Deck 21: Electric Charge and Electric Field

Question 1

Drift velocity: A silver wire has a cross sectional area A = 2.0 mm². A total of 9.4 × 10¹⁸ electrons pass through the wire in 3.0 s. The conduction electron density in silver is 5.8 × 10²⁸ electrons/m³ and e = 1.60 × 10^-19 C. What is the drift velocity of these electrons?

A) 2.7 × 10^-5 m/s
B) 9.1 × 10^-5 m/s
C) 5.2 × 10^-5 m/s
D) 1.1 × 10^-5 m/s
E) 7.4 × 10^-5 m/s

Answer 1

2.7 × 10^-5 m/s

Question 2

Resistivity: A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but 4 times as long. If, however, the resistance of the new wire is to be the same as the resistance of the original wire, the diameter of the new wire must be

A) the same as the diameter of the original wire.
B) 1/2 the diameter of the original wire.
C) 1/4 the diameter of the original wire.
D) 2 times the diameter of the original wire.
E) 4 times the diameter of the original wire.

Answer 2

2 times the diameter of the original wire.

Question 3

Drift velocity: When electric current is flowing in a metal, the electrons are moving

A) at nearly the speed of light.
B) at the speed of light.
C) at the speed of sound in the metal.
D) at the speed of sound in air.
E) at none of the above speeds.

Answer 3

at none of the above speeds.

Question 4

Current density: A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J₀ (r/R), where R is the radius of the beam and J₀ is the current density at the edge. Determine the value of J₀.

A) 25 A/
B) 6.2 A/
C) 12 A/
D) 17 A/

Question 5

Current density: If the current density in a wire or radius R is given by J = kr, 0 < r < R, what is the current in the wire?

A) 2πkR³/3
B) 3πkR³/2
C) kR³/3
D) kR²
E) kR²/2

Question 6

Drift velocity: The figure shows two connected wires that are made of the same material. The current entering the wire on the left is 2.0 A and in that wire the electron drift speed is v_d. What is the electron drift speed in the wire on the right side?

A) 4v_d
B) 2v_d
C) v_d
D) v_d/2
E) v_d/4

Question 7

Current density: A certain fuse "blows" if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of What is the diameter of the wire in the fuse?

A) 0.45 mm
B) 0.63 mm
C) 0.68 mm
D) 0.91 mm

Question 8

Current: The current supplied by a battery as a function of time is What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead? (e = 1.60 × 10^-19C)

A) 1.2 ×
B) 4.4 ×
C) 5.3 ×
D) 3.3 ×

Question 9

Drift velocity: A wire has a cross-sectional area of 0.10 mm². If there are 4.0 × 10²⁸ atoms per cubic meter in this wire, and if each atom contributes 2 free electrons, what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10^-19C)

A) 0.0047 m/s
B) 0.0092 m/s
C) 0.94 m/s
D) 0.019 m/s

Question 10

Current: The current in a wire varies with time according to the equation I(t) = 6.00 A + ( 4.80 A/s)t, where t is in seconds. How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and

Question 11

Current: In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes. A gold ion, Au⁺, has a mass of approximately 3.3 × 10^-22 g. How many grams of gold are deposited by this process?

A) 33 g
B) 16 g
C) 22 g
D) 28 g
E) 97 g

Question 12

Drift velocity: The figure shows a steady electric current passing through a wire with a narrow region. What happens to the drift velocity of the moving charges as they go from region A to region B and then to region C?

A) The drift velocity decreases from A to B and increases from B to C.
B) The drift velocity increases all the time.
C) The drift velocity remains constant.
D) The drift velocity decreases all the time.
E) The drift velocity increases from A to B and decreases from B to C.

Question 13

Ohm's law: When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the current through it is 2 A. If the diameter of this resistor is now tripled, the current will be

A) 2/9 A.
B) 2/3 A.
C) 2 A.
D) 3 A.
E) 18 A.

Question 14

Resistivity: As current flows through a uniform wire, the wire gets hotter because the electrons stop moving and therefore transform their lost kinetic energy into thermal energy in the wire.

Question 15

Ohm's law: Two cables of the same length are made of the same material, except that one cable has twice the diameter of the other cable. When the same potential difference is maintained across both cables, which of the following statements are true? (There may be more than one correct choice.)

A) The same current flows through both cables.
B) Both cables carry the same current density.
C) The electrons have the same drift velocity in both cables.
D) The current in the thin cable is twice as great as the current in the thick cable.
E) The current in the thin cable is four times as great as the current in the thick cable.

Question 16

Current: The figure shows a 2.0-cm diameter roller that turns at 90 rpm. A 4.0-cm wide plastic film is being wrapped onto the roller, and this plastic carries an excess electric charge having a uniform surface charge density of 5.0 nC/cm². What is the current of the moving film?

A) 190 nA
B) 23 μA
C) 30 nA
D) 11 μA

Question 17

Current: In an electroplating process, copper (ionic charge +2e, atomic weight 63.6 g/mol) is deposited using a current of 10.0 A. What mass of copper is deposited in 10.0 minutes? Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C.

A) 3.96 g
B) 2.52 g
C) 0.99 g
D) 1.52 g
E) 1.98 g

Question 18

Drift velocity: The diameter of a copper wire is 2.05 mm. The maximum safe current it can carry (in order to prevent fire danger in building construction) is 20 A. At this current, what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm³ of copper is 8.5 × 10²² and e = 1.60 × 10^-19 C.

A) 0.044 mm/s
B) 0.44 mm/s
C) 0.44 cm/s
D) 0.44 m/s
E) 4.4 cm/s

Question 19

Electric field in a wire: A narrow copper wire of length L and radius b is attached to a wide copper wire of length L and radius 2b, forming one long wire of length 2L. This long wire is attached to a battery, and a current is flowing through it. If the electric field in the narrow wire is E, the electric field in the wide wire is

A) E.
B) 2E.
C) 4E.
D) E/2.
E) E/4.

Question 20

Current density: If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm, what is the average current density in this wire?

A) 7.6 × 10⁵ A/m²
B) 5.2 × 10^-6 A/m²
C) 1.9 × 10⁵ A/m²
D) 3.6 × 10⁵ A/m²
E) 21 × 10^-6 A/m²

Question 21

Resistivity and temperature: A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20.0% from its initial value. What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)^-1.

A) 200°C
B) 400°C
C) 500°C
D) 625°C
E) 300°C

Question 22

Resistivity and temperature: A platinum wire is used to determine the melting point of indium. The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt. What is the melting point of indium? The temperature coefficient of resistivity for platinum is 3.9 × 10^-3(C°)^-1.

A) 120°C
B) 140°C
C) 160°C
D) 240°C
E) 350°C

Question 23

Resistivity: A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω. What is the resistivity of the wire?

A) 5.0 × 10^-7 Ω ∙ m
B) 3.9 × 10^-8 Ω ∙ m
C) 4.0 × 10^-7 Ω ∙ m
D) 16 × 10^-8 Ω ∙ m
E) 0.25 Ω ∙ m

Question 24

Power: A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?

A) 90 mA
B) 1.0 A
C) 5.0 A
D) 11 A
E) 14 A

Question 25

Resistivity: What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

A) 16 mm
B) 16 cm
C) 1.6 m
D) 16 m
E) 160 m

Question 26

Ohm's law: Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is 100 × 10^-8 Ω ∙ m.

A) 17.5 A
B) 30.9 A
C) 61.8 A
D) 388 mA
E) 776 mA

Question 27

Ohm's law: How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

A) 1200 A
B) 9.5 × 10⁸ A
C) 68 nA
D) 710 A

Question 28

Electric field in a wire: A silver wire with resistivity carries a current density of What is the magnitude of the electric field inside the wire?

A) 0.064 V/m
B) 2.5 V/m
C) 0.040 V/m
D) 0.10 V/m

Question 29

Resistivity and temperature: A piece of wire 58.4 cm long carries a current I when a voltage V is applied across its ends at a temperature of 0°C. If the resistivity of the material of which the wire is made varies with temperature as shown in the graph in the figure, what length of the same diameter wire is needed so that the same current flows when the same voltage is applied at temperature 400°C?

Question 30

Resistivity: Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10^-6 Ω ∙ m at room temperature. What length of wire of diameter 0.250 mm is needed to wind a resistor that has 50 ohms at room temperature?

A) 3.66 m
B) 2.45 m
C) 0.61 m
D) 6.54 m
E) 22.4 m

Question 31

Ohm's law: A cylindrical wire of radius 2.0 mm carries a current of 2.5 A. The potential difference between points on the wire that are 46 m apart is 3.7 V.
(a) What is the electric field in the wire?
(b) What is the resistivity of the material of which the wire is made?

Question 32

Resistivity and temperature: The temperature coefficient of resistivity for copper is 0.0068 (C°)^-1. If a copper wire has a resistance of 104 Ω at 20°C, what is its resistance 80°C?

A) 192 Ω
B) 42 Ω
C) 71 Ω
D) 161 Ω
E) 146 Ω

Question 33

Power: The power rating of a 400-Ω resistor is 0.800 W.
(a) What is the maximum voltage that can be applied across this resistor without damaging it?
(b) What is the maximum current this resistor can draw without damaging it?

Question 34

Electric field in a wire: The resistivity of gold is at room temperature. A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA. What is the electric field in the wire?

A) 0.036 V/m
B) 0.0090 V/m
C) 0.028 V/m
D) 0.046 V/m
E) 0.090 V/m

Question 35

Resistivity: What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

A) 0.065 mm
B) 0.65 mm
C) 0.65 cm
D) 0.325 mm
E) 0.0325 mm

Question 36

Electric field in a wire: A tube of mercury with resistivity 9.84 × 10^-7 Ω ∙ m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube. How much current is flowing through this tube if its diameter is 1.0 mm?

A) 18 A
B) 180 A
C) 29 A
D) 280 A

Question 37

Drift velocity: Building codes usually limit the current carried by a 1.6-mm diameter copper wire to 15 A. Many household circuits are wired with this size wire. What is the drift velocity of the electrons in this case?. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 g/mol and its density is 8900 kg/m³. Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C.

A) 5.51 × 10^-4 m/s
B) 4.56 × 10^-4 m/s
C) 1.65 × 10^-3 m/s
D) 4.44 × 10^-2 m/s
E) 4.89 × 10^-5 m/s

Question 38

Power: A light bulb is connected to a 110-V source. What is the resistance of this bulb if it is a 100-W bulb?

A) 100 Ω
B) 8.0 mΩ
C) 6.0 mΩ
D) 120 Ω
E) 240 Ω

Question 39

Ohm's law: When a voltage difference is applied to a piece of metal wire, a current flows through it. If this metal wire is now replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire? The lengths of both wires are the same, and the voltage difference remains unchanged. (The resistivity of the original metal is 1.68 × 10^-8 Ω ∙ m, and the resistivity of silver is 1.59 × 10^-8 Ω ∙ m.)

A) 21 mA
B) 19 mA
C) 11 mA
D) 5.3 mA

Question 40

Power: A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace?

A) 1.0 kΩ
B) 10 Ω
C) 2.4 Ω
D) 0.42 Ω
E) 100 Ω

Question 41

Power: A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh, how much does it cost to run the computer annually for a typical 365-day year?

A) $120
B) $1200
C) $15
D) $17
E) $150

Question 42

Internal battery resistance: The emf and the internal resistance of a battery are as shown in the figure. When the terminal voltage V_ab is equal to 17.4 V, what is the current through the battery, including its direction?

A) 6.8 A, from b to a
B) 8.7 A, from b to a
C) 6.8 A, from a to b
D) 8.7 A, from a to b
E) 16 A, from b to a

Question 43

Power: A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours?

A) 1.5 kJ
B) 3.0 kJ
C) 0.18 MJ
D) 11 MJ
E) 18 MJ

Question 44

Power: The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated at a reduced voltage and the power drawn by the bulb is 36 W, what is the operating voltage of the bulb?

A) 66 V
B) 72 V
C) 78 V
D) 85 V
E) 90 V

Question 45

Basics of ac circuits: A 500-W device is connected to a 230-V ac power source. What is the peak voltage across this device?

A) 330 V
B) 2.2 V
C) 230 V
D) 3.1 V
E) 290 V

Question 46

Internal battery resistance: In the figure, when the terminal voltage V_ab of the battery is equal to 20 V, how much current passes through the battery, including its direction?

A) 4 A, from a to b
B) 5 A, from a to b
C) 6 A, from a to b
D) 4 A, from b to a
E) 5 A, from b to a

Question 47

Power: The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb?

A) 10 W
B) 15 W
C) 20 W
D) 25 W
E) 30 W

Question 48

Power: The resistivity of gold is 2.44 × 10^-8 Ω ∙ m at room temperature. A gold wire that is 1.8 mm in diameter and 11 cm long carries a current of 170 mA. How much power is dissipated in the wire?

A) 0.030 mW
B) 0.0076 mW
C) 0.013 mW
D) 0.019 mW
E) 0.025 mW

Question 49

Internal battery resistance: The emf and the internal resistance of a battery are shown in the figure. If a current of 7.8 A is established through the battery from b to a, what is the terminal voltage V_ab of the battery?

A) -30 V
B) 80 V
C) 30 V
D) -80 V
E) zero

Question 50

Basics of ac circuits: A 500-W device is connected to a 230-V ac power source. What peak current flows through this device?

A) 2.2 A
B) 330 A
C) 3.1 A
D) 290 A
E) 230 A

Question 51

Basics of ac circuits: A 500-W device is connected to a 230-V ac power source. What rms current flows through this device?

A) 290 A
B) 2.2 A
C) 330 A
D) 230 A
E) 3.1 A

Question 52

Internal battery resistance: The emf and the internal resistance of a battery are as shown in the figure. If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery, what is the power dissipated by the resistor R?

A) 440 W
B) 700 W
C) 620 W
D) 530 W
E) 790 W

Question 53

Internal battery resistance: In the figure a current of 6.0 A is drawn from the battery. What is the terminal voltage V_ab of the battery?

A) 0.00 V
B) +12 V
C) +24 V
D) -12 V
E) -24 V

Question 54

Power: The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire, whose diameter is 0.86 mm. The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10^-6 Ω ∙ m. If the toaster is operated at a voltage of 120 V, how much power does it draw?

A) 720 W
B) 700 W
C) 750 W
D) 770 W
E) 800 W