Question 1

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?

Accepted Answer

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. 
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. B

Question 2

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 B

Question 3

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?

Accepted Answer

50 MW

Question 4

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 5

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

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?

Accepted Answer

A) 234 
B) 1350 
C) 2080 
D) 4530 
E) 5630 
A) 234 
B) 1350 
C) 2080 
D) 4530 
E) 5630

Question 7

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 8

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?

Accepted Answer

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

Question 9

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.)

Accepted Answer

Question 10

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

Accepted Answer

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

Question 11

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?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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)

Accepted Answer

The answer of The heating coil of a hot water...

Question 14

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 15

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

Accepted Answer

Question 16

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

Accepted Answer

A) −0.10. 
B) +1.9. 
C) +2.1. 
D) −10. 
E) +10. 
A) −0.10. 
B) +1.9. 
C) +2.1. 
D) −10. 
E) +10.

Question 17

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 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

Accepted Answer

A) −1.84 × 10−6. 
B) +1.84 × 10−6. 
C) −1.84. 
D) −5.43 × 105. 
E) +5.43 × 105. 
A) −1.84 × 10−6. 
B) +1.84 × 10−6. 
C) −1.84. 
D) −5.43 × 105. 
E) +5.43 × 105.

Question 19

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?

Accepted Answer

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

Question 20

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

Exam 28: Current and Resistance

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?

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 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?

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 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 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.)

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

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 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

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)

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?

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

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)

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

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?

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

Getting Started

One-Dimensional Motion

Vectors

Two- and Three-Dimensional Motion

Newtons Laws of Motion

Applications of Newtons Laws of Motion

Gravity

Conservation of Energy

Energy in Nonisolated Systems

Systems of Particles and Conservation of Momentum

Collisions

Rotation I: Kinematics and Dynamics

Rotation II: a Conservation Approach

Static Equilibrium, Elasticity, and Fracture

Fluids

Oscillations

Traveling Waves

Superposition and Standing Waves

Temperature, Thermal Expansion, and Gas Laws

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Electric Forces

Electric Fields

Gausss Law

Electric Potential

Capacitors and Batteries

Direct Current Dc Circuits

Magnetic Fields and Forces

Gausss Law for Magnetism and Amperes Law

Faradays Law of Induction

Inductors and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Diffraction and Interference

Applications of the Wave Model

Reflection and Images Formed by Reflection

Refraction and Images Formed by Refraction

Relativity

Filters

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.)

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

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

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

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?