Deck 16: Electrical Energy and Capacitance

Question 1

Two equal positive charges are separated by d. Then one of the charges is replaced by a negative charge of the same magnitudeTake the potential at infinity to be zero.In which situation is the potential higher midway between the charges;is this value of potential zero?

A)the first situation;yes
B)the first situation;no
C)the second situation;yes
D)the second situation;no

Answer 1

the first situation;no

Question 2

A uniform electric field,with a magnitude of 650 N/C,is directed parallel to the positive x-axis.If the potential at x = 3.0 m is 1 700 V,what is the potential at x = 1.0 m?

A)3 300 V
B)4 050 V
C)3 000 V
D)400 V
E)1 500​ V

Answer 2

3 000 V

Question 3

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

Answer 3

must have a positive charge.

Question 4

A 10-V battery moves 7.0 mC of charge through a circuit running from its positive terminal to its negative terminal.How much energy was delivered to the circuit?

A)1.4 mJ
B)0.67 J
C)0.070 J
D)5.7E+2 J
E)1.4 J

Question 5

If an electron is accelerated from rest through a potential difference of 1 200 V,find its approximate velocity at the end of this process.(e = 1.6 × 10−¹⁹ C;m_e = 9.1 × 10−³¹ kg)

A)2.5E+7 m/s
B)2.1E+8 m/s
C)2.1E+7 m/s
D)4.2E+7 m/s
E)​1.8E+8 m/s

Question 6

Four point charges are on the rim of a circle of radius 10 cm.The charges are (in μC)+0.50,+1.5,−1.0,−0.50.If the electrical potential at the circle's center due to the +0.5 charge alone is 4.5 × 10⁴ V,what is the total potential at the center due to the four charges combined?

A)18 × 10⁴ V
B)4.5 × 10⁴ V
C)zero
D)−4.5 × 10⁴ V

Question 7

An electron in a cathode ray tube is accelerated through a potential difference of 8.0 kV.What kinetic energy does the electron gain in the process? (e = 1.6 × 10−¹⁹ C)

A)1.0E-15 J
B)1.3E-15 J
C)1.0E-21 J
D)5.0E-16 J
E)1.3E-21 J

Question 8

A free electron is in an electric field.With respect to the field,it experiences a force acting:

A)parallel.
B)anti-parallel (opposite in direction).
C)perpendicular.
D)along a constant potential line.

Question 9

A proton (+1.6 × 10−¹⁹ C)moves 20 cm on a path in the direction of a uniform electric field of strength 2.4 N/C.How much work is done on the proton by the electrical field?

A)7.7E-20 J
B)−7.7E-20 J
C)1.8E-19 J
D)−​8.6E-20 J
E)​zero

Question 10

A 10.00-V battery is connected between two parallel metal plates 4.00 mm apart.What is the magnitude of the electric field between the plates?

A)2.50 × 10³ N/C
B)25.0 N/C
C)14.0 N/C
D)4.00 × 10−⁶ N/C
E)​2.90 × 10³ N/C

Question 11

The quantity of electrical potential,the volt,is dimensionally equivalent to:

A)force/charge.
B)force × charge.
C)electric field × distance.
D)electric field/distance.

Question 12

​A proton is released from rest in a uniform electric field.Which statement is correct?

A)​The proton will move in the same direction as the electric field to regions of higher electric potential.
B)​The proton will move in the same direction as the electric field to regions of lower electric potential.
C)​The proton will move in the opposite direction as the electric field to regions of higher electric potential.
D)​The proton will move in the opposite direction as the electric field to regions of lower electric potential.

Question 13

A proton (+1.6 × 10−¹⁹ C)moves 15.0 cm along the direction of an electric field of strength 3.0 N/C.The electrical potential difference between the proton's initial and ending points is:

A)4.5 × 10−¹⁹ V.
B)0.45 V.
C)24 V.
D)0.55 V.
E)​zero

Question 14

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 15

The unit of electrical potential,the volt,is dimensionally equivalent to:

A)J⋅C.
B)J/C.
C)C/J.
D)F⋅C.

Question 16

A positively charged particle is released from rest in a uniform electric field.Which statement regarding the electron is correct?

A)The particle's kinetic energy increases.
B)The particle's total energy increases.
C)The electric potential at the particle's location increases.
D)The particle's associated electric potential energy increases.
E)None of the statements are correct.

Question 17

An electron (charge −1.6 × 10−¹⁹ C)moves on a path perpendicular to the direction of a uniform electric field of strength 2.0 N/C.How much work is done on the electron as it moves 14.0 cm?

A)5.6E-19 J
B)−2.8E-19 J
C)1.6E-19 J
D)3.9E-18​ J
E)​zero

Question 18

In which case does an electric field do positive work on a charged particle?

A)A negative charge moves opposite to the direction of the electric field.
B)A positive charge is moved to a point of higher potential energy.
C)A positive charge completes one circular path around a stationary positive charge.
D)A positive charge completes one elliptical path around a stationary positive charge.

Question 19

An electron and a proton are each released from rest in the same uniform electric field.The electron moves a distance d_electron and the proton moves a distance d_proton as each particle's kinetic energy increases by 1.6 eV.How do d_electron and d_proton compare?

A)d_electron < d_proton
B)d_electron > d_proton
C)d_electron = d_proton
D)The answer depends on the direction of the electric field.

Question 20

Case 1: An electron is released from rest in a uniform electric field.Case 2: A proton is released from rest in a uniform electric field of the same magnitude as in case 1.How does the electric potential energy of the charge-field system behave in these cases?

A)In both cases,the potential energy increases.
B)In both cases,the potential energy decreases.
C)In case 1 the potential energy increases,but in case 2 it decreases.
D)In case 1 the potential energy decreases,but in case 2 it increases.

Question 21

If a doubly-ionized oxygen atom (O^-2)is accelerated from rest by going through a potential difference of 32 V,what will be the change in its kinetic energy?

A)16 eV
B)32 eV
C)64 eV
D)​51 eV
E)​none of the above

Question 22

An electron in a TV picture tube is accelerated through a potential difference of 10 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)1.0E+4 eV
B)1.6E-18 eV
C)1.6E-11 eV
D)6.3E+22 eV
E)​2.6E-15 eV

Question 23

Two particles,each of charge 2.5 × 10^-19 C,are 4.8 × 10^-5 m apart.What is the change in potential energy if they are brought 2.4 × 10^-5 m closer together? (k_e = 8.99 × 10⁹ N·m²/C²)

A)1.2E-23 J
B)4.7E-24 J
C)2.3E-16 J
D)1.4E-15 J
E)2.9E-20 J

Question 24

When charge Q₁ is placed at point P₁,the resulting potential at point P is V₁.When Q₂ is placed at point P₂ after Q₁ is in position at P₁,the resulting potential at P becomes V₂.What is the potential at point P if charge Q₁ is then removed?

A)V₁ + V₂
B)V₁ - V₂
C)V₂ - V₁
D)(V₁ + V₂)/2

Question 25

Electrons in an x-ray machine are accelerated from rest through a potential difference of 60 000 V.What is the kinetic energy of each of these electrons in eV?

A)60 eV
B)96 eV
C)38 eV
D)60 keV
E)​120 eV

Question 26

Find the electrical potential at 0.25 m from a point charge of 7.0 μC.(k_e = 8.99 × 10⁹ N⋅m²/C²)

A)3.4 × 10⁴ V
B)2.5 × 10⁵ V
C)3.2 × 10⁶ V
D)3.2 × 10⁷ V
E)​3.4 × 10⁵ V

Question 27

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 24 V.When the charge q_a is removed,the potential at the midpoint becomes 17 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)11 V
B)7.0 V
C)6.0 V
D)18 V
E)​17 V

Question 28

Consider two charged spheres,one with charge +2 C and the other with −2 C.A proton (a positively charged particle)is at the point halfway between the spheres.What is not zero?

A)the potential energy of the proton
B)the work to move the proton from infinity to that point
C)the force on the proton
D)all of the three above are zero

Question 29

Two point charges of values +3.6 and +6.9 μC are separated by 0.40 m.What is the electrical potential at the point midway between the two point charges? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A)+0.47 MV
B)−0.24 MV
C)+0.24 MV
D)+0.97 MV
E)​−0.47 MV

Question 30

A point charge of +2.5 μC is located at the origin of a coordinate system and a second point charge of −5.6 μC is at x = 1.9 m.At what point on the x axis is the electrical potential zero?

A)+4.3 m
B)+5.3 m
C)+0.59 m
D)+11 m
E)​+1.3 m

Question 31

Which of the following characteristics are held in common by both gravitational and electrostatic forces when dealing with either point masses or charges?

A)inverse square distance law applies
B)forces are conservative
C)potential energy is a function of distance of separation
D)all of the above choices are valid

Question 32

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 33

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 34

At what distance from a point charge of 8.0 μC would the electrical potential be 4.8 × 10⁴ V? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A)1.8 m
B)0.43 m
C)1.5 m
D)5.4 m
E)0.60​ m

Question 35

If the distance between two negative point charges is increased by a factor of three,the resultant potential energy is what factor times the initial potential energy?

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

Question 36

A point charge of +4.0 μC is located at the origin of a coordinate system and a second point charge of −6.6 μC is at x = 1.7 m.What is the electric potential at the x = 0.85 m point? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A)-2.9 × 10⁴ V
B)-27 × 10⁴ V
C)−56 × 10⁴ V
D)-2.7 × 10⁴ V
E)​56 × 10⁴ V

Question 37

There is a hollow,conducting,uncharged sphere with a negative charge inside the sphere.Consider the electrical potential at the inner and outer surfaces of the sphere.Which of the following is true?

A)The potential on the inner surface is greater.
B)The potential on the outer surface is greater.
C)The potentials on both surfaces are zero.
D)The potentials on both surfaces are equal but not zero.

Question 38

Two point charges of values +2.0 and +5.5 μC,respectively,are separated by 0.50 m.What is the potential energy of this 2-charge system? (k_e = 8.99 × 10⁹ N⋅m²/C²)

A)+0.50 J
B)−0.20 J
C)+0.20 J
D)−0.41 J
E)​+0.41 J

Question 39

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 12 V.What is the potential at the midpoint if only the charge q_c is removed from the array of charges?

A)8.0 V
B)5.0 V
C)7.0 V
D)13 V

Question 40

A solid conducting sphere of 10-cm radius has a net charge of 18 nC.If the potential at infinity is taken as zero,what is the potential at the center of the sphere?

A)2.1 μV
B)16 μV
C)1.6 × 10³ V
D)>1.6 × 10⁴ V
E)​13 μV

Question 41

Increasing the voltage across the two plates of a capacitor will produce what effect on the capacitor?

A)increase charge
B)decrease charge
C)increase capacitance
D)decrease capacitance

Question 42

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 43

A parallel-plate capacitor has a capacitance of 25 µF.What potential difference across the plates is required to store 7.2 × 10−⁴ C on this capacitor?

A)2.9E+1 V
B)3.6E+1 V
C)4.5E+9 V
D)2.9E-1 V
E)4.5E+5 V

Question 44

The unit of capacitance,the farad,is dimensionally equivalent to which of the following?

A)V/C
B)V⋅C
C)J/V
D)C/V

Question 45

A 0.75-μF capacitor is connected to a 400-V battery.Find the charge on the capacitor.

A)4.0E-2 C
B)3.0E-4 C
C)1.9E-3 C
D)5.3E-8 C
E)​5.3E+4 C

Question 46

An electron with velocity v = 2.0 × 10⁶ m/s is sent between the plates of a capacitor where the electric field is E = 200 V/m.If the distance the electron travels through the field is 1.0 cm,how far is it deviated (Y)in its path when it emerges from the electric field? (m_e = 9.1 × 10−³¹ kg,e = 1.6 × 10−¹⁹ C)

A)0.84 mm
B)0.44 mm
C)0.44 cm
D)0.84 cm
E)1.4 mm

Question 47

Doubling the voltage across a parallel plate capacitor does not double which of the following?

A)the charge
B)the electric field between the plates
C)the energy stored
D)both a and b

Question 48

If two parallel,conducting plates have equal positive charge,the electric field lines will:

A)leave one plate and go straight to the other plate.
B)leave both plates and go to infinity.
C)enter both plates from infinity.
D)none of the above.

Question 49

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 50

If the distance between two isolated parallel plates that are oppositely charged is doubled,the electric field between the plates is essentially unchanged.However,the:

A)potential difference between the plates will double.
B)charge on each plate will double.
C)force on a charged particle halfway between the plates will get twice as small.
D)force on a charged particle halfway between the plates will get four times as small.

Question 51

An electron is released from rest at the negative plate of a parallel-plate capacitor.If the distance across the plate is 2.0 mm and the potential difference across the plate is 6.0 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)2.1E+5 m/s
B)1.5E+12 m/s
C)5.3E+5 m/s
D)1.5E+6 m/s
E)2.1E+6 m/s

Question 52

Three capacitors of 0.60,1.2,and 2.9 μF are connected in series.Find the combined capacitance.

A)2.8 μF
B)4.7 μF
C)6.8 μF
D)0.35 μF
E)2.1​ μF

Question 53

Two capacitors with capacitances of 2.0 and 3.6 μF,respectively,are connected in series.The system is connected to a 40-V battery.What charge accumulates on the 2.0-μF capacitor?

A)220 μC
B)31 μC
C)2 100 μC
D)51 μC
E)290​ μC

Question 54

Two capacitors with capacitances of 3.25 and 5.00 μF,respectively,are connected in parallel.The system is connected to a 55-V battery.What charge accumulates on the 3.25-μF capacitor?

A)16 μC
B)180 μC
C)0.30 μC
D)3.4 μC
E)1.5​ μC

Question 55

At which location will the electric field between the two parallel plates of a charged capacitor be the strongest in magnitude?

A)near the positive plate
B)near the negative plate
C)midway between the two plates at their ends
D)midway between the two plates nearest their center

Question 56

Two capacitors with C_A greater than C_B and are connected in series with a battery.Which of the following is true?

A)There is more charge stored on C_A.
B)There is more charge stored on C_B.
C)There is the same charge stored on each capacitor.
D)There is the same potential difference across both capacitors.

Question 57

Increasing the separation of the two charged parallel plates of a capacitor,which are disconnected from a battery,will produce what effect on the capacitor?

A)increase charge
B)decrease charge
C)increase capacitance
D)decrease capacitance

Question 58

A 20-μF capacitor is attached across a 1 000-V power supply.What is the net charge on the capacitor?

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

Question 59

Equipotential surfaces around a point charge are

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

Question 60

Four identical 2.5-mF capacitors are connected together electrically.What is the greatest possible capacitance of the combination?

A)0.50 mF
B)0.42 mF
C)0.63 mF
D)10 mF
E)​0.40 mF

Question 61

What is the equivalent capacitance of the combination shown?

A)29 µF
B)10 µF
C)40 µF
D)25 µF

Question 62

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 1.85 m² using paper (κ = 3.7)of thickness 1.5 mm as a dielectric,how much electrical energy would it store at a plate voltage of 1 500 V? (ε₀ = 8.85 × 10−¹² C²/N⋅m²)

A)0.045 J
B)9.1 J
C)910 J
D)1 800 J
E)3 600 J

Question 63

A parallel-plate capacitor stores charge Q.The capacitor is then disconnected from its voltage source,and the space between the plates is filled with a dielectric of constant κ = 2.What is the relationship between the stored energies of the capacitor,where PE_i is the initial stored energy,and PE_f is the stored energy after the dielectric is inserted?​

A)​PEf = 0.25PE_i
B)​PEf = 0.5PE_i
C)​PEf = PE_i
D)​PEf = 2PE_i

Question 64

If C₁ = 30 µF,C₂ = 25 µF,C₃ = 15 µF,and ΔV₀ = 24 V,determine the energy stored by C₂.

A)2.3 mJ
B)4.8 mJ
C)3.6 mJ
D)1.3 mJ
E)3.2 mJ

Question 65

Three capacitors have capacitances C₁ < C₂ < C₃.If these capacitors are connected in series,which of the following is true for the resulting equivalent capacitance?

A)C_eq < C₁
B)C_eq > C₃
C)C_eq = (C₁ + C₂ + C₃)/3
D)None of the above is always correct.

Question 66

Two capacitors with capacitances of 1.5 μF and 0.25 μF,respectively,are connected in parallel.The system is connected to a 40-V battery.What electrical potential energy is stored in the 1.5-μF capacitor?

A)1.1E-4 J
B)2.0E-4 J
C)1.2E-3 J
D)1.1E-3 J
E)​2.0E-3 J

Question 67

Two capacitors with capacitances of 2.0 μF and 0.40 μF,respectively,are connected in series.The system is connected to a 50-V battery.What electrical potential energy is stored in the 2.0-μF capacitor?

A)2.5E-3 J
B)5.0E-4 J
C)8.3E-5 J
D)6.9E-5 J
E)​1.4E-5 J

Question 68

Using a 1.5-mF capacitor,a 2.5-mF capacitor,and a 6.0-mF capacitor,which of the following capacitances cannot be made by a combination that uses all three?

A)10.0 mF
B)0.81 mF
C)6.9 mF
D)0.67 mF
E)​3.3 mF

Question 69

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

A)28 µF
B)17 µF
C)0.29 µF
D)7.0 µF
E)​670 µF

Question 70

What is the equivalent capacitance between points a and b? All capacitors are 5.0 μF.

A)2.6 µF
B)0.19 µF
C)3.0 µF
D)0.33 µF
E)​0.13 µF

Question 71

If C = 36 µF,determine the equivalent capacitance for the combination shown.

A)36 µF
B)28 µF
C)14 µF
D)24 µF
E)33​ µF

Question 72

A capacitor is attached across a battery and charged.Then the battery is removed leaving the capacitor charged.The positive lead of the capacitor is then connected to one lead of a previously uncharged identical capacitor,and then the other lead of the charged capacitor is connected to the other lead of the second capacitor.How does the energy E_o stored in the originally charged capacitor compare to the energy E_f stored in the connected capacitors?

A)E_o < E_f
B)E_o = E_f
C)E_o = 2E_f
D)E_o = 4E_f

Question 73

Four identical 1.5-mF capacitors are connected together electrically.What is the least possible capacitance of the combination?

A)3.0E-4 F
B)2.5E-4 F
C)3.8E-4 F
D)1.5E-3 F
E)​6.7E-4 F

Question 74

If three 2.4-µF capacitors are connected in series,what is the combined capacitance?

A)8.0E-7 F
B)1.4E-5 F
C)7.2E-8 F
D)2.4E-6 F
E)4.6E-6​ F

Question 75

Two capacitors with C_A greater than C_B are connected in parallel with a battery.Which of the following is true?

A)There is more potential difference across C_A.
B)There is more potential difference across C_B.
C)There is the same charge stored on each capacitor.
D)There is the same potential difference across both capacitors.

Question 76

What is the equivalent capacitance of the combination shown?

A)24 µF
B)100 µF
C)12 µF
D)4.6 µF

Question 77

A 0.30-μF capacitor is connected to a 400-V battery.What potential energy is stored in the capacitor?

A)1.3 × 10−³ J
B)6.0 × 10−⁴ J
C)4.8 J
D)0.024 J
E)​0.048 J

Question 78

A "sandwich" is constructed of two flat pieces of metal (0.70 cm on a side)with a 1.0-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)43 pF
B)4.3 nF
C)8.85 µF
D)6.2 pF
E)0.62 nF

Question 79

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 80

A 3.5-μF capacitor is attached to a 20-V power supply.How much energy is stored in the capacitor?

A)7.0E-4 J
B)7.0E-3 J
C)2.5E-4 J
D)2.4E-3 J
E)​2.0E-3 J