Electric Current and Ohm’s Law
27-1. How many electrons pass a point every second in a wire carrying a current of 20 A? How much time is needed to transport 40 C of charge past this point?
Q = It = (20 C/s)(1 s); [pic]; Q = 1.25 x 1020 electrons/s
[pic]; t = 2.00 s
27-2. If 600 C of charge pass a given point in 3 s, what is the electriccurrent in amperes?
[pic] I = 20 A
27-3. Find the current in amperes when 690 C of charge pass a given point in 2 min.
[pic] I = 5.75 A
27-4. If a current of 24 A exists for 50 s, how many coulombs of charge have passed through the wire?
Q = It = (24 A)(50 s); Q = 1200 C
27-5. What is the potential drop across a 4-Ω resistor with a current of 8 A passing through it?
V = IR =(8 A)(4 Ω); V = 32.0 V
27-6. Find the resistance of a rheostat if the drop in potential is 48 V and the current is 4 A.
[pic] R = 12.0 Ω
27-7. Determine the current through a 5-Ω resistor that has a 40-V drop in potential across it?
[pic] I = 8.00 A
27-8. A 2-A fuse is placed in a circuit with a battery having a terminal voltage of 12 V. What is the minimum resistancefor a circuit containing this fuse?
[pic] R = 6.00 Ω
7-9. What emf is required to pass 60 mA through a resistance of 20 kΩ? If this same emf is applied to a resistance of 300 Ω, what will be the new current?
E = IR = 60 x 10-3 A)(20 x 103 Ω); E = 1200 V
[pic]; I = 4.00 A
Electric Power and Heat Loss
27-10. A soldering iron draws 0.75 A at 120 V. How much energy willit use in 15 min?
P = IV = (0.75 A)(120 V); P = 90.0 W; t = 15 min = 900 s
[pic]; E = 81,000 J
27-11. An electric lamp has an 80-Ω filament connected to a 110-V direct-current line. What is the current through the filament? What is the power loss in watts?
[pic] I = 1.38 A
[pic] P = 151 W
27-12. Assume that the cost of energy in a home is 8 cents per kilowatt-hour. Afamily goes on a 2-week vacation leaving a single 80-W light bulb burning. What is the cost?
E = Pt = (80 W)(2 wk)(7 day/wk)(24 h/day)(3600 s/h) = 26.9 kW h
E = (26.9 kW h)(0.08 c/kw h) = $2.15 (Rates vary)
27-13. A 120-V, direct-current generator delivers 2.4 kW to an electric furnace. What current is supplied? What is the resistance?
[pic] I = 20 A; [pic] R = 6.00 Ω27-14. A resistor develops heat at the rate of 250 W when the potential difference across its ends is 120 V. What is its resistance?
[pic] R = 57.6 Ω
27-15. A 120-V motor draws a current of 4.0 A. How many joules of electrical energy is used in one hour? How many kilowatt-hours?
P = VI = (120 V)(4.0 A) = 480 W
[pic] E = 1.73 MJ
[pic] E = 0.480 kW h
27-16. A household hairdryer is rated at 2000 W and is designed to operate on a 120-V outlet. What is the resistance of the device?
[pic] R = 7.20 Ω
27-17. What length of copper wire 1/16 in. in diameter is required to construct a 20-Ω resistor at 200C? What length of nichrome wire is needed?
Copper: ( = 1.78 x 10-8 Ω m ; nichrome: ( = 100 x 10-8 Ω m
[pic] l = 7510 ft
[pic]l = 130 ft
27-18. A 3.0-m length of copper wire (( = 1.78 x 10-8 Ω m) at 200C has a cross section of 4 mm2.What is the electrical resistance of this wire? [ A = 4 mm2 = 4 x 10-6 m2 ]
[pic]; R =12.9 mΩ
27-19. Find the resistance of 40 m of tungsten (( = 5.5 x 10-8 Ω m) wire having a diameter of 0.8 mm at 200C?
[pic]; A = 5.03 x 10-7 m2
[pic]; R = 4.37 Ω27-20. A certain wire has a diameter of 3 mm and a length of 150 m. It has a resistance of 3.00 Ω at 200C. What is the resistivity? [ A = (D2/4 = 7.07 x 10-7 m2. ]
[pic]; ρ = 1.41 x 10-8 Ω m
27-21. What is the resistance of 200 ft of iron (( = 9.5 x 10-8 Ω m) wire with a diameter of 0.002 in. at 200C? (( = 9.5 x 10-8 Ω m). [ 200 ft = 61.0 m; 0.002 in. = 5.08 x 10-5 m ]...