Deck 17: Current and Resistance Electric Current

Question 1

The unit of electric current,the ampere,is equivalent to which of the following?

A) V⋅Ω
B) V/Ω
C) Ω⋅m
D) V/s

Answer 1

V/Ω

Question 2

A high voltage transmission line of diameter 1 cm and length 150 km carries a steady current of 1,000 A.If the conductor is copper with a free charge density of 8 × 10²⁸ electrons/m³,how long does it take one electron to travel the full length of the cable? (e = 1.6 × 10−¹⁹ C)
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A) 1.5 × 10² s
B) 1.5 × 10⁴ s
C) 1.5 × 10⁶ s
D) 1.5 × 10⁸ s
E) 1.5 × 10^-10 s

Answer 2

1.5 × 10⁸ s

Question 3

A metallic conductor has a resistivity of 11 × 10−⁶ Ω⋅m.What is the resistance of a piece that is 27 m long and has a uniform cross sectional area of 5 × 10−⁶ m²?

A) 0.1 Ω
B) 59.4 Ω
C) 12.3 Ω
D) 2 Ω
E) ​1,485 Ω

Answer 3

59.4 Ω

Question 4

A flashlight bulb operating at a voltage of 3 V has a resistance of 10 Ω.How many electrons pass through the bulb filament per second (e = 1.6 × 10−¹⁹ C)?

A) 0.5 × 10¹⁶
B) 4.8 × 10²¹
C) 5.3 × 10¹⁷
D) 1.9 × 10¹⁸
E) ​2.1 × 10²⁰

Question 5

A wire carries a steady current of 0.1 A over a period of 15 s.What total charge passes through the wire in this time interval?
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A) 150 C
B) 15 C
C) 1.5 C
D) 0.007 C
E) ​0.1 C

Question 6

The number density of conduction electrons in a metal can be found from the density ρ of the metal,the mass per mole M of the metal,the number of conduction electrons per metal atom,and Avogadro's number N_A.If we assume one conduction electron per atom,which of the following gives the number density of conduction electrons for a given metal?

A) N_A ρ M
B) N_A ρ /M
C) N_A M/ρ
D) N_A /ρ M

Question 7

You measure a 28-V potential difference across a 7-Ω resistor.What is the current flowing through it?

A) 196 A
B) 4 A
C) 35 A
D) 21 A
E) ​5.6 A

Question 8

The unit of electric resistance,the ohm,is equivalent to which of the following?

A) V/A
B) V⋅m
C) A/s
D) A/m

Question 9

The size of the electric current in a electrical conductor is a function of which of the following?

A) velocity of charge carriers
B) conductor cross sectional area
C) density of charge carriers
D) All of the above choices are valid.

Question 10

If the current in a wire is tripled,what effect does this have on the electron drift velocity in the wire?

A) It stays the same.
B) It triples.
C) It decreases by a factor of three.
D) It increases by a factor of nine.

Question 11

If a certain resistor obeys Ohm's law,its resistance will change:

A) as the voltage across the resistor changes.
B) as the current through the resistor changes.
C) as the energy given off by the electrons in their collisions changes.
D) none of the above,since resistance is a constant for the given resistor.

Question 12

When you flip a switch to turn on a light,the delay before the light turns on is determined by:

A) the number of electron collisions per second in the wire.
B) the drift speed of the electrons in the wire.
C) the speed of the electric field moving in the wire.
D) none of these,since the light comes on instantly.

Question 13

In a certain material there is a current of 12 A flowing through a surface to the right,and there is an equal amount of positive and negative charge passing through the surface producing the current.How much negative charge passes through the surface?
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A) 6 C/s toward the right
B) 6 C/s toward the left
C) 12 C/s toward the right
D) 12 C/s toward the left
E) 24 C/s toward the left

Question 14

If a metallic wire of cross sectional area 3.0 × 10−⁶ m² carries a current of 8.0 A and has a mobile charge density of 4.24 × 10²⁸ carriers/m³,what is the average drift velocity of the mobile charge carriers? (charge value = 1.6 × 10−¹⁹ C)

A) 3.1 × 10³ m/s
B) 1.9 × 10³ m/s
C) 6.3 × 10−⁴ m/s
D) 3.9 × 10−⁴ m/s
E) 8 × 10−6 m/s

Question 15

Materials having resistance changes as voltage or current varies are called:

A) ohmic.
B) inohmic.
C) nonohmic.
D) deohmic.

Question 16

The charge flowing through a light bulb attached to a 12-V battery in 14.0 s is 30.0 C.What is the average power supplied by the battery during this process?
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A) 360 W
B) 12 W
C) 25.7 W
D) 5.6 W
E) 30 W

Question 17

The charge flowing through a light bulb attached to a 11.0-V battery in 14.0 s is 25.0 C.What is the total energy delivered to the filament during this process?

A) 11 J
B) 275 J
C) 3,850 J
D) 154 J
E) ​625 J

Question 18

Wire A and Wire B are each carrying the same current.If the diameter of Wire A is twice that of Wire B,how does the drift velocity v_dA in Wire A compare to that in in Wire B?

A) v_dA = v_dB
B) v_dA = 2 v_dB
C) v_dA = v_dB /2
D) v_dA = v_dB /4

Question 19

The current in an electron beam in a cathode-ray tube is measured to be 50 µA.How many electrons hit the screen in 4.0 s? (e = 1.6 × 10−¹⁹ C)

A) 2.5 × 10¹¹ electrons
B) 2 × 10¹³ electrons
C) 1.2 × 10¹⁵ electrons
D) 3.1× 10¹⁸ electrons
E) 1.6 × 10¹⁷ electrons

Question 20

When an electric current exists within a conducting wire,which of the following statements describes the condition of any accompanying electric field?

A) must be zero
B) must be parallel to current flow
C) must be anti-parallel (opposite direction)to current flow
D) must be perpendicular to current flow

Question 21

A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−³ (°C)−¹ will have what resistance at 95°C?

A) 17 Ω
B) 19 Ω
C) 31 Ω
D) 24 Ω
E) ​7 Ω

Question 22

The temperature coefficient of resistivity is a quantity that is:

A) always positive.
B) always non-negative.
C) sometimes negative.
D) represented by the symbol σ.

Question 23

A resistor is made of a material that has a resistivity that is proportional to the current going through it.If the voltage across the resistor is doubled,what happens to the current through it?

A) It doubles.
B) It quadruples.
C) It increases by a factor of 2^3/2.
D) It increases by a factor of 2^1/2.

Question 24

A Nichrome wire has a radius of 0.9 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.What is the resistance per unit length of this wire?

A) 0.5 Ω/m
B) 3.8 Ω/m
C) 5.8 Ω/m
D) 0.6 Ω/m
E) ​1.9 Ω/m

Question 25

Two cylindrical resistors are made of the same material and have the same resistance.The resistors,R₁ and R₂,have different radii,r₁ and r₂,and different lengths,L₁ and L₂.Which of the following relative values for radii and lengths would result in equal resistances?

A) r₁ = r₂ and L₁ = 2L₂
B) 2r₁ = r₂ and L₁ = 2L₂
C) r₁ = r₂ and 4L₁ = L₂
D) 2r₁ = r₂ and 4L₁ = L₂

Question 26

The resistivity of a material is doubled when heated a certain amount.What happens to the resistance of a resistor made of this material when heated the same amount?

A) It doubles.
B) It quadruples.
C) It halves.
D) It stays the same.

Question 27

How long is a wire made from 50 cm³ of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m.

A) 4.9 m
B) 1.7 × 10² m
C) 1.6 × 10² m
D) 1.5 × 10³ m
E) ​23.5 m

Question 28

Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor?

A) 1/3
B) 1/9
C) 3
D) 9

Question 29

A copper cable needs to carry a current of 250 A with a power loss of only 3 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m).

A) 0.45 cm
B) 1.06 cm
C) 3.19 cm
D) 3.33 cm
E) ​0.17 cm

Question 30

The resistance of a platinum wire is to be calibrated for low-temperature work.A platinum wire with resistance 3 Ω at 27°C is immersed in liquid nitrogen at 75 K (−198°C).If the temperature response of the platinum wire is linear,what is the expected resistance of the platinum wire at −198°C? [α_platinum = 3.92 × 10−³ (°C)−¹].

A) 0.354 Ω
B) 5.011 Ω
C) 5.646 Ω
D) 25.424 Ω
E) ​0.989 Ω

Question 31

Carbon has a negative temperature coefficient of resistance of -0.5 × 10^-3 (°C)−¹.What temperature increase would result in a resistance decrease of 4% for a carbon resistor?

A) 8°C
B) 80°C
C) 19°C
D) 13°C
E) ​400°C

Question 32

Two wires with the same resistance have the same diameter but different lengths.If wire 1 has length L₁ and wire 2 has length L₂,how do L₁ and L₂ compare if wire 1 is made from copper and wire 2 is made from aluminum? The resistivity of copper is 1.7 × 10^-5 Ω·m and the resistivity of aluminum is 2.82 × 10^-5 Ω·m.

A) L₁ = 1.7 L₂
B) L₁ = 0.60 L₂
C) L₁ = 2.8 L₂
D) L₁ = 0.36 L₂

Question 33

Number 10 copper wire (radius = 1.7 mm)is commonly used for electrical installations in homes.What is the voltage drop in 41 m of #10 copper wire if it carries a current of 9 A? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m. )

A) 0.7 V
B) 0.8 V
C) 3.7 V
D) 0.5 V
E) ​0.4 V

Question 34

A 0.2-m-long metal rod has a radius of 3 cm and a resistance of 3 × 10−⁵ Ω.What is the resistivity of the metal?

A) 1.4 × 10−⁸ Ω⋅m
B) 42.4 × 10−⁸ Ω⋅m
C) 1.3 × 10−⁸ Ω⋅m
D) 2.1 × 10−⁸ Ω⋅m
E) ​14.1 × 10−⁸ Ω⋅m

Question 35

A metal wire has a resistance of 15.50 Ω at a temperature of 25.0°C.If the same wire has a resistance of 15.9 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

A) 2.26 Ω
B) 15.1 Ω
C) 5.68 Ω
D) 43.8 Ω
E) 14.2 Ω

Question 36

By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C)−¹.

A) 1.43
B) 1.14
C) 1.29
D) 0.71
E) ​3.93

Question 37

A Nichrome wire has a radius of 0.3 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.If the wire carries a current of 0.7 A,what is the potential difference per unit length along this wire?

A) 0.3 V/m
B) 3.7 V/m
C) 1.1 V/m
D) 0.1 V/m
E) ​36.6 V/m

Question 38

A certain material is in a room at 27°C.If the absolute temperature (K)of the material is doubled,its resistance triples.(Water freezes at 273 K. )What is the value for α,the temperature coefficient of resistivity?

A) 0.074 (°C)−¹
B) 0.01 (°C)−¹
C) 0.0067 (°C)−¹
D) 1.5 (°C)−¹
E) ​0.037 (°C)−¹

Question 39

A metal wire has a resistance of 26 Ω under room temperature conditions of 19°C.When the wire is heated to 79°C the resistance increases by 0.9 Ω.What is the temperature coefficient of resistivity of this metal?

A) 5.8 × 10−⁴ (°C)−¹
B) 4.2 × 10−³ (°C)−¹
C) 18.2 × 10−³ (°C)−¹
D) 4.6 × 10−³ (°C)−¹
E) ​2.1 × 10−⁴ (°C)−¹

Question 40

A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20°C and increases to 4.850 Ω as the indium starts to melt.α_tungsten = 4.50 × 10−³ (°C)−¹.What is the melting temperature of indium?

A) 132°C
B) 157°C
C) 351°C
D) 731°C

Question 41

Ten coulombs of charge start from the negative terminal of a battery,flow through the battery and then leave the positive terminal through a wire,flow through a resistor and then return to the starting point on this closed circuit.In this complete process,the ten coulombs:

A) do positive work on the battery.
B) receive heat energy from the resistor.
C) have a net loss of potential energy.
D) have no net change in potential energy.

Question 42

The unit for rate of energy transformation,the watt,in an electric circuit is equivalent to which of the following?

A) V/s
B) A⋅Ω
C) V⋅A
D) V/Ω

Question 43

An electric toaster requires 900 W at 100 V.What is the resistance of the heating coil?

A) 3 Ω
B) 55 Ω
C) 28 Ω
D) 11 Ω
E) ​32 Ω

Question 44

Which process will double the power given off by a resistor?

A) doubling the current while doubling the resistance
B) doubling the current by making a resistance half as big
C) doubling the current by doubling the voltage
D) doubling the current while making the voltage half as big

Question 45

A light bulb has resistance of 210 Ω when operating at 105 V.Find the current in the light bulb.

A) 2 A
B) 0.25 A
C) 0.5 A
D) 0.7 A
E) ​1.4 A

Question 46

A light bulb,sold as long-lasting,is rated 95 W at 145 V.The "increased" lifetime comes from using it at 105 V.Assuming negligible change in resistance at the different voltage,what is its power consumption at 105 V?

A) 50 W
B) 181 W
C) 177 W
D) 45 W
E) ​119 W

Question 47

If a lamp has a resistance of 105 Ω when it operates at 100 W,what current does it carry?

A) 1.02 A
B) 0.95 A
C) 0.98 A
D) 1.05 A
E) ​1.95 A

Question 48

A 400-W heater carries a current of 4.0 A.How much does it cost to operate the heater for 50 min if electrical energy costs 6 cents per kWh?

A) 2 cents
B) 12 cents
C) 2.9 cents
D) 0.1 cents
E) ​40 cents

Question 49

If electrical energy costs 4 cents per kWh,what does it cost to heat 210 kg water from 30°C to 65°C? (The specific heat of water = 10³ cal/kg⋅°C and 1.0 cal = 4.186 J. )

A) 87 cents
B) 47 cents
C) 40 cents
D) 20 cents
E) ​59 cents

Question 50

The quantity volt is equivalent to which of the following?

A) J⋅m
B) J⋅C
C) C/Ω
D) J/C

Question 51

If a 500-W heater carries a current of 4.00 A,what is the resistance of the heating element?

A) 85.7 Ω
B) 42.8 Ω
C) 31.3 Ω
D) 11.2 Ω

Question 52

An electric clothes dryer draws 23 A at 220 V.If the clothes put into the dryer have a mass of 7 kg when wet and 4 kg dry,how long does it take to dry the clothes? (Assume all heat energy goes into vaporizing water,L_v = 2.26 × 10⁶ J/kg).

A) 52 min
B) 22 min
C) 30 min
D) 6 min
E) ​4 min

Question 53

A steam turbine at an electric power plant delivers 4,600 kW of power to an electrical generator which converts 85% of this mechanical energy into electrical energy.What is the current delivered by the generator if it delivers at 3,200 V?

A) 0.6 × 10³ A
B) 1.7 × 10³ A
C) 1.2 × 10³ A
D) 1 × 10³ A
E) ​0.7 × 10³ A

Question 54

A 55-W light bulb is in a socket supplied with 100 V.What is the current in the bulb?

A) 0.6 A
B) 1.8 A
C) 45 A
D) 5,500 A
E) ​2.8 A

Question 55

If a 550-W heater carries a current of 3 A,what is the voltage across the ends of the heating element?

A) 1,650 V
B) 183.3 V
C) 366.7 V
D) 0.005 V
E) ​8.2 V

Question 56

If a lamp has resistance of 110 Ω when it operates at 100 W,what is the applied voltage?

A) 105 V
B) 121 V
C) 91 V
D) 44 V
E) ​110 V

Question 57

The temperature coefficient of resistivity for a "perfect" ohmic material would be:

A) positive and constant.
B) zero.
C) negative.
D) positive and uniformly increasing.

Question 58

The heating coil of a hot water heater has a resistance of 25 Ω and operates at 220 V.How long a time is required to raise the temperature of 150kg of water from 25°C to 85°C? (The specific heat for water = 10³ cal/kg⋅°C and 1.0 cal = 4.186 J).

A) 1.9 h
B) 7.7 h
C) 2.3 h
D) 5.4 h
E) ​0.9 h

Question 59

A resistor is connected to a battery with negligible internal resistance.If you replace the resistor with one that has quadruple the resistance,by what factor does the power dissipated in the circuit change?

A) 0.25
B) 0.06
C) 4
D) 16
E) ​2

Question 60

If a 12-V battery,with negligible internal resistance,and an 20-Ω resistor are connected in series,what is the amount of electrical energy transformed to heat per coulomb of charge that flows through the circuit?

A) 0.6 J
B) 2 J
C) 12 J
D) 240 J
E) ​32 J

Question 61

Which is a unit of power?

A) kWh
B) W/s
C) A⋅Ω
D) J/s

Question 62

Which is not a force?

A) gravity
B) electrical force
C) voltage
D) friction

Question 63

An electric car is designed to run off a bank of 12-V batteries with total energy storage of 2.1 × 10⁷ J.If the electric motor draws 4,200 W in moving the car at a steady speed of 15 m/s,how far will the car go before it is "out of juice?"
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A) 38 km
B) 75 km
C) 150 km
D) 113 km
E) ​19 km

Question 64

A high-voltage transmission line carries 1,000 A at 600,000 V.What is the power carried by the line?

A) 600 MW
B) 350 MW
C) 100 MW
D) 60 MW
E) ​167 MW

Question 65

Consider some material that has been cooled until it has become a superconductor.If it is cooled even further its resistance will:

A) increase.
B) decrease.
C) stay constant and non-zero.
D) None of the above.

Question 66

A solar panel measures 70 cm × 54 cm.In direct sunlight,the panel delivers 3.1 A at 12 V.If the intensity of sunlight is 1,000 W/m²,what is the efficiency of the solar panel in converting solar energy into electrical energy?
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A) 20%
B) 15%
C) 10%
D) 5%
E) ​8%

Question 67

A wire 1 mm in diameter is connected to one end of a wire of the same material 2 mm in diameter of twice the length.A voltage source is connected to the wires and a current is passed through the wires.If it takes time T for the average conduction electron to traverse the 1-mm wire,how long does it take for such an electron to traverse the 2-mm wire?

A) T/4
B) T
C) 4T
D) 8T

Question 68

When current is flowing in a superconductor,which statement is not true?

A) A battery is needed to keep the current going.
B) Electrical charges are moving.
C) The resistance is zero.
D) No power is given off in the form of heat.

Question 69

When a superconductor's temperature drops below the critical temperature,its resistance:

A) equals that of a semiconductor of equal dimensions.
B) increases by two.
C) drops to zero.
D) reduces to one half.

Question 70

A superconducting wire's chief characteristic is which of the following?

A) an extremely great length
B) a large cross sectional area
C) an extremely high temperature
D) no resistance

Question 71

An 5.00-Ω resistor is dissipating 80 watts.What are the current through it and the difference of potential across it?
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A) 16 A,20 V
B) 20 A,4 V
C) 4 A,20 V
D) 4 A,16 V
E) 16 A,80 V

Question 72

Suppose that a voltage surge produces 160 V for a moment in a 140-V line.What will temporarily be the output of a 100-W light bulb assuming its resistance does not change?
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A) 105 W
B) 85 W
C) 118 W
D) 131 W
E) ​66 W

Question 73

Superconductivity was discovered by:

A) Volta.
B) Ohm.
C) Onnes.
D) Bednorz and Müller.

Question 74

A resistor is made of a material that has a resistivity that is proportional to the current going through it.If the voltage across the resistor is doubled,what happens to the power dissipated by it?

A) It doubles.
B) It quadruples.
C) It increases by a factor of 2^3/2.
D) It increases by a factor of 2^1/2.

Question 75

An electric car is designed to run off a bank of 12-V batteries with total energy storage of 3.0 × 10⁷ J.If the electric motor draws 5,400 W,what current will be delivered to the motor?
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A) 450 A
B) 225 A
C) 675 A
D) 338 A
E) ​113 A

Question 76

A wire has resistance R.A second wire has twice the length,twice the diameter,and twice the resistivity of the first wire.What is its resistance?

A) 8 R
B) R
C) R/4
D) The resistance is not given.

Question 77

Some superconductors are capable of carrying a very large quantity of current.If the measured current is 1.00 × 10⁵ A,how many electrons are moving through the superconductor per second? (e = 1.60 × 10−¹⁹ C)

A) 6.25 × 10²³
B) 3.13 × 10²²
C) 6.25 × 10²¹
D) 3.13 × 10²⁰
E) 3.13 × 10^-23

Question 78

A water pump draws about 3.7 A when connected to 200 V.What is the cost (with electrical energy at 9 cents per kWh)of running the pump for 12 h?

A) 5.8 cents
B) 21 cents
C) 79.9 cents
D) 159.8 cents
E) ​59.9 cents

Question 79

A high-voltage transmission line carries 2,000 A at 1,400 kV for a distance of 300 miles.If the resistance in the wire is 1 Ω/mile,what is the power loss due to resistive losses?
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A) 60 kW
B) 600 kW
C) 60 MW
D) 600 MW
E) 600 W

Question 80

A light bulb with a tungsten filament is attached to a source of variable voltage.As the voltage is increased on the bulb,

A) the bulb's resistance decreases.
B) the bulb's resistance increases.
C) the current in the bulb decreases.
D) the power dissipated remains constant.