Deck 25: Capacitance

Question 1

A farad is the same as a:

A) J/V
B) V/J
C) C/V
D) V/C
E) N/C

Answer 1

C/V

Question 2

The capacitance of a single isolated spherical conductor with radius R is proportional to:

A) R
B) R²
C) 1/R
D) 1/R²
E) none of these

Answer 2

R

Question 3

Pulling the plates of an isolated charged capacitor apart:

A) increases the capacitance
B) increases the potential difference
C) does not affect the potential difference
D) decreases the potential difference
E) does not affect the capacitance

Answer 3

increases the potential difference

Question 4

Each plate of a capacitor stores a charge of magnitude 1 mC when a 100-V potential difference is applied. The capacitance is:

A) 5 $\mu$ F
B) 10 $\mu$ F
C) 50 $\mu$ F
D) 100 $\mu$ F
E) none of these

Question 5

If both the plate area and the plate separation of a parallel-plate capacitor are doubled, the capacitance is:

A) doubled
B) halved
C) unchanged
D) one-fourth the original
E) quadrupled

Question 6

The capacitance of a cylindrical capacitor can be increased by:

A) decreasing both the radius of the inner cylinder and the length
B) increasing both the radius of the inner cylinder and the length
C) increasing the radius of the outer cylindrical shell and decreasing the length
D) decreasing the radius of the inner cylinder and increasing the radius of the outer cylindrical shell
E) only by decreasing the length

Question 7

Two conducting spheres have radii of R₁ and R₂ with R₁ greater than R₂. If they are far apart the capacitance is proportional to:

A) R₁R₂/(R₁ - R₂)
B)
C) (R₁ - R₂)/R₁R₂
D)
E) none of these

Question 8

The capacitance of a parallel-plate capacitor is:

A) proportional to the plate area
B) proportional to the charge stored
C) independent of any material inserted between the plates
D) proportional to the potential difference of the plates
E) proportional to the plate separation

Question 9

A parallel-plate capacitor has a plate area of 0.2 m² and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 4 *10^-6 C the potential difference across the plates is approximately:

A) 0 V
B) 4 * 10^-2 V
C) 2 *10² V
D) 2 *10⁵ V
E) 4 * 10⁸ V

Question 10

If the charge on a parallel-plate capacitor is doubled:

A) the capacitance is halved
B) the capacitance is doubled
C) the electric field is halved
D) the electric field is doubled
E) the surface charge density is not changed on either plate

Question 11

A parallel-plate capacitor C has a charge Q. The actual charges on its plates are:

A) Q, Q
B) Q/2, Q/2
C) Q, -Q
D) Q/2, -Q/2
E) Q, 0

Question 12

The units of capacitance are equivalent to:

A) J/C
B) V/C
C) J²/C
D) C/J
E) C²/J

Question 13

The capacitance of a parallel-plate capacitor with plate area A and plate separation d is given by:

A) $\varepsilon$ ₀d/A
B) $\varepsilon$ ₀d/2A
C) $\varepsilon$ ₀A/d
D) $\varepsilon$ ₀A/2d
E) $\varepsilon$ d/ $\varepsilon$ ₀

Question 14

The capacitance of a parallel-plate capacitor can be increased by:

A) increasing the charge
B) decreasing the charge
C) increasing the plate separation
D) decreasing the plate separation
E) decreasing the plate area

Question 15

To charge a 1-F capacitor with 2 C requires a potential difference of:

A) 0.2 V
B) 0.5 V
C) 2 V
D) 5 V
E) none of these

Question 16

If the plate separation of an isolated charged parallel-plate capacitor is doubled:

A) the electric field is doubled
B) the potential difference is halved
C) the charge on each plate is halved
D) the surface charge density on each plate is doubled
E) none of the above

Question 17

The capacitance of a spherical capacitor with inner radius a and outer radius b is proportional to:

A) a/b
B) b - a
C) b² - a²
D) ab/(b - a)
E) ab/(b² - a²)

Question 18

If the plate area of an isolated charged parallel-plate capacitor is doubled:

A) the electric field is doubled
B) the potential difference is halved
C) the charge on each plate is halved
D) the surface charge density on each plate is doubled
E) none of the above

Question 19

The plate areas and plate separations of five parallel plate capacitors are Rank these according to their capacitances, least to greatest.

A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 5, then 3 and 4 tie, then 1, then 2
D) 4, then 1 and 2 tie, then 5, then 3
E) 3, then 5, then 1 and 2 tie, then 4

Question 20

A parallel-plate capacitor has a plate area of 0.2 m² and a plate separation of 0.1 mm. To obtain an electric field of 2.0 * 10⁶ V/m between the plates, the magnitude of the charge on each plate should be:

A) 3.5 * 10^-6 C
B) 7.1 *10^-6 C
C) 1.4 *10^-5 C
D) 1.8 * 10^-5 C
E) 8.9 *10^-5 C

Question 21

Each of the three 25- $\mu$ F capacitors shown is initially uncharged. How many coulombs of charge pass through the ammeter A after the switch S is closed?

A) 0.033 C
B) 0.10 C
C) 0.30 C
D) 10 C
E) none of these

Question 22

Capacitors C₁ and C₂ are connected in series and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

A) the charge on C₁
B) the sum of the charges on C₁ and C₂
C) the difference of the charges on C₁ and C₂
D) the product of the charges on C₁ and C₂
E) none of the above

Question 23

A parallel-plate capacitor has a plate area of 0.3 m² and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 5 *10^-6 C then the force exerted by one plate on the other has a magnitude of about:

A) 5 N
B) 9 N
C) 1 *10⁴ N
D) 9 * 10⁵ N
E) 2 * 10⁷ N

Question 24

Capacitors C₁ and C₂ are connected in parallel and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

A) the charge on C₁
B) the sum of the charges on C₁ and C₂
C) the difference of the charges on C₁ and C₂
D) the product of the charges on C₁ and C₂
E) none of the above

Question 25

Capacitor C₁ is connected alone to a battery and charged until the magnitude of the charge on each plate is 4.0 * 10 ^{- 8} C. Then it is removed from the battery and connected to two other capacitors C₂ and C₃, as shown. The charge on the positive plate of C₁ is then 1.0 * 10 ^{- 8} C. The charges on the positive plates of C₂ and C₃ are:

A) q₂ = 3.0 *10 ^{- -8} C and q₃ = 3.0 *10 1^{- 8} C
B) q₂ = 2.0* 10 ^{- 8} C and q₃ = 2.0 *10 ^- 0⁸ C
C) q₂ = 5.0 *10 ^{- 8} C and q₃ = 1.0 * 10 ^{- 8} C
D) q₂ = 3.0 * 10 ^{- 8} C and q₃ = 1.0 *10 ^{- 8} C
E) q₂ = 1.0 *10 ^{- 8} C and q₃ = 3.0 *10 ^{- 8} C

Question 26

Each of the four capacitors shown is 500 $\mu$ F. The voltmeter reads 1000V. The magnitude of the charge on each capacitor plate is:

A) 0.2 C
B) 0.5 C
C) 20 C
D) 50 C
E) none of these

Question 27

Two identical capacitors, each with capacitance C, are connected in parallel and the combination is connected in series to a third identical capacitor. The equivalent capacitance of this arrangement is:

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

Question 28

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in series and charged from a battery. They store charges P and Q, respectively. When disconnected and charged separately using the same battery, they have charges R and S, respectively. Then:

A) R > S > Q = P
B) P > Q > R = S
C) R > P = Q > S
D) R = P > S = Q
E) R > P > S = Q

Question 29

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in parallel and a potential difference is applied across the combination. The 2- $\mu$ F capacitor has:

A) twice the charge of the 1- $\mu$ F capacitor
B) half the charge of the 1- $\mu$ F capacitor
C) twice the potential difference of the 1- $\mu$ F capacitor
D) half the potential difference of the 1- $\mu$ F capacitor
E) none of the above

Question 30

Two parallel-plate capacitors with the same plate area but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:

A) potential difference
B) energy density
C) electric field between the plates
D) charge on the positive plate
E) plate separation

Question 31

Capacitors C₁ and C₂ are connected in series. The equivalent capacitance is given by:

A) C₁C₂/(C₁ + C₂)
B) (C₁ + C₂)/C₁C₂
C) 1/(C₁ + C₂)
D) C₁/C₂
E) C₁ + C₂

Question 32

Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:

A) potential difference
B) energy density
C) electric field between the plates
D) charge on the positive plate
E) dielectric constant

Question 33

Two identical capacitors are connected in series and two, each identical to the first, are connected in parallel. The equivalent capacitance of the series connection is ________ the equivalent capacitance of parallel connection.

A) twice
B) four times
C) half
D) one fourth
E) the same as

Question 34

Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:

A) potential difference
B) stored energy
C) energy density
D) electric field between the plates
E) charge on the positive plate

Question 35

A battery is used to charge a series combination of two identical capacitors. If the potential difference across the battery terminals is V and total charge Q flows through the battery during the charging process then the charge on the positive plate of each capacitor and the potential difference across each capacitor are:

A) Q/2 and V/2, respectively
B) Q and V, respectively
C) Q/2 and V, respectively
D) Q and V/2, respectively
E) Q and 2V, respectively

Question 36

Two parallel-plate capacitors with different plate separation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:

A) potential difference
B) stored energy
C) electric field between the plates
D) charge on the positive plate
E) dielectric constant

Question 37

The diagram shows six 6- $\mu$ F capacitors. The capacitance between points a and b is:

A) 1 $\mu$ F
B) 3 $\mu$ F
C) 4 $\mu$ F
D) 6 $\mu$ F
E) 9 $\mu$ F

Question 38

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in series and a potential difference is applied across the combination. The 2- $\mu$ F capacitor has:

A) twice the charge of the 1- $\mu$ F capacitor
B) half the charge of the 1- $\mu$ F capacitor
C) twice the potential difference of the 1- $\mu$ F capacitor
D) half the potential difference of the 1- $\mu$ F capacitor
E) none of the above

Question 39

A battery is used to charge a parallel combination of two identical capacitors. If the potential difference across the battery terminals is V and the total charge Q flows through the battery during the charging process then the charge on the positive plate of each capacitor and the potential difference across each capacitor are:

A) Q/2 and V/2, respectively
B) Q and V, respectively
C) Q/2 and V, respectively
D) Q and V/2, respectively
E) Q and 2V, respectively

Question 40

Capacitor C₁ and C₂ are connected in parallel. The equivalent capacitance is given by:

A) C₁C₂/(C₁ + C₂)
B) (C₁ + C₂)/C₁C₂
C) 1/(C₁ + C₂)
D) C₁/C₂
E) C₁ + C₂

Question 41

A certain capacitor has a capacitance of 5.0 $\mu$ F. After it is charged to 5 $\mu$ C and isolated, the plates are brought closer together so its capacitance becomes 10 $\mu$ F. The work done by the agent is about:

A) 0 J
B) 1.25 * 10^-6 J
C) -1.25 *10^-6 J
D) 8.3 *10^-7 J
E) -8.3 * 10^-7 J

Question 42

What happens to the atoms in a dielectric when it is placed between the plates of a charged capacitor?

A) They begin to conduct electricity.
B) They create an induced electric field that is in the opposite direction of the field due to the charges on the plates.
C) They create an induced electric field that is in the same direction as the field due to the charges on the plates.
D) They completely cancel the electric field due to the charges on the plates.
E) They rotate so their positive ends are towards the positively charged plate.

Question 43

A dielectric slab is slowly inserted between the plates of a parallel plate capacitor while the capacitor is connected to a battery. As it is being inserted:

A) the capacitance, the potential difference between the plates, and the charge on the positive plate all increase
B) the capacitance, the potential difference between the plates, the charge on the positive plate all decrease
C) the potential difference between the plates increases, the charge on the positive plate decreases, and the capacitance remains the same
D) the capacitance and the charge on the positive plate decrease but the potential difference between the plates remains the same
E) the capacitance and the charge on the plate increase but the potential difference between the plates remains the same

Question 44

The quantity (1/2) $\varepsilon$ ₀E² has the dimensions of:

A) energy/farad
B) energy/coulomb
C) energy
D) energy/volume
E) energy/volt

Question 45

A 20-µF capacitor is charged to 200 V. Its stored energy is:

A) 4000 J
B) 4 J
C) 0.4 J
D) 0.1 J
E) 0.004 J

Question 46

To store a total of 0.040 J of energy in the two identical capacitors shown, each should have a capacitance of:

A) 0.50 $\mu$ F
B) 1.0 $\mu$ F
C) 1.5 $\mu$ F
D) 2.0 $\mu$ F
E) 4.0 $\mu$ F

Question 47

An air-filled capacitor is charged, and then a dielectric is inserted. As a result, there is an induced charge on the dielectric. What is the difference between induced charge and free charge?

A) There is no difference.
B) Induced charge does not result in a net charge on the dielectric.
C) Induced charge is smaller than free charge.
D) Free charge creates an electric field, but induced charge does not.
E) Free charge creates an electric potential, but induced charge does not.

Question 48

Let Q denote charge, V denote potential difference and U denote stored energy. Of these quantities, capacitors in parallel must have the same:

A) Q only
B) V only
C) U only
D) Q and U only
E) V and U only

Question 49

A charged capacitor stores 10 C at 40 V. Its stored energy is:

A) 400 J
B) 200 J
C) 4 J
D) 2.5 J
E) 1.25 J

Question 50

A parallel-plate capacitor has a plate area of 0.30 m² and a plate separation of 0.10 mm. If the charge on each plate has a magnitude of 5.0 *10^-6 C, what is the energy density in its electric field?

A) 0.16 J/m³
B) 3.5 J/m³
C) 7.8 J/m³
D) 16 J/m³
E) 24 J/m³

Question 51

An air-filled parallel-plate capacitor has a capacitance of 1 pF. The plate separation is then doubled and a wax dielectric is inserted, completely filling the space between the plates. As a result, the capacitance becomes 2 pF. The dielectric constant of the wax is:

A) 0.25
B) 0.50
C) 2.0
D) 4.0
E) 8.0

Question 52

What is the difference between a polar dielectric and a nonpolar dielectric?

A) A polar dielectric has a permanent electric field.
B) A nonpolar dielectric never has an internal electric field.
C) The molecules of a polar dielectric have a permanent electric dipole moment.
D) A nonpolar dielectric can have an induced electric field in any direction.
E) A polar dielectric is always aligned with the Earth's electric field.

Question 53

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in series and charged by a battery. They store energies P and Q, respectively. When disconnected and charged separately using the same battery, they have energies R and S, respectively. Then:

A) R > P > S > Q
B) P > Q > R > S
C) R > P > Q > S
D) P > R > S > Q
E) R > S > Q > P

Question 54

A parallel-plate capacitor, with air dielectric, is charged by a battery, after which the battery is disconnected. A slab of glass dielectric is then slowly inserted between the plates. As it is being inserted:

A) a force repels the glass out of the capacitor
B) a force attracts the glass into the capacitor
C) no force acts on the glass
D) a net charge appears on the glass
E) the glass makes the plates repel each other

Question 55

One of the materials listed below is to be placed between two identical metal sheets, with no air gap, to form a parallel-plate capacitor. Which produces the greatest capacitance?

A) material of thickness 0.1 mm and dielectric constant 2
B) material of thickness 0.2 mm and dielectric constant 3
C) material of thickness 0.3 mm and dielectric constant 2
D) material of thickness 0.4 mm and dielectric constant 8
E) material of thickness 0.5 mm and dielectric constant 11

Question 56

There are approximately 10 explosions in the US every year due to agricultural grain (corn and soybean) dust. Why is corn dust so dangerous?

A) Corn contains a lot of oil and is therefore very flammable.
B) Grain elevators use a lot of flammable material while processing the corn.
C) Corn dust has a lot of surface area and can be ignited by even a very small spark, which can be created simply by a person walking around.
D) Due to the presence of lots of agricultural material, grain elevators are especially rich in oxygen.
E) Workers are not careful about where they throw their cigarette butts, and sometimes set the corn on fire.

Question 57

A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the plates are pulled apart to twice their original separation. This process will double the:

A) capacitance
B) surface charge density on each plate
C) stored energy
D) electric field between the two places
E) charge on each plate

Question 58

Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy and capacitor B is uncharged. The capacitors are then connected in parallel. The total stored energy in the capacitors is now:

A) 16 J
B) 8 J
C) 4 J
D) 2 J
E) 1 J

Question 59

Let Q denote charge, V denote potential difference and U denote stored energy. Of these quantities, capacitors in series must have the same:

A) Q only
B) V only
C) U only
D) Q and U only
E) V and U only

Question 60

Which of the following is not a dielectric?

A) silicon
B) germanium
C) polystyrene
D) titanium
E) paper

Question 61

Two capacitors are identical except that one is filled with air and the other with oil. Both capacitors carry the same charge. The ratio of the electric fields E_air/E_oil is:

A) between 0 and 1
B) 0
C) 1
D) between 1 and infinity
E) infinite