Question 1

In the Drude model of electrical conduction, the current density is NOT directly proportional to

Accepted Answer

A)  the average time interval between successive collisions. 
B)  the number of charge carriers per unit volume. 
C)  the square of the electron charge. 
D)  the electric field present in the wire. 
E)  the resistivity of the wire. 
A)  the average time interval between successive collisions. 
B)  the number of charge carriers per unit volume. 
C)  the square of the electron charge. 
D)  the electric field present in the wire. 
E)  the resistivity of the wire.

Question 2

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?

Accepted Answer

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 
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 3

A high-voltage transmission line carries 1 000 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?

Accepted Answer

The answer of A high-voltage transmission line carries 1 000...

Question 4

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?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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)

Accepted Answer

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

Question 7

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?

Accepted Answer

A)  R 
B)  2 R 
C)  4 R 
D)  (ln2)R 
E)  R/(ln2) 
A)  R 
B)  2 R 
C)  4 R 
D)  (ln2)R 
E)  R/(ln2)

Question 8

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

Accepted Answer

A)  0.019. 
B)  0.10. 
C)  0.18. 
D)  9.8. 
E)  53. 
A)  0.019. 
B)  0.10. 
C)  0.18. 
D)  9.8. 
E)  53.

Question 9

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?

Accepted Answer

Question 10

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?

Accepted Answer

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

Question 11

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)

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

In the Drude model of electrical conduction, the current density is directly proportional to

Accepted Answer

A)  the average time interval between successive collisions. 
B)  the number of charge carriers per unit volume. 
C)  the square of the electron charge. 
D)  the electric field present in the wire. 
E)  the product of all four quantities listed above. 
A)  the average time interval between successive collisions. 
B)  the number of charge carriers per unit volume. 
C)  the square of the electron charge. 
D)  the electric field present in the wire. 
E)  the product of all four quantities listed above.

Question 14

A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that

Accepted Answer

A)  Icrockpot kettle and Rcrockpot kettle. 
B)  Icrockpot kettle and Rcrockpot > Rkettle. 
C)  Icrockpot = Ikettle and Rcrockpot = Rkettle. 
D)  Icrockpot > Ikettle and Rcrockpot kettle. 
E)  Icrockpot > Ikettle and Rcrockpot > Rkettle. 
A)  Icrockpot kettle and Rcrockpot kettle. 
B)  Icrockpot kettle and Rcrockpot > Rkettle. 
C)  Icrockpot = Ikettle and Rcrockpot = Rkettle. 
D)  Icrockpot > Ikettle and Rcrockpot kettle. 
E)  Icrockpot > Ikettle and Rcrockpot > Rkettle.

Exam 27: Current and Resistance

In the Drude model of electrical conduction, the current density is NOT directly proportional to

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 high-voltage transmission line carries 1 000 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?

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?

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

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)

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?

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?

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)

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?

In the Drude model of electrical conduction, the current density is directly proportional to

A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that

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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?

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)