Deck 26: Capacitors and Dielectrics

Question 1

The capacitance of a conductor is increased by the ability of

A) storing a smaller amount of charge at a higher potential.
B) storing a smaller amount of charge at a lower potential.
C) storing a larger amount of charge at a lower potential.
D) storing a larger amount of charge at a higher potential.

Answer 1

storing a larger amount of charge at a lower potential.

Question 2

Knowing the potential V and the charge Q, we can derive the capacitance C by

A) $C = V / Q$
B) $C = Q ^ { 2 } V$
C) $C = Q V$
D) $C = Q / V$

Answer 2

$C = Q / V$

Question 3

A hollow metal spherical shell of radius 2.3 cm has a 12-V potential (relative to a location at infinity). The capacitance of the shell is

A) $1.5 \times 10 ^ { - 12 } \mathrm {~F}$
B) $2.6 \times 10 ^ { - 12 } \mathrm {~F}$
C) $5.1 \times 10 ^ { - 13 } \mathrm {~F} \text {. }$
D) $6.5 \times 10 ^ { - 13 } \mathrm {~F}$

Answer 3

$2.6 \times 10 ^ { - 12 } \mathrm {~F}$

Question 4

A hollow metal spherical shell of radius 2.3 cm has a 12-V potential (relative to a location at infinity). The total charge on the shell is

A) $4.6 \times 10 ^ { - 12 } \mathrm { C }$
B) $8.5 \times 10 ^ { - 12 } \mathrm { C }$
C) $1.5 \times 10 ^ { - 11 } \mathrm { C }$
D) $3.1 \times 10 ^ { - 11 } \mathrm { C } \text {. }$

Question 5

Compare two different-sized, metal spherical shells; the shell has the greater capacitance:

A) smaller-radius shell.
B) larger-radius shell.
C) neither; both have the same capacitance.
D) unknown; we need to know the potential of each shell.

Question 6

The capacitance of a metal parallel-plate capacitor is a function of

A) the charge on the plates.
B) the potential across the plates.
C) the geometry of the plates (area and separation).
D) both (a) and (b).

Question 7

A parallel-plate capacitor has capacitance of $6.5 \times 10 ^ { - 8 }$ F and charge of $8.1 \times 10 ^ { - 11 }$ C. The potential across the plates is

A) 1.2 mV.
B) 520 mV.
C) 802 V.
D) 8.0 V.

Question 8

We can effectively increase the capacitance of a charged parallel-plate capacitor by decreasing the separation distance between the plates until

A) the potential reaches zero.
B) the plates touch.
C) the charge (on one of the plates) reaches zero.
D) the dielectric breakdown of the air occurs.

Question 9

One farad is also known as

A) coulomb/volt.
B) voltcoulomb. .
C) volt/coulomb.
D) amperecoulomb. .

Question 10

The capacitance of a solid metal sphere having a radius of 20 cm is

A) 0 F.
B) 43 pF.
C) 36 pF.
D) 22 pF.

Question 11

A parallel-plate capacitor has (one) plate area of 26 cm $2$ and a separation distance between the two plates of 1.1 mm. The potential across the plates is 12 V. The capacitance is

A) 2.8 $\mu$ F
B) 53 pF.
C) 21 pF.
D) 18 $\mu$ F.

Question 12

A parallel-plate capacitor has (one) plate area of 26 cm $2$ and a separation distance between the two plates of 1.1 mm. The potential across the plates is 12 V. The charge (on one plate) is

A) $7.6 \times 10 ^ { - 10 } \mathrm { C }$
B) $5.1 \times 10 ^ { - 10 } \mathrm { C } \text {. }$
C) $2.5 \times 10 ^ { - 10 } \mathrm { C }$
D) $1.3 \times 10 ^ { - 10 } \mathrm { C }$

Question 13

A parallel-plate capacitor has (one) plate area of 26 cm $2$ and a separation distance between the two plates of 1.1 mm. The potential across the plates is 12 V. The electric field between the plates is

A) 170 N/C.
B) 11,000 N/C.
C) 1700 N/C.
D) 5600 N/C.

Question 14

A 7.5 $\mu$ F parallel-plate capacitor having a plate separation distance of 0.25 mm has 8.2 mC of charge (magnitude per plate). The electric field between the plates is

A) $8.6 \times 10 ^ { 3 }$ N/C.
B) $4.4 \times 10 ^ { 6 }$ N/C.
C) $7.5 \times 10 ^ { 4 }$ N/C.
D) $1.6 \times 10 ^ { 5 }$ N/C.

Question 15

A set of 1-F, 2-F, and 3-F capacitors is connected together so that the voltage across each capacitor is the same. The effective capacitance, as seen by the source, is

A) 0.5 F.
B) 2 F.
C) 3 F.
D) 6 F.

Question 16

A set of 1-F, 2-F, and 3-F capacitor are connected together so that the charge on each capacitor is the same. The effective capacitance, as seen by the source, is

A) 0.5 F.
B) 2 F.
C) 3 F.
D) 6 F.

Question 17

A set of 1-F, 2-F, and 3-F capacitors is connected together so that the charge on each capacitor is the same. The source voltage is 6 V. The charge on one of the capacitors is

A) 3.3 C.
B) 0.26 C.
C) 1.2 C.
D) 0.16 C.

Question 18

Three capacitors, A, B, and C, are connected in series to a source. The effective capacitance as seen by the source is

A) $A B C / ( A + B + C )$
B) $( A + B + C ) / ( A B C )$
C) $A + B + C$
D) $A B C / ( A B + B C + C A )$

Question 19

Three capacitors, A, B, and C, are connected in parallel to a source. The effective capacitance as seen by the source is

A) $A B C / ( A + B + C )$
B) $( A + B + C ) / ( A B C )$
C) $A + B + C$
D) $A B C / ( A B + B C + C A )$

Question 20

Three equal capacitors, each of capacitance A, are connected in series. The effective capacitance (as seen by the source)

A) is 3 A.
B) is A/3.
C) is A.
D) cannot be determined (we need to know A).

Question 21

Consider capacitors $$c _ { 1 } = 1 \mathrm {~F} , c _ { 2 } = 4 \mathrm {~F} , c _ { 3 } = 9 \mathrm {~F} , c _ { 4 } = 16 \mathrm {~F} , \ldots , c _ { n } = n ^ { 2 } \mathrm {~F}$$ , with $n \rightarrow \infty$ . If these infinite number of capacitors are connected in parallel, the effective capacitance as seen by the source is

A) 0 F.
B) $\infty \mathrm { F } .$
C) $6 / \pi ^ { 2 } \mathrm {~F} .$
D) 3/7 F.

Question 22

Consider capacitors $$c _ { 1 } = 1 \mathrm {~F} , c _ { 2 } = 4 \mathrm {~F} , c _ { 3 } = 9 \mathrm {~F} , c _ { 4 } = 16 \mathrm {~F} , \ldots , c _ { n } = n ^ { 2 } \mathrm {~F}$$ with $n \rightarrow \infty$ . If these infinite number of capacitors are connected in series, the effective capacitance as seen by the source is

A) 0 F.
B) $\infty \mathrm { F } .$
C) $6 / \pi ^ { 2 } \mathrm {~F} .$
D) 3/7 F.

Question 23

A vacuum dielectric, parallel-plate capacitor has a potential across the plates of 13.3 V and a plate separation distance of 1.1 mm. A polystyrene dielectric, $x = 2.5$ , is inserted between the plates (the potential remains constant). The electric field between the plates is now

A) 30,000 N/C.
B) 15,000 N/C.
C) 4800 N/C.
D) 2100 N/C.

Question 24

A parallel-plate capacitor has (one) plate area of 7.6 cm $2$ and a separation distance between the two plates of 0.55 mm. There is a nylon dielectric, $k = 3.5$ , between the plates. The potential across the plates is 12 V. The electric field between the plates is

A) 2500 N/C.
B) 3100 N/C.
C) 4300 N/C.
D) 6200 N/C.

Question 25

A parallel-plate capacitor, having a vacuum dielectric, has capacitance of 620 $\mu$ F. A Plexiglas dielectric, $k = 3.4$ , is inserted between the plates. The new capacitance is

A) 180 $\mu$ F.
B) 1400 $\mu$ F.
C) 2100 $\mu$ F.
D) 620 $\mu$ F.

Question 26

A solid spherical dielectric having $K = 3.1$ and radius of 6.2 cm has -3.5 nC of charge uniformly distributed throughout the sphere. The magnitude of the electric field at the surface is

A) 1800 N/C.
B) 2600 N/C.
C) 780 N/C.
D) 3800 N/C.

Question 27

A 500- $\mu$ F capacitor has 3.7 $\mu$ C of charge on the plates. The electric potential energy stored in the capacitor is

A) $7.1 \times 10 ^ { - 8 }$ J.
B) $5.5 \times 10 ^ { - 9 }$ J.
C) $1.4 \times 10 ^ { - 8 }$ J.
D) $8.6 \times 10 ^ { - 9 }$ J.

Question 28

A 5.5- $\mu$ F capacitor has 1.3 mJ of potential energy stored in it. The potential across the plates is

A) 22 V.
B) 15 V.
C) 11 V.
D) 7.1 V.

Question 29

An unknown capacitor has a potential of 18 V across the plates; the amount of charge on one of the plates is 4.7 mC. The potential energy stored in the capacitor is

A) 71 mJ.
B) 8.5 mJ.
C) 130 mJ.
D) 42 mJ.

Question 30

A 1,300-N/C electric field (in a vacuum) has an energy density of

A) $5.1 \times 10 ^ { - 5 } \mathrm {~J} / \mathrm { m } ^ { 3 } \text {. }$
B) $6.3 \times 10 ^ { - 7 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
C) $9.5 \times 10 ^ { - 5 } \mathrm {~J} / \mathrm { m } ^ { 3 }$
D) $7.5 \times 10 ^ { - 6 } \mathrm {~J} / \mathrm { m } ^ { 3 }$

Question 31

A 1300-N/C electric field in a polyethylene dielectric, $K = 2.3$ , has an energy density of

A) $1.7 \times 10 ^ { - 5 }$ J/m $3$
B) $2.9 \times 10 ^ { - 7 }$ J/m $3$
C) $5.6 \times 10 ^ { - 5 }$ j/m $3$
D) $8.5 \times 10 ^ { - 6 }$ j/m $3$

Question 32

The capacitance of a metal sphere of radius R is given by

A) $\pi \varepsilon _ { 0 } R ^ { 2 }$
B) $4 \pi \varepsilon _ { o } R ^ { 2 }$
C) $\pi \varepsilon _ { 0 } R$
D) $4 \pi \varepsilon _ { 0 } R$

Question 33

When the vacuum (dielectric) of a capacitor is replaced with a dielectric, we can find the new capacitance from the previous capacitance by

A) multiplying it by the dielectric constant squared.
B) multiplying it by the dielectric constant.
C) dividing it by the dielectric constant.
D) dividing it by the dielectric constant squared.

Question 34

Consider the potential across the plates of a parallel-plate capacitor. As the potential is increased, the following occur:

A) The capacitance remains constant and the charge decreases.
B) The capacitance increases and the charge remains constant.
C) The capacitance increases and the charge increases.
D) The capacitance remains constant and the charge increases.

Question 35

The energy density associated with an electric field is proportional to

A) E².
B) E.
C) $\sqrt { E }$
D) ln E.

Question 36

In the region near the ends (but not close to either plate) of two very large parallel conducting plates with opposite electric charges, the energy density in the region between the plates is

A) larger than it is far from the ends.
B) the same as it is far from the ends.
C) smaller than it is far from the ends.
D) Hold it! The concept loses its meaning near the ends.

Question 37

Regarding the "self-energy" of a point charge, all of the following points are valid except

A) it is an unsolved problem of physics.
B) a straightforward calculation produces an infinite answer.
C) its constant value renders it irrelevant where energy differences account for observable effects.
D) Hold it! There are no exceptions.

Question 38

We can calculate the electric potential energy of a system by considering the contributions from

A) all possible charge pairs.
B) specially selected charge pairs.
C) specially selected charge groups (not pairs).
D) none of the above.

Question 39

The relatively simple dependence of the electrical energy density on the E-field described in the textbook is exact

A) only for ideal parallel plates with no fringing.
B) only for plates with a rectangular surface area.
C) only for plates that conduct perfectly.
D) for any E-field distribution.

Question 40

There can be electrical energy in the absence of

A) electric charge.
B) electric fields.
C) Both of the first two responses are valid.
D) Neither of the first two responses is valid.