Deck 27: Current and Resistance

Question 1

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

Answer 1

5.6 × 10²¹

Question 2

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

Answer 2

16R

Question 3

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

Answer 3

0.50 mm

Question 4

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 5

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

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

Question 7

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

Question 8

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 9

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 10

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

Question 11

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 12

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)1 350
C)2 080
D)4 530
E)5 630

Question 13

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.

Question 14

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 15

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 16

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)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 17

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 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 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 20

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

Question 21

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

Question 22

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

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 23

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 24

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

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 25

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 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)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 27

What is the resistance of 1 000 m of 4-mm diameter copper wire?
(ρ_Cu = 1.7 × 10^-8 Ω ⋅ m)

Question 28

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 29

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 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

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

A)I_crockpot < I_kettle and R_crockpot < R_kettle.
B)I_crockpot < I_kettle and R_crockpot > R_kettle.
C)I_crockpot = I_kettle and R_crockpot = R_kettle.
D)I_crockpot > I_kettle and R_crockpot < R_kettle.
E)I_crockpot > I_kettle and R_crockpot > R_kettle.

Question 32

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 33

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?

Question 34

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?