Chapter 27 Current and Resistance Multiple Choice 1.
A rod of 2.0-m length and a square (2.0 mm × 2.0 mm) cross section is made of a material with a resistivity of 6.0 × 10–8 Ω ⋅ m. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod? a. b. c. d. e.
2.
An electric device, which heats water by immersing a resistance wire in the water, generates 50 cal of heat per second when an electric potential difference of 12 V is placed across its leads. What is the resistance of the heater wire? (Note: 1 cal = 4.186 J) a. b. c. d. e.
3.
0.94 Ω 0.81 Ω 0.58 Ω 0.69 Ω 1.5 Ω
A light bulb is rated at 30 W when operated at 120 V. How much charge enters (and leaves) the light bulb in 1.0 min? a. b. c. d. e.
4.
3.0 W 5.3 W 8.3 W 1.3 W 17 W
17 C 15 C 14 C 13 C 60 C
What maximum power can be generated from an 18-V emf using any combination of a 6.0-Ω resistor and a 9.0-Ω resistor? a. b. c. d. e.
54 W 71 W 90 W 80 W 22 W
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An electric heater is constructed by applying a potential difference of 110 V across a wire with a resistance of 5.0 Ω. What is the power rating of the heater? a. b. c. d. e.
6.
How much energy is dissipated as heat during a two-minute time interval by a 1.5-kΩ resistor which has a constant 20-V potential difference across its leads? a. b. c. d. e.
7.
21 V 32 V 27 V 37 V 54 V
How many electrons pass through a 20-Ω resistor in 10 min if there is a potential drop of 30 volts across it? a. b. c. d. e.
10.
7.5 × 1021 5.6 × 1021 6.6 × 1021 8.4 × 1021 2.1 × 1021
If 5.0 × 1021 electrons pass through a 20-Ω resistor in 10 min, what is the potential difference across the resistor? a. b. c. d. e.
9.
58 J 46 J 32 J 72 J 16 J
A 4.0-Ω resistor has a current of 3.0 A in it for 5.0 min. How many electrons pass through the resistor during this time interval? a. b. c. d. e.
8.
2.0 kW 2.4 kW 1.7 kW 1.5 kW 60 kW
5.6 × 1021 7.5 × 1021 9.4 × 1021 1.1 × 1021 3.8 × 1021
A wire (length = 2.0 m, diameter = 1.0 mm) has a resistance of 0.45Ω. What is the resistivity of the material used to make the wire? a. b. c. d. e.
5.6 × 10–7 Ω ⋅ m 1.2 × 10–7 Ω ⋅ m 1.8 × 10–7 Ω ⋅ m 2.3 × 10–7 Ω ⋅ m 7.1 × 10–7 Ω ⋅ m
Current and Resistance
11.
What is the resistance of a wire made of a material with a resistivity of 3.2 × 10 −8 Ω ⋅ m if its length is 2.5 m and its diameter is 0.50 mm? a. b. c. d. e.
12.
1.6 1.3 0.62 0.79 0.88
If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7 × 10–8 Ω ⋅ m, what is the diameter of the wire? (1 mile = 1.6 km) a. b. c. d. e.
15.
6.0 × 10–7 Ω ⋅ m 3.8 × 10–7 Ω ⋅ m 7.5 × 10–7 Ω ⋅ m 3.0 × 10–7 Ω ⋅ m 4.8 × 10–7 Ω ⋅ m
Most telephone cables are made of copper wire of either 24 or 26 gauge. If the resistance of 24-gauge wire is 137 Ω/mile and the resistance of 26-gauge wire is 220 Ω/mile, what is the ratio of the diameter of 24-gauge wire to that of 26-gauge wire? a. b. c. d. e.
14.
0.16 Ω 0.10 Ω 1.28 Ω 0.41 Ω 0.81 Ω
A rod (length = 80 cm) with a rectangular cross section (1.5 mm × 2.0 mm) has a resistance of 0.20 Ω. What is the resistivity of the material used to make the rod? a. b. c. d. e.
13.
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0.40 mm 0.50 mm 0.63 mm 0.80 mm 0.25 mm
A conductor of radius r, length and resistivity ρ has resistance R. What is the new resistance if it is stretched to 4 times its original length? a. b. c. d. e.
1 R 16 1 R 4 R 4R 16R
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A small bulb is rated at 7.5 W when operated at 125 V. Its resistance (in ohms) is a. b. c. d. e.
17.
A small bulb is rated at 7.5 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 4.5 × 10 −3 / °C . When the filament is hot and glowing, its temperature is seven times room temperature (20 °C). What is the resistance of the filament (in ohms) at room temperature? a. b. c. d. e.
18.
1280. 1350. 1911. 4530. 5630.
The temperature coefficient of resistivity of iron is 5.0 × 10 −3 / °C ; that of carbon is − 0.50 × 10 −3 /°C . When an iron wire and a carbon rod, each having the same 10 Ω resistance at 20 °C , are cooled from that temperature to −80 °C , the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is a. b. c. d. e.
19.
0.45. 7.5. 17. 940. 2100.
-0.10. +1.9. +2.1. -10. +10.
A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. ( ρ Al = 2.82 × 10 −8 Ω ⋅ m ; α Al = 3.9 × 10 −3 /°C ; ρ nichrome = 1.50 × 10 −6 Ω ⋅ m ;
α nichrome = 0.40 × 10 −3 /°C .) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is a. b. c. d. e.
0.019. 0.10. 0.18. 9.8. 53.
Current and Resistance
20.
The electron density in copper is 8.49 × 10 28 electrons/m 3 . The electron charge is e = −1.60 × 10 −19 C . When a 1.00 A current is present in a copper wire with a 0.40 cm2 cross-section, the electron drift velocity, in m/s, with direction defined relative to the current density, is a. b. c. d. e.
21.
the average time interval between successive collisions. the number of charge carriers per unit volume. the square of the electron charge. the electric field present in the wire. the resistivity of the wire.
A conductor of radius r, length and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is a. b. c. d. e.
24.
the average time interval between successive collisions. the number of charge carriers per unit volume. the square of the electron charge. the electric field present in the wire. the product of all four quantities listed above.
In the Drude model of electrical conduction, the current density is NOT directly proportional to a. b. c. d. e.
23.
− 1.84 × 10 −6 . + 1.84 × 10 −6 . −1.84 . − 5.43 × 10 5 . + 5.43 × 10 5 .
In the Drude model of electrical conduction, the current density is directly proportional to a. b. c. d. e.
22.
99
1 R 16 1 R 4 R 4R 16R
Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct? a. b. c. d. e.
The 60 W bulb has a greater resistance and greater current than the 100 W bulb. The 60 W bulb has a greater resistance and smaller current than the 100 W bulb. The 60 W bulb has a smaller resistance and smaller current than the 100 W bulb. The 60 W bulb has a smaller resistance and greater current than the 100 W bulb. We need to know the resistivities of the filaments to answer this question.
100
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CHAPTER 27
Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why? a. b. c. d. e.
26.
Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why? a. b. c. d. e.
27.
Arnell, because the resistivity of the wire increases when it is heated. Arnell, because the resistivity of the wire decreases when it is heated. Jadeen, because the resistivity of a wire is inversely proportional to its area and directly proportional to its length. Jadeen, because the resistivity of a copper wire does not decrease and might increase when it is hammered.. Both are correct because (a) and (d) are both correct.
A cook plugs a 500 W crockpot and a 1000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that a. b. c. d. e.
28.
Arnell, because the conductivity of the wire increases when it is heated. Arnell, because the conductivity of the wire decreases when it is heated. Jadeen, because the conductivity of a wire is directly proportional to its area and inversely proportional to its length. Jadeen, because the conductivity of a copper wire does not increase and might decrease when it is hammered. Both are correct because (b) and (d) are both correct.
I crockpot I crockpot I crockpot I crockpot I crockpot
< I kettle < I kettle = I kettle > I kettle > I kettle
and Rcrockpot < Rkettle . and Rcrockpot > Rkettle . and Rcrockpot = Rkettle . and Rcrockpot < Rkettle . and Rcrockpot > Rkettle .
To increase the current density in a wire of length a. b. c. d. e.
and diameter D, you can
decrease the potential difference between the two ends of the wire. increase the potential difference between the two ends of the wire. decrease the magnitude of the electric field in the wire. heat the wire to a higher temperature. combine both (b) and (d).
Current and Resistance
101
Open-Ended Problems 29.
What is the resistance of 1000 m of 4-mm diameter copper wire? ( ρ Cu = 1.7 × 10 8 Ω ⋅ m )
30.
A high-voltage transmission line carries 1000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?
31.
The heating coil of a hot water heater has a resistance of 20 ohms and operates at 210 V. If electrical energy costs 5.5 cents per kW-hr, what does it cost to raise the 200 kg of water in the tank from 15°C to 80°C? (The specific heat of water is 4186 J/kg°C)
32.
A copper cable is to be designed to carry a current of 300 A with a power loss of only 2 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10–8 Ω ⋅ m.)
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CHAPTER 27
Current and Resistance
Chapter 27 Current and Resistance 1.
c
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b
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d
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b
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1.35 ohm
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b
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50 MW
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83 cents
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e
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1.6 cm
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