Deck 31: Electric Circuits

Question 1

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 1

at none of the above speeds.

Question 2

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

Answer 2

190 nA

Question 3

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

Answer 3

v_d/4

Question 4

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 5

In the circuit shown in the figure,four identical resistors labeled A to D are connected to a battery as shown.S₁ and S₂ are switches.Which of the following actions would result in the GREATEST amount of current through resistor A?

A) closing both switches
B) closing S₁ only
C) closing S₂ only
D) leaving both switches open as shown.

Question 6

Two light bulbs,B₁ and B₂,are connected to a battery having appreciable internal resistance as shown in the figure.What happens to the brightness of bulb B₁ when we close the switch S?

A) The brightness of B₁ increases permanently.
B) The brightness of B₁ decreases permanently.
C) The brightness of B₁ does not change.
D) The brightness of B₁ increases temporarily but gradually decreases back to its original brightness.
E) The brightness of B₁ decreases temporarily but gradually increases back to its original brightness.

Question 7

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 8

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 9

A light bulb is connected in the circuit shown in the figure with the switch S open.All the connecting leads have no appreciable resistance and the battery has no internal resistance.When we close the switch,which statements below accurately describe the behavior of the circuit? (There may be more than one correct choice.)

A) The brightness of the bulb will increase.
B) The brightness of the bulb will decrease.
C) The brightness of the bulb will not change.
D) The potential drop across R₂ will decrease.
E) The potential drop across R₂ will not change.

Question 10

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 11

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 12

You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor.
(a)If you want to achieve the SMALLEST possible resistance,you should attach the leads to the opposite faces that measure
A)3 cm × 5 cm.
B)3 cm × 8 cm.
C)5 cm × 8 cm.
D)Any pair of faces produces the same resistance.
(b) If you want to achieve the LARGEST possible resistance,you should attach the leads to the opposite faces that measure
A)3 cm × 5 cm.
B)3 cm × 8 cm.
C)5 cm × 8 cm.
D)Any pair of faces produces the same resistance

Question 13

A gold wire that is 1.8 mm in diameter and 15 cm long carries a current of 260 mA.How many electrons per second pass a given cross section of the wire? (e = 1.60 × 10^-19C)

A) 1.6 × 10¹⁸
B) 1.6 × 10¹⁷
C) 1.5 × 10²³
D) 3.7 × 10¹⁵

Question 14

A resistor is made out of a long wire having a length L.Each end of the wire is attached to a terminal of a battery providing a constant voltage V₀.A current I flows through the wire.If the wire were cut in half,making two wires of length L/2,and both wires were attached to the battery (the end of both wires attached to one terminal,and the other ends attached to the other terminal),what would be the total current flowing through the two wires?

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

Question 15

An electric device delivers a current of 5.0 A to a device.How many electrons flow through this device in 10 s? (e = 1.60 × 10^-19C)

A) 0.20
B) 20
C) 2.0
D) 3.1 × 10²⁰

Question 16

As more resistors are added in parallel across a constant voltage source,the power supplied by the source

A) increases.
B) decreases.
C) does not change.

Question 17

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 18

In the circuit shown in the figure,all the lightbulbs are identical.Which of the following is the correct ranking of the brightness of the bulbs?

A) B and C have equal brightness, and A is the dimmest.
B) A and B have equal brightness, and C is the dimmest.
C) A is brightest, C is dimmest, and B is in between.
D) A is the brightest, and B and C have equal brightness but less than A.
E) All three bulbs have the same brightness.

Question 19

The figure shows three identical lightbulbs connected to a battery having a constant voltage across its terminals.What happens to the brightness of lightbulb 1 when the switch S is closed?

A) The brightness will increase momentarily then return to its previous level.
B) The brightness increases permanently.
C) The brightness will decrease momentarily then return to its previous level.
D) The brightness remains the same as before the switch is closed.
E) The brightness decreases permanently.

Question 20

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 t = 3.00 s?

Question 21

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 22

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 23

The diameter of a 12-gauge copper wire is 0.081 in. 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 24

A certain fuse "blows" if the current in it exceeds 1.0 A,at which instant the fuse melts with a current density of 620 A/cm². 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 25

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 26

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 27

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 28

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

Question 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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/m²
B) 6.2 A/m²
C) 12 A/m²
D) 17 A/m²

Question 40

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 41

Three resistors are connected across an ideal 2.0-V DC battery as shown in the figure.
(a)At what rate does the battery supply energy to the resistors?
(b)At what rate is heat produced in the 6.0-Ω resistor?

Question 42

When a 100-Ω resistor is connected across the terminals of a battery of emf ε and internal resistance r,the battery delivers 0.794 W of power to the 100-Ω resistor. When the 100-Ω resistor is replaced by a 200-Ω resistor,the battery delivers 0.401 W of power to the 200-Ω resistor.What are the emf and internal resistance of the battery?

A) ε = 10.0 V, r = 5.02 Ω
B) ε = 4.50 V, r = 4.00 Ω
C) ε = 9.00 V, r = 2.04 Ω
D) ε = 9.00 V, r = 1.01 Ω
E) ε = 12.0 V, r = 6.00 Ω

Question 43

For the circuit shown in the figure,I = 0.50 A and R = 12 Ω.What is the value of the emf ε?

A) 18 V
B) 24 V
C) 6.0 V
D) 12 V
E) 48 V

Question 44

Three resistors having resistances of 4.0 Ω,6.0 Ω,and 10.0 Ω are connected in parallel. If the combination is connected in series with an ideal 12-V battery and a 2.0-Ω resistor,what is the current through the 10.0-Ω resistor?

A) 0.59 A
B) 2.7 A
C) 6.4 A
D) 11.2 A
E) 16 A

Question 45

When four identical resistors are connected to an ideal battery of voltage V = 10 V as shown in the figure,the current I is equal to 0.20 A.What is the value of the resistance R of the resistors?

A) 20 Ω
B) 40 Ω
C) 30 Ω
D) 50 Ω
E) 10 Ω

Question 46

A 5.0-Ω resistor and a 9.0-Ω resistor are connected in parallel. A 4.0-Ω resistor is then connected in series with this parallel combination.An ideal 6.0-V battery is then connected across the series-parallel combination of the three resistors.What is the current through
(a)the 4.0-Ω resistor?
(b)the 5.0-Ω resistor?
(c)the 9.0-Ω resistor?

Question 47

When a 20.0-ohm resistor is connected across the terminals of a 12.0-V battery,the voltage across the terminals of the battery falls by 0.300 V.What is the internal resistance of this battery?

A) 3.60 Ω
B) 1.56 Ω
C) 0.98 Ω
D) 0.30 Ω
E) 0.51 Ω

Question 48

A 4.00-Ω resistor,an 8.00-Ω resistor,and a 24.0-Ω resistor are connected together.
(a)What is the maximum resistance that can be produced using all three resistors?
(b)What is the minimum resistance that can be produced using all three resistors?
(c)How would you connect these three resistors to obtain a resistance of 10.0 Ω?
(d)How would you connect these three resistors to obtain a resistance of 8.00 Ω?

Question 49

Two unknown resistors are connected together.When they are connected in series their equivalent resistance is 15 Ω.When they are connected in parallel,their equivalent resistance is 3.3 Ω.What are the resistances of these resistors?

Question 50

For the circuit shown in the figure,what current does the ideal ammeter read?

A) 0.033 A
B) 0.078 A
C) 0.23 A
D) 0.12 A

Question 51

For the circuit shown in the figure,what is the current through resistor R₁?

A) 0.071 A
B) 0.13 A
C) 0.029 A
D) 0.016 A

Question 52

Four resistors are connected across an 8-V DC battery as shown in the figure.The current through the 9-Ω resistor is closest to

A) 1 A.
B) 0.7 A.
C) 0.5 A.
D) 0.9 A.
E) 2 A.

Question 53

For the circuit shown in the figure,all quantities are accurate to 3 significant figures.What is the power dissipated in the 2-Ω resistor?

A) 5.33 W
B) 8.0 W
C) 6.67 W
D) 2.67 W
E) 3.56 W

Question 54

For the circuit shown in the figure,what is the current through resistor R₃?

A) 0.043 A
B) 1.5 A
C) 0.028 A
D) 0.086 A

Question 55

For the circuit shown in the figure,the current in the 8-Ω resistor is 0.50 A,and all quantities are accurate to 2 significant figures.What is the current in the 2-Ω resistor?

A) 2.25 A
B) 0.75 A
C) 4.5 A
D) 9.5 A
E) 6.4 A

Question 56

Thirteen resistors are connected across points A and B as shown in the figure.If all the resistors are accurate to 2 significant figures,what is the equivalent resistance between points A and B?

A) 4.0 Ω
B) 6.0 Ω
C) 8.0 Ω
D) 10 Ω
E) 12 Ω

Question 57

Two identical resistors of resistance R = 24 Ω and a variable resistor R_x are connected to an ideal battery of voltage V as shown in the figure. What should be the value of the variable resistance R_x to make the voltage across the two parallel resistors equal to .

A) 4.0 Ω
B) 24 Ω
C) 8.0 Ω
D) 16 Ω
E) 40 Ω

Question 58

In the circuit shown in the figure,an ideal ohmmeter is connected across ab with the switch S open.All the connecting leads have negligible resistance.The reading of the ohmmeter will be closest to

A) 7.5 Ω.
B) 10 Ω.
C) 30 Ω.
D) 40 Ω.
E) 60 Ω.

Question 59

What is the maximum current that can be drawn from a 1.50-V battery with an internal resistance of 0.30 ohm?

A) 2.5 A
B) 5.0 A
C) 0.45 A
D) 0.20 A
E) 4.5 A

Question 60

For the circuit shown in the figure,determine the current in
(a)the 1.0-Ω resistor.
(b)the 3.0-Ω resistor.
(c)the 4.0-Ω resistor.

Question 61

Consider the circuit shown in the figure.Note that two currents are shown.Calculate the emfs ε₁ and ε₃.

Question 62

For the circuit shown in the figure,determine the current in
(a)the 7.0-Ω resistor.
(b)the 8.0-Ω resistor.
(c)the 4.0-Ω resistor.

Question 63

A multiloop circuit is shown in the figure.Some circuit quantities are not labeled.It is not necessary to solve the entire circuit.The emf ε is closest to

A) +3 V.
B) +19 V.
C) -3 V.
D) -10 V.
E) -1 V.

Question 64

A multiloop circuit is shown in the figure.It is not necessary to solve the entire circuit.Compared to the polarity shown in the figure,the emf ε₁ is closest to

A) -5 V.
B) 5 V.
C) 45 V.
D) 51 V.
E) -51 V.

Question 65

A multiloop circuit is shown in the figure.Some circuit quantities are not labeled.It is not necessary to solve the entire circuit.The current I₂ is closest to

A) +0.1 A.
B) +0.3 A.
C) +0.5 A.
D) -0.1 A.
E) -0.3 A.

Question 66

A multiloop circuit is shown in the figure.It is not necessary to solve the entire circuit.The current I₂ is closest to

A) -6 A.
B) 6 A.
C) 8 A.
D) -8 A.
E) zero.

Question 67

A multiloop circuit is shown in the figure.Some circuit quantities are not labeled.It is not necessary to solve the entire circuit.The current I₁ is closest to

A) zero.
B) +0.2 A.
C) +0.4 A.
D) -0.2 A.
E) -0.4 A.

Question 68

For the circuit shown in the figure,all quantities are accurate to 2 significant figures.What is the value of the current I₁?

A) 0.32 A
B) 0.11 A
C) 0.29 A
D) 0.61 A
E) 0.89 A