x 1022 cm "3? How long is th e conductor?

10.7. The coil of a hot p la te carries a c u rre n t of 2.7 A w ith an electric field stre n g th of 3.1 V /m . D eterm in e th e m o b ility of th e conduction electrons if th e ir num ber d e n sity in th e coil is 1023 cm ’ 3, and th e cross-sectional area of th e w ire is 0.10 m m 2.

10.8. D eterm ine th e c u rre n t d e n sity in a conductor if 0.15 C of e le c tricity pass per second through a cross-sectiQnal area of 6 m m 2. Is th e adm issible c u rre n t d en sity im p o rta n t when choosing the w ire for a resid e n tial building?

10.9. A co n stan t c u rre n t of 3.6 mA is m ain tained when gold p latin g an article 1.2 x 15 cm 2 in area. D eterm ine the current density.

10.10. W h at m ust the d iam eter of a copper wire be if it is to carry a cu rren t of 1000 A and the adm issible cu rren t d ensity is 2.5 A /m m 2?

120___________ Ch. II. F undam entals of E lectrodynam ics

10.11. D eterm ine the cu rren t d ensity in th e ex citatio n w inding of the tra c tio n m otor of a locom otive if the cross- sectional area of the w inding is 4.7 x 25 m m 2 and the nom inal current is 725 A.

10.12. W hat is the resistance of an alu m inium wire 2 m long and having a cross-sectional area of 1 m m 2? W hat w ill the resistan ce of th e same length of w ire w ith tw ice the cross-sectional area be?

10.13. Two wires, one of nickeline and th e other of nich- rom e, have the same leng th and diam eter. W hich of them has a higher resistance? W h at is the ra tio between th e ir resistances?

10.14. An iron wire and a tungsten wire of the sam e length and d iam eter are connected in tu rn to an accum ulator. In which wire w ill the cu rrent be stronger? W h at is the ratio of th e currents?

10.15. A long conductor was cut into two halves which were th en tw isted along th e whole length. How does the resistance of the wire change?

10.16. D eterm ine the capacitance of a cap acitor th e v o lt­ age across whose plates is 1 V as a resu lt of charging for 12 s w ith a cu rrent of 10‘ 6 A.

10.17. An electric c irc u it whose conductance is 2.4 x 10-2 S is connected to a d.c. source of 50 V. D eterm ine the cu rren t in the circu it and its resistance,

10.18. D eterm ine the length of a m anganin wire required to m ake a po ten tiom eter rated a t a m axim um resistance of 1500 Q if the diam eter of the wire is 0.3 mm.

10.19. A p o ten tiom eter is m ade of 2.25 m of con stantan wire hav in g a d iam eter of 0.15 mm. D eterm ine the resistance of th e p otentiom eter.

10.20. A bundle of copper wire having a mass of 3.6 kg has a resistance of 22.5 Q. D eterm ine the length of the wire in th e bundle.

10.21. A coil m ade of 75 m of co nstantan wire whose d i­ am eter is 0.1 mm is connected to a current source supplying a voltage of 12 V. D eterm ine the current in the coil.

10.22. The adm issible cu rren t d ensity of the w iring in a room is 6 A /m m 2. W h at is the voltage drop in the copper wire if its len gth is 30 m?

10.23. D eterm ine the voltag e drop and the cu rrent d en sity in the w inding of the m agnetic pole of a locom otive m otor.

§ 10. Electric Current in Metals. Ohm’s Law 121

The w inding is m ade of copper s trip having a cross-sectional area of 28 X 4.7 m m 2, th e average len gth of a tu rn being 1.5 m, and th e num ber of tu rn s is 40. The cu rren t in the w inding is 352 A.

10.24. An electric appliance is 0.5 km from a c u rre n t source and is connected to it through a wire haying a cross- sectional area of 5 m m 2. The appliance is moved 1 km fu rth e r away from the source. W h at should the cross-sectional area of th e w ire be for the voltage drop to rem ain unchanged?

10.25. How m uch copper is required to m anufacture th e co n tact wire of a tra m c irc u it hav in g a resistance of 0.2 Q if the cross-sectional area of th e wire is 85 m m 2?

10.26. D eterm ine the resistance of 1 km of tra m steel ra ils if the m ass of the rails is 55 kg/m .

10.27. Two wires, one of copper and one of nichrom e, of the same len gth and d iam eter are heated through 5 K . The resistance of which wire changes more? W h at is the ra tio of

the resistances?

10.28. The series resistance connected to th e ig n itio n coil of a “M oskvich” m otor car is 1.35 Q a t 293 K and 2 Q at 373 K . D eterm ine the m ate ria l of which it is m ade.

10.29. The s ta rte r rh eo sta t of an electric tra in is m ade of a cast iron p late and a ferro-alum inium high-resistance r ib ­ bon alloy. I ts resistance is 4 Q a t 298 K . W hat w ill the change in its re s is ta n c e be when the tem p erature is 723 K ?

10.30. W h at m ust the tem p eratu re resistance coefficient of the m aterial used for potentiom eters be?

10.31. The tung sten filam ent of an incandescent lam p has a resistance of 20 £2 when cold. W hat w ill its operating re ­ sistance be, i.e. when the filam ent is heated to 2100°G?

10.32. W h at is th e increase in th e tem p eratu re of the cop­ per w inding of a d.c. m otor arm atu re as a resu lt of pro­ longed operatio n d uring w hich th e resistance has increased from 2 to 2.2 £2?

10.33. An electric arc rate d for a voltage of 45 V and a curren t of 10 A is connected to a circu it a t a voltage of 110 V. D eterm ine th e required resistance of th e series re­ sistor if the resistance of th e leads is 0.5 £2.

10.34. W h at is th e increase in the tem p eratu re of a poten­ tiom eter m ade of iron w ire if its resistance has doubled? 10.35. The voltage a t an electric su b sta tio n is 600 V (Fig. 32). The two copper cables A B and CD connecting the

122 Ch. II. Fundam entals of E lectrodynam ics

su b sta tio n w ith a tro lle y b u s’ contacts are each 440 m long and 400 mm2 in cross-sectional area. The co n tact wires are m ade of copper and have a cross-sectional area of 85 m m 2. The cu rren t in the trolley bus m otor is 200 A. D eterm ine the

voltage across the current collectors of th e tro lley .

10.36. The experim ental d.c. transm ission line between