Deck 18: Direct-Current Circuits Sources of EMF: Part A

Question 1

A point charge of +3.0 μC is located at the origin of a coordinate system and a second point charge of −9.0 μC is at x = 1.0 m.At what point on the x axis is the electrical potential zero?

A) +0.33 m
B) −0.25 m
C) +0.25 m
D) +0.75 m

Answer 1

+0.25 m

Question 2

A proton (+1.6 × 10−¹⁹ C)moves 10 cm along the direction of an electric field of strength 4.0 N/C.The electrical potential difference between the proton's initial and ending points is:

A) 4.8 × 10−¹⁹ V.
B) 0.40 V.
C) 0.044 V.
D) 6.4 × 10−¹⁹ V.

Answer 2

0.40 V.

Question 3

When charges q_a,q_b,and q_c are placed respectively at the corners a,b,and c of a right triangle,the potential at the midpoint of the hypotenuse is 20 V.When the charge q_a is removed,the potential at the midpoint becomes 15 V.When,instead,the charge q_b is removed (q_a and q_c both in place),the potential at the midpoint becomes 13 V.What is the potential at the midpoint if both charges q_a and q_c are removed?

A) 13 V
B) 7 V
C) 5 V
D) 8 V

Answer 3

7 V

Question 4

When charges q_a,q_b,and q_c are placed respectively at the corners a,b,and c of a right triangle,the potential at the midpoint of the hypotenuse is 20 V.When the charge q_a is removed,the potential at the midpoint becomes 15 V.When,instead,the charge q_b is removed (q_a and q_c both in place),the potential at the midpoint becomes 13 V.What is the potential at the midpoint if only the charge q_c is removed from the array of charges?

A) 12 V
B) 8 V
C) 7 V
D) 5 V

Question 5

An electron is released from rest at the negative plate of a parallel-plate capacitor.If the distance across the plates is 5.0 mm and the potential difference across the plates is 20 V,with what velocity does the electron hit the positive plate? (m_e = 9.1 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

A) 1.3 × 10⁶ m/s
B) 1.0 × 10⁶ m/s
C) 2.7 × 10⁶ m/s
D) 5.3 × 10⁶ m/s

Question 6

Two charges,each of charge q,are separated by a distance d.The distance between the charges is doubled.If the original potential energy of the arrangement was 40 mJ,by how much does the potential energy change when the charges are moved to the increased distance?

A) It decreases by more than 20 mJ.
B) It decreases by less than 20 mJ
C) More information is needed.
D) It decreases by 20 mJ.

Question 7

Find the electrical potential at 0.055 m from a point charge of 6.0 μC.(k_e = 8.99 × 10⁹ N⋅m²/C²)

A) 1.5 × 10⁵ V
B) 1.2 × 10⁷ V
C) 9.8 × 10⁵ V
D) 3.6 × 10⁵ V

Question 8

An ion is released from rest and moves due to the force from an electric field from a position in the field having a potential of 14 V to a position having a potential of 8 V.The ion:

A) can have either a positive or a negative charge.
B) must be neutral.
C) must have a positive charge.
D) must have a negative charge.

Question 9

A solid conducting sphere of 10 cm radius has a net charge of 40 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

A) 360 μV
B) 3.6 × 10³ V
C) >3.6 × 10⁴ V
D) 36 μV

Question 10

An electron in a cathode ray tube is accelerated through a potential difference of 10 kV.What kinetic energy does the electron gain in the process? (e = 1.6 × 10−¹⁹ C)

A) 8.0 × 10−¹⁶ J
B) 1.6 × 10−¹⁵ J
C) 8.0 × 10²² J
D) 1.6 × 10−¹⁶ J

Question 11

A proton (+1.6 × 10−¹⁹ C)moves 10 cm on a path in the direction opposite to a uniform electric field of strength 3.0 N/C.How much work is done on the proton by the electrical field?

A) 4.8 × 10−²⁰ J
B) 1.6 × 10−²⁰ J
C) zero
D) −4.8 × 10−²⁰ J

Question 12

Two particles each have the same mass but particle #1 has four times the charge of particle #2.Particle #1 is accelerated from rest through a potential difference of 10 V and attains speed v.Particle #2 is accelerated from rest also through a potential difference of 10 V.What speed does particle #2 attain?

A) 2v
B) v/2
C) v/4
D)

Question 13

A 9.0-V battery moves 200 mC of charge through a circuit running from its positive terminal to its negative terminal.How much energy was delivered to the circuit?

A) 4.5 x 10³ J
B) 1.8 J
C) 2.2 mJ
D) 0.18 J

Question 14

At what distance from a point charge of 14 μC would the electrical potential be 4.2 × 10⁴ V? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A) 0.76 m
B) 0.58 m
C) 3.0 m
D) 1.7 m

Question 15

A point charge of +3.0 μC is located at the origin of a coordinate system and a second point charge of −9.0 μC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A) −5.4 × 10⁴ V
B) 11 × 10⁴ V
C) 16 × 10⁴ V
D) −11 × 10⁴ V

Question 16

An electron (charge −1.6 × 10−¹⁹ C)moves on a path perpendicular to the direction of a uniform electric field of strength 3.0 N/C.How much work is done on the electron as it moves 20 cm?

A) 1.6 × 10−²⁰ J
B) −4.8 × 10−²⁰ J
C) 4.8 × 10−²⁰ J
D) zero

Question 17

If an electron is accelerated from rest through a potential difference of 300 V,find its approximate speed at the end of this process.(e = 1.6 × 10−¹⁹ C;m_e = 9.1 × 10−³¹ kg)

A) 2.5 × 10⁷ m/s
B) 2.1 × 10⁷ m/s
C) 1.0 × 10⁷ m/s
D) 1.4 × 10⁷ m/s

Question 18

A uniform electric field,with a magnitude of 600 N/C,is directed parallel to the positive x axis.If the potential at x = 4.0 m is 1000 V,what is the potential at x = 2.0 m?

A) −800 V
B) 2200 V
C) 2800 V
D) 1600 V

Question 19

Two protons,each of charge 1.60 × 10−¹⁹ C,are 3.00 × 10−⁵ m apart.What is the change in potential energy if they are brought 1.00 × 10−⁵ m closer together? (k_e = 8.99 × 10⁹ N·m²/C²)

A) 3.84 × 10−²⁴ J
B) 3.20 × 10−¹⁶ J
C) 1.15 × 10−²³ J
D) 3.20 × 10−¹⁹ J

Question 20

A uniform electric field,with a magnitude of 600 N/C,is directed parallel to the positive x axis.If the potential at x = 4.0 m is 1000 V,what is the change in potential energy of a proton as it moves from x = 4.0 m to x = 1.0 m? (q_p = 1.6 × 10−¹⁹ C)

A) 500 J
B) 2.9 × 10−¹⁶ J
C) 1.9 × 10−¹⁶ J
D) 8.0 × 10−¹⁷ J

Question 21

Two capacitors with capacitances of 1.5 μC and 0.25 μF,respectively,are connected in parallel.The system is connected to a 40-V battery.What charge accumulates on the 1.5-μF capacitor?

A) 100 μC
B) 75 μC
C) 60 μC
D) 33 μC

Question 22

Electrons in an x-ray machine are accelerated from rest through a potential difference of 80,000 V.What is the kinetic energy of each of these electrons in eV?

A) 128 eV
B) 40 eV
C) 80 eV
D) 80 keV

Question 23

Suppose two charges,one positive and one negative,are separated by a distance d.Where can two equipotential surfaces at different potentials intersect in the region near the charges?

A) halfway between the charges if the charges have the same magnitude
B) closer to the smaller negative charge than the larger positive charge if the charges are not equal
C) Equipotential surfaces at different potentials cannot intersect.
D) closer to the smaller positive charge than the larger negative charge if the charges are not equal

Question 24

If C = 48 µF,determine the equivalent capacitance for the combination shown.

A) 32 µF
B) 48 µF
C) 24 µF
D) 28 µF

Question 25

Suppose two equipotential surfaces are the planes x = 3 m and x = 5 m.If the potential at the x = 3 m surface is 10 V and the potential at the x = 5 m surface is 50 V,what is the magnitude of the electric field between the two surfaces?

A) 40 N/C
B) 20 N/C
C) 15 N/C
D) 10 N/C

Question 26

If a doubly-ionized oxygen atom is accelerated from rest by going through a potential difference of 10 V,what will be the change in its kinetic energy?

A) 10 eV
B) 40 eV
C) 20 eV
D) none of the above

Question 27

A 6.0-μF capacitor is attached to a 20-V power supply.How much energy is stored in the capacitor?

A) 2.0 × 10−³ J
B) 5.2 × 10−⁴ J
C) 2.0 × 10−⁴ J
D) 1.2 × 10−³ J

Question 28

Two capacitors with capacitances of 1.5 μF and 0.25 μF,respectively,are connected in parallel.The system is connected to a 100-V battery.What electrical potential energy is stored in the 1.5-μF capacitor?

A) 1.2 × 10−³ J
B) 1.9 × 10−³ J
C) 0.50 × 10−³ J
D) 7.5 × 10−³ J

Question 29

Two capacitors with capacitances of 1.0 μF and 0.50 μF,respectively,are connected in series.The system is connected to a 50-V battery.What electrical potential energy is stored in the 1.0-μF capacitor?

A) 5.6 × 10−⁴ J
B) 4.3 × 10−³ J
C) 0.065 × 10−³ J
D) 1.4 × 10−⁴ J

Question 30

If three 3.0-µF capacitors are connected in parallel,what is the combined capacitance?

A) 0.46 μF
B) 1.0 μF
C) 9.0 μF
D) 0.75 μF

Question 31

An electron in a TV picture tube is accelerated through a potential difference of 20 kV before it hits the screen.What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 × 10−¹⁹ J)

A) 6.25 × 10²² eV
B) 1.0 × 10⁴ eV
C) 2.0 × 10⁴ eV
D) 3.2 × 10−²² eV

Question 32

Two capacitors with capacitances of 1.0 μC and 0.50 μF,respectively,are connected in series.The system is connected to a 150 V battery.What charge accumulates on the 1.0-μF capacitor?

A) 50 μC
B) 150 μC
C) 100 μC
D) 33 μC

Question 33

A 0.50-μF capacitor is connected to a 400-V battery.What potential energy is stored in the capacitor?

A) 0.020 J
B) 0.040 J
C) 1.0 × 10−⁴ J
D) 1.2 × 10−¹² J

Question 34

A parallel-plate capacitor has a capacitance of 20 µF.What potential difference across the plates is required to store 22 × 10−⁵ C on this capacitor?

A) 2.2 × 10^-2 V
B) 1.4 × 10−⁸ V
C) 11 V
D) 70 V

Question 35

A solid metal sphere of radius r is inside a metal concentric spherical shell of inner radius 2r and outer radius 3r.A charge is place on the solid metal sphere and it is found that the potential at its surface is V​₁ (at r)and that the potential at the outer surface of the spherical shell is V​₃ (at 3r).In terms of V​₁ and V​₃,what is the potential at the inner surface of the metal shell (at 2r)?

A) 3V​₁/2
B) V​₃
C) V​₁
D) 2V​₃/2

Question 36

A 0.50-μF capacitor is connected to a 400 V battery.Find the charge on the capacitor.

A) 2.0 × 10−⁴ C
B) 0.020 C
C) 1.0 × 10−⁴ C
D) 1.2 × 10−¹² C

Question 37

If C = 14 µF,what is the equivalent capacitance for the combination shown?

A) 5.8 µF
B) 6.5 µF
C) 8.2 µF
D) 7.0 µF

Question 38

What is the equivalent capacitance between points a and b? All capacitors are 2.0 μF.

A) 1.2 µF
B) 0.25 µF
C) 4.0 µF
D) 0.60 µF

Question 39

Equipotential surfaces around a point charge are

A) spherical.
B) cylindrical.
C) planar.
D) none of these choices.

Question 40

If the plane x = 4 m is an equipotential surface,in which of the following directions can the electric field be in the region immediately adjacent to this plane?

A) the positive y direction
B) both the positive and negative z directions
C) the positive x direction
D) more than one of these choices

Question 41

Two parallel-plate capacitors have the same plate area,and the gap between the plates is filled with a dielectric with a dielectric constant equal to 6.The gap in capacitor A is three times that in capacitor B.What is the ratio of the capacitance of A to B?

A) 1/3
B) The ratio is not given.
C) 3
D) 18

Question 42

If the electric field is halved in a region of space,what happens to the electric field energy in a 10 cm³ volume of this space.

A) It quadruples.
B) It becomes one fourth as much.
C) It halves.
D) It doubles.

Question 43

How much charge can be placed on a capacitor of plate area 20 cm² with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 × 10⁶ V/m? (ε₀ = 8.85 × 10−¹² C²/N⋅m²)

A) 6.6 × 10−⁷ C
B) 2.7 × 10−⁸ C
C) 5.3 × 10−⁸ C
D) 4.0 × 10−⁷ C

Question 44

Capacitor #1 has parallel plates of length L and width W,plate separation d,and is filled with dielectric with constant κ.Capacitor #2 has parallel plates of length 2L and width 2W,plate separation 2d,and is filled with dielectric with constant 2κ.If a voltage V is applied to capacitor #1 and a voltage 2V is applied to capacitor #2,which capacitor stores more energy and by what factor?

A) Capacitor #2 by a factor of 8
B) Capacitor #2 by a factor of 16
C) Capacitor #1 by a factor of 4
D) Both capacitors store the same energy.

Question 45

A parallel-plate capacitor has dimensions 4.0 cm × 5.0 cm.The plates are separated by a 1.0-mm thickness of paper (dielectric constant κ = 3.7).What is the charge that can be stored on this capacitor,when connected to a 6.0-V battery? (ε₀ = 8.85 × 10−¹² C²/N⋅m²)

A) 4.8 × 10−⁹ C
B) 4.8 × 10−¹¹ C
C) 9.8 × 10−¹¹ C
D) 3.9 × 10−¹⁰ C

Question 46

A pair of parallel plates,forming a capacitor,are charged.The plates are pulled apart to triple the original separation,the charges on the plates remaining the same.What is the ratio of the final energy stored to the original energy stored?

A) 1/9
B) 1.5
C) 1/3
D) 3

Question 47

A parallel-plate capacitor is attached to a fixed voltage supply.If the plates are then separated to double the initial value,what happens to the energy stored by the capacitor?

A) It halves,go figure!
B) It stays the same since the volume doubles while the electric field halves.
C) It doubles since the volume between the plates doubles.
D) It quadruples since both the volume and the field double in this case.

Question 48

A capacitor is made by taking two sheets of aluminum foil,each 0.022 mm thick and placing between them 2 sheets of paper which comes from a ream of 500 sheets,the ream being 5.5 cm thick,with sheets measuring 216 mm by 279 mm (the usual 8
By 11).What is the capacitance of the capacitor made this way if the dielectric constant of the paper is 3.7? (ε₀ = 8.85 × 10 ^-12 C²/N × m²)

A) 18 nF
B) 24 nF
C) 9.0 nF
D) 36 nF

Question 49

A pair of parallel plates,forming a capacitor,are connected to a battery.While the capacitor is still connected to the battery maintaining a constant voltage,the plates are pulled apart to triple their original distance.What is the ratio of the final energy stored to the original energy stored?

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

Question 50

If C₁ = 25 µF,C₂ = 20 µF,C₃ = 10 µF,and ΔV₀ = 42 V,determine the energy stored by C₃.

A) 3.6 mJ
B) 0.32 mJ
C) 1.8 mJ
D) 0.40 mJ

Question 51

Very large capacitors have been considered as a means for storing electrical energy.If we constructed a very large parallel-plate capacitor of plate area 10 m² using paper (κ = 3.7)of thickness 1.0 mm as a dielectric,how much electrical energy would it store at a plate voltage of 5000 V? (ε₀ = 8.85 × 10−¹² C²/N⋅m²)

A) 4.1 J
B) 8200 J
C) 0.41 J
D) 82,000 J

Question 52

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side)with a 3.00-mm thick piece of a dielectric called rutile (κ = 100)in between them.What is the capacitance? (ε₀ = 8.85 × 10−¹² C²/N⋅m²)

A) 177 pF
B) 118 pF
C) 100 µF
D) 8.85 µF

Question 53

The dielectric strength of rutile is 6.0 × 10⁶ V/m,which corresponds to the maximum electric field that the dielectric can sustain before breakdown.What is the maximum charge that a 10−¹⁰-F capacitor with a 0.50-mm thickness of Rutile can hold?

A) 0.30 μC
B) 6.0 C
C) 0.60 µC
D) 1.7 nC

Question 54

A parallel plate capacitor has the voltage applied to it doubled.Is the force between the plates attractive or repulsive,and what happens to the force between the plates when the voltage is doubled?

A) The force is attractive and it quadruples.
B) The force is attractive and it doubles.
C) The force is repulsive and it halves.
D) There is no force between the plates since the net charge is zero on the capacitor.