*25. (Ill) For some applications, it is important that the

1. (I) A current of 1.30 A flows in a wire. How many electrons are flowing past any point in the wire per second?

2. (I) A service station charges a battery using a current of 6.7 A for 5.0 h. How much charge passes through the battery?

3. (I) What is the current in amperes if 1200 Na+ ions flow across a cell membrane in 3.5 jus? The charge on the sodium is the same as on an electron, but positive.

4. (I) What is the resistance of a toaster if 120 V produces a current of 4.2 A?

5. (I) What voltage will produce 0.25 A of current through a 3800-11 resistor?

6. (II) A hair dryer draws 7.5 A when plugged into a 120-V line, (a) What is its resistance? (b) How much charge passes through it in 15 min? (Assume direct current.)

7. (II) An electric clothes dryer has a healing element with a resistance of 9.611. (a) What is the current in the element when it is connected to 240 V? (b) How much charge passes through the element in 50 min ?

8. (II) A 9.0-V battery is connected to a bulb whose resistance is 1.611. How many electrons leave the battery per minute?

9. (II) A bird stands on a dc electric transmission line carrying 2800 A (Fig. 18-34). The line has 2.5 X 10"5ft resistance per meter, and the bird's feet are 4.0 cm apart. What is the potential difference between the birds feet?

10. (II) An electric device draws 6.50 A at 240 V. (a) If the voltage drops by 15%. what will be the current, assuming nothing else changes? (b) If the resistance of the device were reduced by 15%, what current would be drawn at 240 V?

11. (II) A 12-V battery causes a current of 0.60 A through a resistor, (a) What is its resistance, and (/>) how many joules of energy does the battery lose in a minute?

12. (I) What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.32 il?

13. (I) What is the resistance of a 3.5-m length of copper wire 1.5 mm in diameter?

14. (II) Calculate the ratio of the resistance of 10.0m of aluminum wire 2.0 mm in diameter, to 20.0 m of copper wire 2.5 mm in diameter.

15. (II) Can a 2.5-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details.

16. (II) A certain copper wire has a resistance of 10.0 H. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

17. (II) Howr much wrould you have to raise the temperature of a copper wire (originally at 20CC) to increase its resistance by 15%?

18. (II) Estimate at what temperature copper will have the same resistivity as tungsten does at 20C.

19. (II) A 100-W lightbulb has a resistance of about 12 fl when cold (20cC) and 140H when on (hot). Estimate the temperature of the filament when hot assuming an average temperature coefficient of resistivity a = 0.0060 (C0)"1.

20. (II) Compute the voltage drop along a 26-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

21. (II) A rectangular solid made of carbon has sides of lengths 1.0 cm. 2.0 cm. and 4.0 cm. lying along the x, y, and z axes, respectively (Fig. 18-35). Determine the resistance for current that passes through the solid in (a) the .v direction. (b) the y direction, and (c) the z direction. Assume the resistivity is p = 3.0 x 10-sn -m.

22. (II) Two aluminum wrires have the same resistance. If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire?

* 23. (II) A length of aluminum wire is connected to a precision 10.00-V powrer supply, and a current of 0.4212 A is precisely measured at 20.0C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3618 A. What is the unknown temperature?

24. (Ill) A 10.0-m length of wire consists of 5.0m of copper followed by 5.0 m of aluminum, both of diameter 1.0 mm. A voltage difference of 85 mV is placed across the composite wire, (a) What is the total resistance (sum) of the twro wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?

*25. (Ill) For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 4.70-kO resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances. What value should each of these resistors have (at 0C) so that the combination is temperature independent?

26. (I) The healing element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be the resistance of the element?

27. (I) What is the maximum power consumption of a 3.0-V portable CD player that draws a maximum of 320 m A of current ?

28. (I) What is the maximum voltage that can be applied across a 2.7-kH resistor rated at J watt?

29. (I) (a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source voltage of 120 V. (b) Repeat for a 440-W bulb.

30. (II) A 115-V fish-tank heater is rated at 110 W. Calculate (a) the current through the heater when it is operating, and (b) its resistance?

31. (II) A 120-V hair dryer has two settings: 850 W and 1250 W. (<?) At which setting do you expect the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting: and (c) the higher setting.

32. (II) You buy a 75-W lightbulb in Europe, where electricity is delivered to homes at 240 V. If you use the lightbulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: assume roughly that brightness is proportional to power consumed.)

33. (II) How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of 15 min? At a cost of 9.0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

34. (II) At $0,095 per kWh. what does it cost to leave a 25-W porch light on day and night for a year?

35. (II) An ordinary flashlight uses two D-cell 1.5-V batteries connected in series as in Fig. 184b (Fig. 18-36). The bulb draws 450 mA when turned on. () Calculate the resistance of the bulb and the power dissipated. (b) By what factor would the power increase if four D-cells in scries were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn't you try this?

36. (II) What is the total amount of energy stored in a 12-V, 85-A-h car battery when it is fully charged?

37. (II) How many 100-W lightbulbs.connected to 120 V as in Fig. 18-20. can be used without blowing a 15-A fuse?

38. (II) An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m (9 ft) is connected to an electric heater which draws 15.0 A on a 120-V line. How much power is dissipated in the cord?

39. (II) A power station delivers 620 kW of power at 12.000 V to a factory through wires with total resistance 3.011. How much less power is wasted if the electricity is delivered at 50.000 V rather than 12,000 V?

40. (Ill) The current in an electromagnet connected to a 240-V line is 17.5 A. At what rate must cooling water pass over the coils if the water temperature is to rise by no more than 7.50 C?

41. (Ill) A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 mL of water from 25CC to 95C in 8.0 min, (a) approximately how much current does it draw from the car's 12-V battery, and (/?) what is its resistance? Assume the manufacturer's claim of 60% efficiency.

42. (I) Calculate the peak current in a 2.2-kli resistor connected to a 220-V rms ac source.

43. (I) An ac voltage, whose peak value is 180 V, is across a 330-11 resistor. What are the rms and peak currents in the resistor?

44. (II) Estimate the resistance of the 120-Vnm circuits in your house as seen by the power company, when (a) everything electrical is unplugged, and (b) there is a lone 75-W lightbulb burning.

45. (II) The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across it?

46. (II) An 1800-W arc welder is connected to a 660-Vrins ac line. Calculate (a) the peak voltage and (b) the peak current.

47. (II) (a) What is the maximum instantaneous power dissipated by a 3.0-hp pump connected to a 240-Vrms ac power source? (b) What is the maximum current passing through the pump?

48. (II) A heater coil connected to a 240-Vrms ac line has a resistance of 3411. (a) What is the average power used? (b) What are the maximum and minimum values of the instantaneous power?

*49. (II) A 0.65-mm-diameter copper wire carries a tiny current of 2.3 fiA. What is the electron drift speed in the wire?

* 50. (II) A 5.80-m length of 2.0-mm-diameter wire carries a 750-mA current when 22.0 mV is applied to its ends. If the drift speed is 1.7 X lO'^m/s, determine (a) the resistance R of the wire, (b) the resistivity p, and (c) the number n of free electrons per unit volume.

*51. (Ill) At a point high in the Earth's atmosphere. He2+ ions in a concentration of 2.8 X 10,2/m3 are moving due north at a speed of 2.0 x 106m/s. Also, a 7.0 x 10n/m3 concentration of O2 ions is moving due south at a speed of 7.2 X 10Am/s. Determine the magnitude and direction of the net current passing through unit area (A/m2).

* 52. (I) What is the magnitude of the electric field across an axon membrane 1.0 X 10 8m thick if the resting potential is 70 mV?

* 53. (II) A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.40 cm down the axon 0.0052 s later. When the action potential is detected 7.20 cm from the point of stimulation, the time required is 0.0063 s. What is the speed of the electric pulse along the axon? (Why are two measurements needed instead of only one?)

* 54. (Ill) Estimate how much energy is required to transmit one action potential along the axon of Example 18-15. [Hint, the energy to transmit one pulse is equivalent to the energy stored by charging the axon capacitance: see Section 17-9). What minimum average power is required for 104 neurons each transmitting 100 pulses per second?

*55. (Ill) During an action potential. Na+ ions move into the cell at a rate of about 3 X 10-7mol/m2*s. How much power must be produced by the active Na+ pumping'' system to produce this flow against a +30-mV potential difference? Assume that the axon is 10 cm long and 20yxm in diameter.

56. How many coulombs are there in 1.00 ampere-hour?

57. What is the average current drawn by a 1.0-hp 120-V motor? (1 hp = 746 W.)

58. A person accidentally leaves a car with the lights on. If each of the two headlights uses 40 W and each of the two taillights 6W, for a total of 92 W. how long will a fresh 12-V batter}' last if it is rated at 95 Ah? Assume the full 12 V appears across each bulb.

59. 'I*he heating element of a 110-V, 1500-W heater is 5.4 m long. If it is made of iron, what must its diameter be?

60. The conductance G of an object is defined as the reciprocal of the resistance R: that is, G = 1 /R. The unit of conductance is a mho (= ohm-1), which is also called the siemens (S). What is the conductance (in siemens) of an object that draws 730 mA of current at 3.0 V?

61. A small city requires about 10 MW of power. Suppose that instead of using high-voltage lines to supply the power, the power is delivered at 120 V. Assuming a two-wire line of 0.50-cm-diameter copper wire, estimate the cost of the energy lost to heat per hour per meter. Assume the cost of electricity is about 10 cents per kWh.

62. (<?) A particular household uses a 1.8-kW heater 3.0 h/day (onv time), four 100-W lightbulbs 6.0 h/day. a 3.0-kW electric stove element for a total of 1.4 h/day. and miscellaneous power amounting to 2.0kWh/day. If electricity costs $0,105 per kWh, what will be their monthly bill (30 d)? (h) How much coal (which produces 7000kcal/kg) must be burned by a 35%-efficient power plant to provide the yearly needs of this household?

63. A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original wire?

64. A 1200-W hair dryer is designed for 117 V. (a) What will be the percentage change in power output if the voltage drops to 105 V? Assume no change in resistance. (b) How would the actual change in resistivity with temperature affect your answer?

65. The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 35 A and produce no more than 1.8 W of heat per meter of length?

66. Suppose a current is given by the equation / = 1.80 sin 210/. where / is in amperes and / in seconds, (a) What is the frequency? (b) What is the rms value of the current? (c) If this is the current through a 42.0-fl resistor, write the equation that describes the voltage as a function of time.

67. A microwave oven running at 65% efficiency delivers 950 W of energy per second to the interior. Find (a) the power drawn from the source, and (b) the current drawn. Assume a source voltage of 120 V.

68. A 1.00-0 wire is stretched uniformly to 3.00 times its original length. What is its resistance now?

69. 220 V is applied to two different conductors made of the same material. One conductor is twice as long and twice the diameter of the second. What is the ratio of the power transformed in the first relative to the second?

70. An electric heater is used to heat a room of volume 62 m3. Air is brought into the room at 5CC and is completely-replaced twice per hour. Heat loss through the walls amounts to approximately 850 keal/h. If the air is to be maintained at 20C. what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg-C.)

71. A 2200-W oven is hooked to a 240-V source, (a) What is the resistance of the oven? (b) Howr long will it take to bring 120 ml. of 15C water to 100nC assuming 75% efficiency? (c) How much will this cost at 11 cents/kWh?

72. A projected electric vehicle makes use of storage batteries as its source of energy. Its mass is 1560 kg and it is powered by 24 batteries, each 12 V. 95 A h. Assume that the car is driven on level roads at an average speed of 45 km/h. and the average friction force is 240 N. Assume 100% efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesn't need to idle. (a) Determine the horsepower required. (b) After approximately how many kilometers must the batteries be recharged?

73. A 12.5-11 resistor is made from a coil of copper wire whose total mass is 18.0 g. What is the diameter of the wrirc, and how long is it?

74. A 100-W. 120-V lightbulb has a resistance of 12II when cold (20WC) and 14011 when on (hot). Calculate its power consumption at (a) the instant it is turned on. and (b) after a few' moments when it is hot.

* 75. The Tevatron accelerator at Fermilab (Illinois) is designed to carry an Tl-mA beam of protons traveling at very nearly the speed of light (3.0 x 10s m/s) around a ring 6300 m in circumference. How' many protons are stored in the beam?

76. An air conditioner draw's 12 A at 220-V ac. The connecting cord is copper wire with a diameter of 1.628 mm. (a) How much power does the air conditioner draw? (6) If the total length of wire is 15 m. howr much power is dissipated in the wiring? (c) If no. 12 wire, with a diameter of 2.053 mm. wras used instead. howr much pow-er would be dissipated? (d) Assuming that the air conditioner is run 12 h per day. how much money per month (30 days) would be saved by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

77. A fish-tank heater is rated at 95 W when connected to 120 V. The heating element is a coil of Nichrome wrire. When uncoiled, the wire has a total length of 3.8 m. What is the diameter of the wire?

78. In an automobile, the system voltage varies from about 12 V when the car is off to about 13.8 V wrhen the car is on and the charging system is in operation, a difference of 15%. By what percentage does the power delivered to the headlights vary as the voltage changes from 12 V to 13.8 V? Assume the headlight resistance remains constant.

79. Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications, (a) What is the current through each bulb? (b) What is the resistance of each bulb? (c) In one hour, how much charge passes through each bulb? (d) In one hour, how much energy does each bulb use? (e) Which bulb requires larger diameter wires to connect its power source and the bulb?

80. Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 2250 W of pow er total. (a) What powrer is wasted in 25.0 m of this w'ire? (b) What is your answer if wire of diameter 0.412 cm is used?

81. A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (Fig. 18-37). What is the resistance of 10.0 m of this pipe?

82. If a wire of resistance R is stretched uniformly so that its length doubles, by what factor does the powrer dissipated in the wire change, assuming it remains hooked up to the same voltage source?

* 83. A tungsten filament used in a flashlight bulb operates at 0.20 A and 3.2 V. If its resistance at 20C is 1.5 ft, what is the temperature of the filament when the flashlight is on ?