Deck 24: Capacitance, Dielectrics, Electric Energy Storage

Question 1

Briefly discuss some of the uses for capacitors in electronic circuits.

Answer 1

Capacitors are devices that can store electric charge. They store charge for later use, such as in a camera flash, and as energy backup in computers if the power fails. Capacitors can also block surges of charge and energy to protect circuits. Very tiny capacitors serve as memory for the "ones" and "zero" of the binary code in the random access memory of computers.

Question 2

If the voltage between the plates of a parallel-plate capacitor is doubled, the capacitance of the capacitor

A)is tripled.
B)is halved.
C)is doubled.
D)quadruples.
E)remains the same.

Answer 2

remains the same.

Question 3

Three identical capacitors are connected in series to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

A)9Q
B)3Q
C)Q
D)Q/3
E)Q/9

Answer 3

Q

Question 4

Capacitors in series share the same charge and capacitors in parallel share the same voltage.

Question 5

When two or more capacitors are connected in parallel to a battery,

A)the voltage across each capacitor is the same.
B)each capacitor carries the same amount of charge.
C)the equivalent capacitance of the combination is less than the capacitance of any one of the capacitors.
D)all of the given answers
E)none of the given answers

Question 6

A capacitor consists of a set of two parallel plates of area A separated by a distance d. The capacitor plates cary charges +Q and -Q. If the separation between the plates is doubled, the potential difference between the plates will

A)double.
B)quadruple.
C)be cut in half.
D)be cut in fourth.
E)not change.

Question 7

If the voltage applied to a parallel-plate capacitor is doubled, the electric field between the plates

A)is halved.
B)quadruples.
C)is tripled.
D)remains the same.
E)is doubled.

Question 8

When two or more capacitors are connected in series to a battery,

A)the total voltage across the combination is the algebraic sum of the voltages across the individual capacitors.
B)each capacitor carries the same amount of charge.
C)the equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
D)all of the given answers
E)none of the given answers

Question 9

Describe the process of storing electrical energy in a capacitor.

Question 10

If you were a parallel plate capacitor manufacturer, state three ways you might make larger valued capacitors.

Question 11

The energy stored in a capacitor will be equal to the work done to charge it.

Question 12

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. During this process, the amount of charge on the plates must

A)increase.
B)decrease.
C)remain constant.
D)either increase or decrease. There is no way to tell from the information given.

Question 13

As more and more capacitors are connected in series, the equivalent capacitance of the combination increases.

Question 14

A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel combination then being connected in series with a 3 pF capacitor. The resulting combination is then connected across a battery.
(a) Which capacitor has the greatest charge?
(b) Which capacitor has the greatest voltage?

Question 15

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field during this process?

A)It increases.
B)It decreases.
C)It remains constant.
D)cannot be determined from the information given

Question 16

If the voltage between the plates of a parallel-plate capacitor is doubled, the charge on the capacitor

A)is tripled.
B)is doubled.
C)is halved.
D)quadruples.
E)remains the same.

Question 17

A 1 mF, a 2 mF, and a 3 mF capacitor are connected in parallel, the combination being connected across a 9 volt battery.
(a) Which capacitor has the greatest charge?
(b) Which capacitor has the greatest voltage?

Question 18

State three reasons for adding a dielectric material between the plates of a capacitor.

Question 19

A 1 mF, a 2 mF, and a 3 mF capacitor are connected in series, the combination being connected across a 9 volt battery.
(a) Which capacitor has the greates charge?
(b) Which capacitor has the greatest voltage?

Question 20

As more and more capacitors are connected in parallel, the equivalent capacitance of the combination increases.

Question 21

A dielectric is inserted between the plates of an isolated parallel-plate capacitor that carries a charge Q. What happens to the potential energy stored in the capacitor?

A)The potential energy of the capacitor decreases.
B)The potential energy of the capacitor increases or decreases depending on the value of the dielectric constant of the capacitor.
C)The potential energy of the capacitor remains the same.
D)The potential energy of the capacitor increases.
E)More information is needed to answer the question.

Question 22

Three identical capacitors are connected in parallel to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

A)9Q
B)3Q
C)Q
D)Q/3
E)Q/9

Question 23

FIGURE 24-4
Two parallel-plate capacitors are connected in series to a battery as shown in Fig. 24-4. A dielectric is inserted in capacitor C₁. What happens to the charge on capacitor C₂?

A)The charge on C₂ increases or decreases depending on the value of the voltage of the battery.
B)The charge on C₂ increases.
C)The charge on C₂ increases or decreases depending on the value of the dielectric constant of the dielectric.
D)The charge on C₂ decreases.
E)The charge on C₂ remains the same.

Question 24

A parallel-plate capacitor is charged by a battery and then the battery is removed and a dielectric of constant K is used to fill the gap between the plates. Inserting the dielectric changes the energy stored by a factor of

A)1/K.
B)K.
C)2.
D)K - 1.
E)1 (no change).

Question 25

A capacitor consists of a set of two parallel plates of area A separated by a distance d. The capacitor plates carry charges +Q and -Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will

A)double.
B)quadruple.
C)be cut in half.
D)be cut in fourth.
E)not change.

Question 26

A parallel-plate capacitor of capacitance C is connected to a battery of voltage V until it is fully charged. The energy density in the capacitor is then equal to u. If the same capacitor is then connected to a battery of voltage 2V its energy density becomes equal to

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

Question 27

Capacitance of capacitors depends upon

A)the material between the conductors.
B)the geometry of the conductors.
C)the space between the conductors.
D)all of these answers.
E)none of these answers.

Question 28

FIGURE 24-1
Fig. 24-1 shows 3 capacitors, of equal capacitance C, connected to a battery of voltage V. What is the equivalent capacitance of this combination?

A)3C/2
B)C/2
C)2C/3
D)3 C
E)C/3

Question 29

A dielectric material such as paper is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field between the plates?

A)no change
B)becomes stronger
C)becomes weaker
D)reduces to zero
E)cannot be determined without additional information

Question 30

FIGURE 24-3
Three capacitors C₁, C₂, and C₃ are connected to a battery as shown in Fig. 24-3. The three capacitors have equal capacitances. Which capacitor stores the most potential energy?

A)C₃
B)C₂
C)C₁
D)C₂ or C₃. They store the same amount of energy
E)All three capacitors store the same amount of energy.

Question 31

5.00 μF, 10.0 μF, and 50.0 μF capacitors are connected in series across a 12.0-V battery.
(a) How much charge is stored in the 5.00-μF capacitor?
(b) What is the potential difference across the 10.0-μF capacitor?

Question 32

A 15-μF capacitor is connected to a 50-V battery and becomes fully charged. The battery is removed and a slab of dielectric that completely fills the space between the plates is inserted. The dielectric has a dielectric constant of 5.0.
(a) What is the capacitance of the capacitor after the slab is inserted?
(b) What is the voltage across the capacitor's plates after the slab is inserted?

Question 33

A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery.
(a) What is the electric field between the plates?
(b) What is the capacitance of the capacitor?
(c) What is the charge on the capacitor?

Question 34

Two capacitors of 6.00 μF and 8.00 μF are connected in parallel. The combination is then connected in series with a 12.0-V battery and a 14.0-μF capacitor.
(a) What is the equivalent capacitance?
(b) What is the charge on the 6.00-μF capacitor?
(c) What is the voltage across the 6.00-μF capacitor?

Question 35

When a parallel-plate capacitor of capacitance C is connected to a battery of voltage V, the energy density in the capacitor is u. If the voltage of battery is doubled, which of the following changes would keep the energy density equal to its previous value u?

A)doubling the spacing of the plates
B)doubling the size of the plates
C)reducing the size of the plates by half
D)reducing the spacing of the plates
E)The energy density is unaffected by a change in the voltage.

Question 36

FIGURE 24-5
Four capacitors are connected across a 90-V DC source as shown in Fig. 24-5.
(a) What is the charge on the 4.0-μF capacitor?
(b) What is the charge on a 2.0-μF capacitor?
(c) What is the charge on the 3.0-μF capacitor?
(d) What is the voltage across the 6-μF capacitor?

Question 37

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. If the separation between the plates is doubled, the magnitude of the electrical energy stored on the capacitor will

A)double.
B)quadruple.
C)be cut in half.
D)be cut in fourth.
E)not change.

Question 38

If the voltage on a capacitor is doubled, then the energy stored by the capacitor

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

Question 39

FIGURE 24-2
Fig. 24-2 shows three capacitors connected to a battery. The capacitances are such that C₁ = 2 C₂ and C₁ = 3C₃. Which capacitor stores the smallest amount of charge?

A)C₂
B)C₃
C)C₁
D)C₂ or C₃
E)All three capacitors store the same amount of charge.

Question 40

A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V battery.
(a) What is the voltage across the 1.0-μF capacitor?
(b) What is the voltage across the 2.0-μF capacitor?

Question 41

A parallel-plate capacitor has a voltage V = 6.0 V between its plates. Each plate carries a surface charge density σ = 7.0 nC/m². What is the separation of the plates?

A)8.2 mm
B)2.5 mm
C)1.2 mm
D)5.6 mm
E)7.6 mm

Question 42

The capacitance per unit length of a coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm?

A)3.0 mm
B)2.0 mm
C)4.0 mm
D)0.50 mm
E)1.0 mm

Question 43

A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 4.0 × 10^-2 m². What is the capacitance of this capacitor with air between these plates?

A)8.9 × 10^-11 F
B)8.9 × 10^-12 F
C)8.9 × 10^-13 F
D)8.9 × 10^-14 F
E)8.9 × 10^-15 F

Question 44

The magnitude of the charge on each plate of a parallel plate capacitor is 4 μC and the potential difference between the plates is 80 V. What is the capacitance of this capacitor?

A)0.1 × 10^-6 F
B)300 × 10^-6 F
C)100 × 10^-6 F
D)20 × 10^-6 F
E)5 × 10^-8 F

Question 45

FIGURE 24-8
A system of capacitors is connected across a 90 V DC voltage source as shown in Fig. 24-8. What is the equivalent capacitance of this system?

A)1.5 μF
B)15 μF
C)3.6 μF
D)3.3 μF
E)None of the other answers is correct.

Question 46

A 4.0 μF and a 6.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 6.0 μF capacitor?

A)2.0 μC
B)4.0 μC
C)12 μC
D)25 μC
E)19 μC

Question 47

FIGURE 24-6
Three capacitors are connected as shown in Fig. 24-6. What is the equivalent capacitance between points A and B?

A)1.7 μF
B)4.0 μC
C)7.1 μF
D)12 μF
E)8.0 μF

Question 48

A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel combination then being connected in series with a 3 pF capacitor. The resulting equivalent capacitance is

A)1.5 pF.
B)6 pF.
C)3 pF.
D)4.5 pF.
E)5 pF.

Question 49

What charge appears on the plates of a 6.0-μF capacitor when it is charged to 40 V?

A)60 μC
B)120 μC
C)180 μC
D)240 μC
E)350μC

Question 50

A 2.0 μF and a 4.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 2.0 μF capacitor?

A)2.0 μC
B)4.0 μC
C)12 μC
D)11 μC
E)25 μC

Question 51

The potential difference between the plates of a parallel plate capacitor is 35 V and the electric field between the plates has a strength of 750 V/m. If the plate area is 4.0 × 10^-2 m², what is the capacitance of this capacitor?

A)7.6 × 10^-14 F
B)7.6 × 10^-12 F
C)7.6 × 10^-11 F
D)7.6 × 10^-10 F
E)None of the other choices is correct.

Question 52

A parallel-plate capacitor has a plate separation of 5.0 cm. If the potential difference between the plates is 2000 V, with the top plate at the higher potential, what is the electric field between the plates?

A)100 N/C upward
B)100 N/C downward
C)4000 N/C downward
D)40000 N/C upward
E)40000 N/C downward

Question 53

FIGURE 24-9
In Fig. 24-9, three capacitors with capacitances C₁ = 4 μF, C₂ = 3μF, and C₃ = 2 μF, are connected to a battery of voltage V = 12 V. What is the charge on capacitor C₂ ?

A)16 μC
B)32 μC
C)2μC
D)8 μC
E)4 μC

Question 54

FIGURE 24-10
Fig. 24-10 shows three capacitors connected to a battery of voltage V = 6 V. The charges on the capacitors are known to be Q = 24 μC for C₁ and C₂, and Q₃ = 96 μC for C₃. What are the values of the capacitances C₁, C₂, and C₃?

A)C₁ = 8 μF, C₂ = 16 μF, C₃ = 24 μF
B)C₁ = 6 μF, C₂ = 12 μF, C₃ = 16 μF
C)C₁ = 10 μF, C₂ = 20 μF, C₃ = 30 μF
D)C₁ = 21 μF, C₂ = 7 μF, C₃ = 3 μF
E)C₁ = 5 μF, C₂ = 14 μF, C₃ = 18 μF

Question 55

Two concentric conducting spheres of radii a = 5 cm and b = 10 cm have a potential difference V = 100 V between them. What is the charge carried by each sphere?

A)100 nC
B)5.5 nC
C)1.1 nC
D)10 nC
E)2.2 nC

Question 56

A metal cylinder of radius 2.0 mm is concentric with another metal cylinder of radius 5.0 mm. If the space between the cylinders is filled with air and the length of the cylinders is 50 cm, the capacitance of the arrangement is

A)33 pF.
B)60 pF.
C)22 pF.
D)30 pF.
E)11 pF.

Question 57

A parallel-plate capacitor has plates of area 0.80 m² separated by a distance of 3.0 mm. What is this capacitor's capacitance?

A)270 F
B)70 F
C)2.4 × 10^-9 F
D)4.8 × 10^-10 F
E)3.6 × 10^-10 F

Question 58

A 5.0 μF and a 7.0 μF capacitor are connected in series across an 8.0-V DC source. What is the voltage across the 5.0 μF capacitor?

A)0 V
B)8.0 V
C)2.7 V
D)3.6 V
E)4.7 V

Question 59

A 12 mF capacitor is connected in series with a 4 mF capacitor, the combination being connected across a 6 V power supply. The charge on the 12 mF capacitor is

A)24 mC.
B)12 mC.
C)18 mC.
D)72 mC.
E)36 mC.

Question 60

FIGURE 24-7
What is the equivalent capacitance of the capacitor network shown in Fig. 24-7? (All the capacitors have a capacitance C = 5 μF. The voltage of the battery is V = 6V.)

A)20 μF
B)3 μF
C)10 μF
D)5 μF
E)1 μF

Question 61

A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 6.0 × 10^-2 m². What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates?

A)3.7 × 10^-12 F
B)3.7 × 10^-14 F
C)16 × 10^-14 F
D)32 × 10^-14 F
E)32 × 10^-12 F

Question 62

A 20-μF capacitor has a charge of 60 μC. How much energy is stored in this capacitor?

A)70 μJ
B)80 μJ
C)90 μJ
D)100 μJ
E)110 μJ

Question 63

A parallel-plate capacitor is filled with a dielectric with K = 4. The plate area is 3 m² and the plate separation is 2 mm. The capacitance of this capacitor is

A)8 nF.
B)210 nF.
C)18 nF.
D)53 nF.
E)13 nF.

Question 64

A parallel plate capacitor has a potential difference between the plates of 80 V. If the charge on one of the plates of the capacitor is +8.0 μC, what is the electrical energy stored by this capacitor?

A)640 × 10^-6 J
B)320 × 10^-6 J
C)5.0 × 10^-8 J
D)6.0 × 10^-8 J
E)3.0 × 10^-8 J

Question 65

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V battery. How much work was done in charging this capacitor?

A)6.00 μJ
B)24.0 μJ
C)12.0 μJ
D)144 μJ
E)576 J

Question 66

A 6.00-μF parallel plate capacitor has a charge of + 40.0 μC and - 40.0 μC on each plate, respectively. The potential energy stored in this capacitor is:

A)103 μJ
B)113 μJ
C)123 μJ
D)133 μJ
E)143 μJ

Question 67

A parallel-plate capacitor has a capacitance of 10 mF and charged with a 20 V power supply. The power supply is then removed and a dielectric of dielectric constant 4 is used to fill the space between the plates. The energy now stored by the capacitor is

A)250 mJ.
B)125 mJ.
C)500 mJ.
D)zero.
E)62.5 mJ.

Question 68

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20 V power supply. The power supply is then removed and a dielectric of dielectric constant 4 is used to fill the space between the plates. The voltage now across the capacitor is

A)zero.
B)20 V.
C)5 V.
D)10 V.
E)80 V.

Question 69

A 6.0-μF air capacitor is connected across a 100-V battery. After the battery fully charges the capacitor, the capacitor is immersed in transformer oil (dielectric constant = 4.5). How much additional charge flows from the battery, which remained connected during the process?

A)1.2 mC
B)1.5 mC
C)1.7 mC
D)2.1 mC
E)2.5 mC

Question 70

Two large non-conducting plates of surface area A = 0.25 m² carry equal but opposite charges Q = 75 μC. What is the energy density of the electric field between the two plates?

A)1.7 × 10⁷ J/m³
B)5.1 × 10¹⁵ J/m³
C)3.4 × 10⁷ J/m³
D)0
E)2.5 × 10¹⁵ J/m³

Question 71

A cylindrical capacitor is made of two concentric cylinders. The inner cylinder has radius r₁ = 4 mm, and the outer one a radius r₂ = 8 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference V = 4 V is applied between the inner and outer cylinder?

A)9.6 × 10^-8 J
B)1.3 × 10^-8 J
C)6.3 × 10^-8 J
D)0.34 × 10^-8 J
E)4.6 × 10^-8 J

Question 72

A parallel-plate capacitor stores a charge Q = 4.00 nC when connected to a battery of voltage V = 10.0 V. The energy density is then u = 3.62 × 10^-4 J/m³. What is the surface area of the plates?

A)0.0250 m²
B)0.0500 m²
C)0.0923 m²
D)0.0387 m²
E)0.0103 m²

Question 73

A 4-μF capacitor has a potential drop of 20 V between its plates. The electric potential energy stored in this capacitor is:

A)0.8 μJ
B)8 μJ
C)80 μJ
D)800 μJ
E)8000 μJ