Deck 28: Current and Resistance

Question 1

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)17 C
B)15 C
C)14 C
D)13 C
E)60 C

Answer 1

15 C

Question 2

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)54 W
B)71 W
C)90 W
D)80 W
E)22 W

Answer 2

90 W

Question 3

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)−0.10.
B)+1.9.
C)+2.1.
D)−10.
E)+10.

Answer 3

+2.1.

Question 4

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)58 J
B)46 J
C)32 J
D)72 J
E)16 J

Question 5

If 5.0 × 10²¹ electrons pass through a 20-Ω resistor in 10 min, what is the potential difference across the resistor?

A)21 V
B)32 V
C)27 V
D)37 V
E)54 V

Question 6

A small bulb is rated at 7.50 W when operated at 125 V. The tungsten filament has a temperature coefficient of resistivity α = 4.50 × 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)234
B)1350
C)2080
D)4530
E)5630

Question 7

A small bulb is rated at 7.5 W when operated at 125 V. Its resistance (in ohms) is

A)0.45.
B)7.5.
C)17.
D)940.
E)2 100.

Question 8

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)0.94 Ω
B)0.81 Ω
C)0.58 Ω
D)0.69 Ω
E)1.5 Ω

Question 9

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)1.6
B)1.3
C)0.62
D)0.79
E)0.88

Question 10

What is the resistance of a wire made of a material with a resistivity of 3.2 × 10⁻⁸Ω ⋅ m if its length is 2.5 m and its diameter is 0.50 mm?

A)0.16 Ω
B)0.10 Ω
C)1.28 Ω
D)0.41 Ω
E)0.81 Ω

Question 11

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) R
B) R
C)R
D)4R
E)16R

Question 12

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)3.0 W
B)5.3 W
C)8.3 W
D)1.3 W
E)17 W

Question 13

A wire (length = 2.0 m, diameter = 1.0 mm) has a resistance of 0.45 Ω. What is the resistivity of the material used to make the wire?

A)5.6 × 10⁻⁷ Ω ⋅ m
B)1.2 × 10⁻⁷ Ω ⋅ m
C)1.8 × 10⁻⁷ ⋅ m
D)2.3 × 10⁻⁷ ⋅ m
E)7.1 × 10⁻⁷ ⋅ m

Question 14

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)6.0 × 10⁻⁷ Ω ⋅ m
B)3.8 × 10⁻⁷ Ω ⋅ m
C)7.5 × 10⁻⁷ Ω ⋅ m
D)3.0 × 10⁻⁷ Ω ⋅ m
E)4.8 × 10⁻⁷ Ω ⋅ m

Question 15

How many electrons pass through a 20-Ω resistor in 10 min if there is a potential drop of 30 volts across it?

A)5.6 × 10²¹
B)7.5 × 10²¹
C)9.4 × 10²¹
D)1.1 × 10²¹
E)3.8 × 10²¹

Question 16

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)2.0 kW
B)2.4 kW
C)1.7 kW
D)1.5 kW
E)60 kW

Question 17

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)0.40 mm
B)0.50 mm
C)0.63 mm
D)0.80 mm
E)0.25 mm

Question 18

The electron density in copper is 8.49 × 1028 electrons/m³. 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)−1.84 × 10⁻⁶.
B)+1.84 × 10⁻⁶.
C)−1.84.
D)−5.43 × 10⁵.
E)+5.43 × 10⁵.

Question 19

A nichrome wire and an aluminum wire, each with the same initial resistance, have the same change in resistance when heated separately. (ρAl = 2.82 × 10⁻⁸ Ω ⋅ m; αAl = 3.9 × 10⁻³ / °C; ρnichrome = 1.50 × 10−6 Ω ⋅ m; αnichrome = 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)0.019.
B)0.10.
C)0.18.
D)9.8.
E)53.

Question 20

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)7.5 × 10²¹
B)5.6 × 10²¹
C)6.6 × 10²¹
D)8.4 × 10²¹
E)2.1 × 10²¹

Question 21

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) R.
B) R.
C)R.
D)4R.
E)16R.

Question 22

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)Arnell, because the conductivity of the wire increases when it is heated.
B)Arnell, because the conductivity of the wire decreases when it is heated.
C)Jadeen, because the conductivity of a wire is directly proportional to its area and inversely proportional to its length.
D)Jadeen, because the conductivity of a copper wire does not increase when it is hammered.
E)Both are correct because (b) and (d) are both correct.

Question 23

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?

Question 24

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)Arnell, because the resistivity of the wire increases when it is heated.
B)Arnell, because the resistivity of the wire decreases when it is heated.
C)Jadeen, because the resistivity of a wire is inversely proportional to its area and directly proportional to its length.
D)Jadeen, because the resistivity of a copper wire does not decrease when it is hammered.
E)Both are correct because (a) and (d) are both correct.

Question 25

A cook plugs a 500-W crock-pot 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)Icrock-pot < Ikettle and Rcrock-pot < Rkettle.
B)Icrock-pot < Ikettle and Rcrock-pot > Rkettle.
C)Icrock-pot = Ikettle and Rcrock-pot = Rkettle.
D)Icrock-pot > Ikettle and Rcrock-pot < Rkettle.
E)Icrock-pot > Ikettle and Rcrock-pot > Rkettle.

Question 26

An aluminum wire of cross-sectional area 4.0 mm² is carrying a current of 8.0 A. The density of aluminum is 2.7 g/cm³, and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire?

Question 27

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 4 186 J/kg°C)

Question 28

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)The 60-W bulb has a greater resistance and greater current than the 100-W bulb.
B)The 60-W bulb has a greater resistance and smaller current than the 100-W bulb.
C)The 60-W bulb has a smaller resistance and smaller current than the 100-W bulb.
D)The 60-W bulb has a smaller resistance and greater current than the 100-W bulb.
E)We need to know the resistivities of the filaments to answer this question.

Question 29

What is the resistance of 1000 m of 4-mm diameter copper wire?
(ρCu = 1.7 × 10⁻⁸ Ω ⋅ m)

Question 30

A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10⁻⁸ Ω ⋅ m.)

Question 31

To increase the current density in a wire of length and diameter D, you can

A)decrease the potential difference between the two ends of the wire.
B)increase the potential difference between the two ends of the wire.
C)decrease the magnitude of the electric field in the wire.
D)heat the wire to a higher temperature.
E)combine both (b) and (d).

Question 32

A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors?

A)R
B)2R
C)4R
D)(ln 2)R
E)R/(ln 2)