Deck 26: Capacitance and Dielectrics

Question 1

What is the equivalent capacitance of the combination shown?

A)29 μF
B)10 μF
C)40 μF
D)25 μF
E)6.0 μF

Answer 1

10 μF

Question 2

Determine the equivalent capacitance of the combination shown when C = 24 μF.

A)20 μF
B)36 μF
C)16 μF
D)45 μF
E)27 μF

Answer 2

16 μF

Question 3

Determine the energy stored in the 60-μF capacitor.

A)2.4 mJ
B)3.0 mJ
C)3.6 mJ
D)4.3 mJ
E)6.0 mJ

Answer 3

3.0 mJ

Question 4

Determine the equivalent capacitance of the combination shown when C = 45 μF.

A)28 μF
B)36 μF
C)52 μF
D)44 μF
E)23 μF

Question 5

What is the total energy stored by C₃ when C₁ = 50 μF,C₂ = 30 μF,C₃ = 36 μF,C₄ = 12 μF,and V₀ = 30 V?

A)6.3 mJ
B)25 mJ
C)57 mJ
D)1.6 mJ
E)14 mJ

Question 6

Determine the energy stored in the 40-μF capacitor.

A)2.4 mJ
B)1.6 mJ
C)2.0 mJ
D)2.9 mJ
E)4.0 mJ

Question 7

What is the potential difference across C₂ when C₁ = 5.0 μF,C₂ = 15 μF,C₃ = 30 μF,and V₀ = 24 V?

A)21 V
B)19 V
C)16 V
D)24 V
E)8.0 V

Question 8

Determine the equivalent capacitance of the combination shown when C = 12 pF.

A)48 pF
B)12 pF
C)24 pF
D)6.0 pF
E)59 pF

Question 9

Determine the energy stored in C₂ when C₁ = 15 μF,C₂ = 10 μF,C₃ = 20 μF,and V₀ = 18 V.

A)0.72 mJ
B)0.32 mJ
C)0.50 mJ
D)0.18 mJ
E)1.60 mJ

Question 10

Determine the equivalent capacitance of the combination shown when C = 15 mF.

A)20 mF
B)16 mF
C)12 mF
D)24 mF
E)75 mF

Question 11

Determine the energy stored in C₁ when C₁ = 10 μF,C₂ = 12 μF,C₃ = 15 μF,and V₀ = 70 V.

A)6.5 mJ
B)5.1 mJ
C)3.9 mJ
D)8.0 mJ
E)9.8 mJ

Question 12

If C = 10 μF,what is the equivalent capacitance for the combination shown?

A)7.5 μF
B)6.5 μF
C)7.0 μF
D)5.8 μF
E)13 μF

Question 13

Determine the energy stored by C₄ when C₁ = 20 μF,C₂ = 10 μF,C₃ = 14 μF,C₄ = 30 μF,and V₀ = 45 V.

A)3.8 mJ
B)2.7 mJ
C)3.2 mJ
D)2.2 mJ
E)8.1 mJ

Question 14

Determine the equivalent capacitance of the combination shown when C = 45 μF.

A)36 μF
B)32 μF
C)34 μF
D)30 μF
E)38 μF

Question 15

How much energy is stored in the 50-μF capacitor when V_a − V_b = 22V?

A)0.78 mJ
B)0.58 mJ
C)0.68 mJ
D)0.48 mJ
E)0.22 mJ

Question 16

What is the equivalent capacitance of the combination shown?

A)20 μF
B)90 μF
C)22 μF
D)4.6 μF
E)67 μF

Question 17

Determine the charge stored by C₁ when C₁ = 20 μF,C₂ = 10 μF,C₃ = 30 μF,and V₀ = 18 V.

A)0.37 mC
B)0.24 mC
C)0.32 mC
D)0.40 mC
E)0.50 mC

Question 18

What is the total energy stored in the group of capacitors shown if the charge on the 30-μF capacitor is 0.90 mC?

A)29 mJ
B)61 mJ
C)21 mJ
D)66 mJ
E)32 mJ

Question 19

What total energy is stored in the group of capacitors shown if the potential difference V_ab is equal to 50 V?

A)48 mJ
B)27 mJ
C)37 mJ
D)19 mJ
E)10 mJ

Question 20

Determine the equivalent capacitance of the combination shown when C = 12 nF.

A)34 nF
B)17 nF
C)51 nF
D)68 nF
E)21 nF

Question 21

A 3.0-μF capacitor charged to 40 V and a 5.0-μF capacitor charged to 18 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 3.0-μF capacitor?

A)11 μC
B)15 μC
C)19 μC
D)26 μC
E)79 μC

Question 22

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them.After the plates are 2d apart,the new capacitance and the potential difference between the plates are

A) C₀, V₀
B) C₀,V₀
C) C₀,2V₀
D)C₀,2V₀
E)2C₀,2V₀

Question 23

When a capacitor has a charge of magnitude 80 μC on each plate the potential difference across the plates is 16 V.How much energy is stored in this capacitor when the potential difference across its plates is 42 V?

A)1.0 mJ
B)4.4 mJ
C)3.2 mJ
D)1.4 mJ
E)1.7 mJ

Question 24

A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other.What is the final charge on the 6.0-mF capacitor?

A)20 mC
B)8.0 mC
C)10 mC
D)12 mC
E)230 mC

Question 25

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart,the capacitance of the capacitor and the magnitude of the charge on the plates are

A) C₀, Q₀
B) C₀,Q₀
C)C₀,Q₀
D)2C₀,Q₀
E)2C₀,2Q₀

Question 26

A 25-μF capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other,with the two positive plates connected and the two negative plates connected.The final potential difference across the 25-μF capacitor is 36 V.What is the value of the capacitance of C?

A)43 μF
B)29 μF
C)22 μF
D)58 μF
E)63 μF

Question 27

A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-μF capacitor.If the final potential difference across the 60-μF capacitor is 40 V,determine C.

A)49 μF
B)32 μF
C)40 μF
D)90 μF
E)16 μF

Question 28

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added,the magnitude of the charge on the plates and the potential difference between them are

A) Q₀, V₀
B)Q₀, V₀
C)Q₀,V₀
D)3Q₀,V₀
E)3Q₀,3V₀

Question 29

A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor.What is the final potential difference across the 30-μF capacitor?

A)15 V
B)24 V
C)18 V
D)21 V
E)40 V

Question 30

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them.After the plates are 2d apart,the magnitude of the charge on the plates and the potential difference between them are

A) Q₀, V₀
B)Q₀, V₀
C)Q₀,V₀
D)Q₀,2V₀
E)2Q₀,2V₀

Question 31

A 15-μF capacitor and a 25-μF capacitor are connected in parallel,and charged to a potential difference of 60 V.How much energy is then stored in this capacitor combination?

A)50 mJ
B)18 mJ
C)32 mJ
D)72 mJ
E)45 mJ

Question 32

A 30-μF capacitor is charged to an unknown potential V₀ and then connected across an initially uncharged 10-μF capacitor.If the final potential difference across the 10-μF capacitor is 20 V,determine V₀.

A)13 V
B)27 V
C)20 V
D)29 V
E)60 V

Question 33

A 6.0-μF capacitor charged to 50 V and a 4.0-μF capacitor charged to 34 V are connected to each other,with the two positive plates connected and the two negative plates connected.What is the total energy stored in the 6.0-μF capacitor at equilibrium?

A)6.1 mJ
B)5.7 mJ
C)6.6 mJ
D)7.0 mJ
E)3.8 mJ

Question 34

If V_A − V_B = 50 V,how much energy is stored in the 36-μF capacitor?

A)50 mJ
B)28 mJ
C)13 mJ
D)8.9 mJ
E)17 mJ

Question 35

A 15-μF capacitor and a 30-μF capacitor are connected in series,and charged to a potential difference of 50 V.What is the resulting charge on the 30-μF capacitor?

A)0.70 mC
B)0.80 mC
C)0.50 mC
D)0.60 mC
E)0.40 mC

Question 36

A 20-μF capacitor charged to 2.0 kV and a 40-μF capacitor charged to 3.0 kV are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20-μF capacitor after the two are so connected?

A)53 mC
B)27 mC
C)40 mC
D)80 mC
E)39 mC

Question 37

A 30-μF capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C.If the final potential difference across the 30-μF capacitor is 20 V,determine C.

A)60 μF
B)75 μF
C)45 μF
D)90 μF
E)24 μF

Question 38

A 15-μF capacitor is charged to 40 V and then connected across an initially uncharged 25-μF capacitor.What is the final potential difference across the 25-μF capacitor?

A)12 V
B)18 V
C)15 V
D)21 V
E)24 V

Question 39

If V_A − V_B = 50 V,how much energy is stored in the 54-μF capacitor?

A)50 mJ
B)13 mJ
C)28 mJ
D)8.9 mJ
E)17 mJ

Question 40

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart,the magnitude of the charge on the plates and the potential difference between them are

A) Q₀, V₀
B) Q₀,V₀
C)Q₀,V₀
D)2Q₀,V₀
E)2Q₀,2V₀

Question 41

Which of the following statements is incorrect?

A)Capacitance is always positive.
B)The symbol for potential difference between the plates of a capacitor is .
C)Water is a polar molecule.
D)When a dielectric is placed in a capacitor it serves to reduce the electric field.
E)Nonpolar molecules cannot be used for dielectric material in a capacitor.

Question 42

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added,the magnitudes of the charge on the plates and the potential difference between them are

A) Q₀, V₀.
B)Q₀, V₀.
C)Q₀,V₀.
D)Q₀,3V₀.
E)3Q₀,3V₀.

Question 43

Which of the following materials has the highest dielectric constant?

A)air
B)Mylar
C)paper
D)Pyrex glass
E)water

Question 44

A 0.120 pF parallel-plate capacitor is charged to a potential difference of 10.0 V and then disconnected from the battery.A cosmic ray burst creates 1.00 × 10⁶ electrons and 1.00 × 10⁶ positive charges between the plates.If the charges do not recombine,but reach the oppositely charged plates,by how much is the potential difference between the capacitor plates reduced?

A)1.33 V
B)7.34 V
C)8.67 V
D)1,330 V
E)8,670 V

Question 45

Into the gap between the plates of a parallel plate capacitor of capacitance
A slab of metal is inserted halfway between the plates filling one fourth of the gap between the plates.What is the resulting new capacitance?

A)
B)
C)
D)
E)

Question 46

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 × 10⁷ electrons are now placed on the negative plate of the capacitor,the voltage between the plates changes by

A)−5.0 V.
B)−1.1 V.
C)0 V.
D)+1.1 V.
E)+5.0 V.

Question 47

Which of the following is not a capacitance?

A)
B)
C)
D)
E)

Question 48

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.While it is connected to the battery,the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added,the magnitude of the charge on the plates and the new capacitance are

A) Q₀, C₀
B)Q₀, C₀
C)Q₀,C₀
D)3Q₀,C₀
E)3Q₀,3C₀

Question 49

The equivalent capacitance of the circuit shown below is

A)0.2 C.
B)0.4 C.
C)1 C.
D)4 C.
E)5 C.

Question 50

A 0.16 pF parallel-plate capacitor is charged to 10 V.Then the battery is disconnected from the capacitor.When 1.00 × 10⁷ positive charges of magnitude |e| are now placed on the positive plate of the capacitor,the voltage between the plates changes by

A)−5.0 V.
B)−1.1 V.
C)0 V.
D)+1.1 V.
E)+5.0 V.

Question 51

An electric dipole having dipole moment of magnitude p is placed in a uniform electric field having magnitude E.What is the magnitude of the greatest change in potential energy that can happen for this dipole in this field?

A)pE
B)
C)4pE
D)
E)No answer given is correct.

Question 52

An initially uncharged parallel plate capacitor of capacitance C is charged to potential V by a battery.The battery is then disconnected.Which statement is correct?

A)There is no charge on either plate of the capacitor.
B)The capacitor can be discharged by grounding any one of its two plates.
C)Charge is distributed evenly over both the inner and outer surfaces of the plates.
D)The magnitude of the electric field outside the space between the plates is approximately zero.
E)The capacitance increases when the distance between the plates increases.

Question 53

The equivalent capacitance of the circuit shown below is

A)0.2 C.
B)0.4 C.
C)1 C.
D)4 C.
E)5 C.

Question 54

A parallel plate capacitor is connected to a battery and charged to voltage V.Leah says that the charge on the plates will decrease if the distance between the plates is increased while they are still connected to the battery.Gertie says that the charge will remain the same.Which one,if either,is correct,and why?

A)Gertie,because the maximum voltage is determined by the battery.
B)Gertie,because the capacitance of the capacitor does not change.
C)Leah,because the capacitance decreases when the plate separation is increased.
D)Leah,because the capacitance increases when the plate separation is increased.
E)Neither,because the charge increases when the plate separation is increased.

Question 55

Two spheres are made of conducting material.Sphere #2 has twice the radius of Sphere #1.What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1?

A)1,since all conducting spheres have the same capacitance.
B)2
C)4
D)8
E)A single sphere has no capacitance since a second concentric spherical shell is necessary to make a spherical capacitor.Thus,none of the answers above is correct.

Question 56

The plates of a parallel plate capacitor of capacitance
Are horizontal.Into the gap a slab of dielectric material with
Is placed,filling the bottom half of the gap between the plates.What is the resulting new capacitance?

A)
B)
C)
D)
E)

Question 57

A parallel plate capacitor is charged to voltage V and then disconnected from the battery.Leopold says that the voltage will decrease if the plates are pulled apart.Gerhardt says that the voltage will remain the same.Which one,if either,is correct,and why?

A)Gerhardt,because the maximum voltage is determined by the battery.
B)Gerhardt,because the charge per unit area on the plates does not change.
C)Leopold,because charge is transferred from one plate to the other when the plates are separated.
D)Leopold,because the force each plate exerts on the other decreases when the plates are pulled apart.
E)Neither,because the voltage increases when the plates are pulled apart.

Question 58

Is it feasible to construct an air-filled parallel-plate capacitor that has its two plates separated by 0.10 mm and has a capacitance of 1.0 F? Why or why not?

Question 59

The equivalent capacitance of the circuit shown below is

A)0.50 C.
B)1.0 C.
C)1.5 C.
D)2.0 C.
E)2.5 C.

Question 60

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them.When it is connected to a battery of voltage V₀,it has charge of magnitude Q₀ on its plates.It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added,the magnitudes of the capacitance and the potential difference between the plates are

A) C₀, V₀.
B)C₀, V₀.
C)C₀,V₀.
D)3C₀, V₀.
E)3C₀,3V₀.

Question 61

A 200-volt battery is connected to a 0.50-microfarad parallel-plate,air-filled capacitor.Now the battery is disconnected,with care taken not to discharge the plates.Some Pyrex glass is then inserted between the plates,completely filling up the space.What is the final potential difference between the plates? (The dielectric constant for Pyrex is κ = 5.6. )

Question 62

An electron is released from rest at the negative plate of a parallel plate capacitor.If the distance between the plates is 5 mm and the potential difference across the plates is 5 V,with what velocity does the electron hit the positive plate? (m_e = 9.1 × 10−³¹ kg,q_e = 1.6 × 10−¹⁹ C. )

Question 63

Regarding the Earth and a cloud layer 800 m above the Earth as the "plates" of a capacitor,calculate the capacitance if the cloud layer has an area of 1.0 km².If an electric field of 2.0 × 10⁶ N/C makes the air break down and conduct electricity (lightning),what is the maximum charge the cloud can hold?