section, and 1.8 X 10~6 resistivity is, 20 X 616 X 160 X 1.8 X 10~6 = 33.2 ohms, 0.106 and the e.m.f. required, 6.95 X 33.2 = 230 volts.