• Home
  • Textbooks
  • College Physics
  • Electric Potential, Energy, and Capacitance

College Physics

Jerry D. Wilson, Anthony J. Buffa, Bo Lou

Chapter 16

Electric Potential, Energy, and Capacitance - all with Video Answers

Educators

+ 1 more educators

Chapter Questions

01:04

Problem 1

A pair of parallel plates is charged by a 12-V battery. If the electric field between the plates is $1200 \mathrm{~N} / \mathrm{C}$, how far apart are the plates?

Shahab Ullah
Shahab Ullah
Numerade Educator
01:57

Problem 2

A pair of parallel plates is charged by a 12-V battery. How much work is required to move a particle with a charge of $-4.0 \mu C$ from the positive to the negative plate?

Shahab Ullah
Shahab Ullah
Numerade Educator
01:52

Problem 3

If it takes $+1.6 \times 10^{-5} \mathrm{~J}$ to move a positively charged particle between two charged parallel plates, (a) what is the charge on the particle if the plates are connected to a 6.0-V battery? (b) Was it moved from the negative to the positive plate or from the positive to the negative plate?

Shahab Ullah
Shahab Ullah
Numerade Educator
02:48

Problem 4

An electron is accelerated by a uniform electric field $(1000 \mathrm{~V} / \mathrm{m})$ pointing vertically upward. Use Newton's laws to determine the electron's velocity after it moves $0.10 \mathrm{~cm}$ from rest.

Shahab Ullah
Shahab Ullah
Numerade Educator
04:29

Problem 5

(a) Repeat Exercise $4,$ but find the speed by using energy methods. Find the direction in which the electron is moving by considering electric potential energy changes.
(b) Does the electron gain or lose potential energy?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:03

Problem 6

Consider two points at different distances from a positive point charge. (a) The point closer to the charge is at a (1) higher, (2) equal, (3) lower potential than the point farther away. Why? (b) How much different is the electric potential $20 \mathrm{~cm}$ from a charge of $5.5 \mu \mathrm{C}$ compared to $40 \mathrm{~cm}$ from the same charge?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
06:48

Problem 7

(a) At one-third the original distance from a positive point charge, by what factor is the electric potential changed: $(1) 1 / 3,(2) 3,(3) 1 / 9,$ or (4) $9 ?$ Why? (b) How far from $a+1.0-\mu C$ charge is a point with an electric potential value of $10 \mathrm{kV} ?$ (c) How much of a change in potential would occur if the point were moved to three times that distance?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:25

Problem 8

According to the Bohr model of the hydrogen atom (see Chapter 27 ), the electron can exist only in circular orbits of certain radii about a proton. (a) Will a larger orbit have (1) a higher, (2) an equal, or
(3) a lower electric potential than a smaller orbit? Why? (b) Determine the potential difference between two orbits of radii $0.21 \mathrm{nm}$ and $0.48 \mathrm{nm}$.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
05:39

Problem 9

In Exercise $8,$ by how much does the potential energy of the atom change if the electron changes location (a) from the lower to the higher orbit, (b) from the higher to the lower orbit, and (c) from the larger orbit to a very large distance?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:30

Problem 10

How much work is required to completely separate two charges (each $-1.4 \mu \mathrm{C}$ ) and leave them at rest if they were initially $8.0 \mathrm{~mm}$ apart?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:31

Problem 11

In Exercise 10 , if the two charges are released at their initial separation distance, how much kinetic energy would each have when they are very distant from one another?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:50

Problem 12

It takes +6.0 J of work to move two charges from a large distance apart to $1.0 \mathrm{~cm}$ from one another. If the charges have the same magnitude, (a) how large is each charge, and (b) what can you tell about their signs?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:07

Problem 13

$\mathrm{A}+2.0-\mu \mathrm{C}$ charge is initially $0.20 \mathrm{~m}$ from a fixed $-5.0-\mu C$ charge and is then moved to a position $0.50 \mathrm{~m}$ from the fixed charge. (a) How much work is required to move the charge? (b) Does the work depend on the path through which the charge is moved?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
06:04

Problem 14

An electron is moved from point $A$ to point $B$ and then to point $C$ along two legs of an equilateral triangle with sides of length $0.25 \mathrm{~m}$ ( $\mathbf{v}$ Fig. 16.23 ). If the horizontal electric field is $15 \mathrm{~V} / \mathrm{m},$ (a) what is the magnitude of the work required? (b) What is the potential difference between points $\mathrm{A}$ and $\mathrm{C} ?$ (c) Which point is at a higher potential?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:27

Problem 15

Compute the energy necessary to bring together (from a very large distance) the charges in the configuration shown in $>$ Fig. 16.24

Susan Hallstrom
Susan Hallstrom
Numerade Educator
05:22

Problem 16

Compute the energy necessary to bring together (from a very large distance) the charges in the configuration shown in $v$ Fig. $16.25 .$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
07:35

Problem 17

What is the value of the electric potential at (a) the center of the triangle and (b) a point midway between $q_{2}$ and $q_{3}$ in Fig. $16.24 ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
07:25

Problem 18

What is the value of electric potential at (a) the center of the square and (b) a point midway between $q_{1}$ and $q_{4}$ in Fig. $16.25 ?$

Vishal Gupta
Vishal Gupta
Numerade Educator
03:01

Problem 19

In a computer monitor, electrons are accelerated from rest through a potential difference in an "electron gun" arrangement (veig. 16.26). (a) Should the left side of the gun be at (1) a higher, (2) an equal, or (3) a lower potential than the right side? Why? (b) If the potential difference in the gun is $5.0 \mathrm{kV}$, what is the "muzzle speed" of the electrons emerging from the gun? (c) If the gun is directed at a screen $25 \mathrm{~cm}$ away, how long do the electrons take to reach the screen?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:31

Problem 20

A uniform electric field of $10 \mathrm{kV} / \mathrm{m}$ points vertically upward. How far apart are the equipotential planes that differ by $100 \mathrm{~V} ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:27

Problem 21

In Exercise 20 , if the ground is designated as zero potential, how far above the ground is the equipotential surface corresponding to $7.0 \mathrm{kV} ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:30

Problem 22

Determine the potential $2.5 \mathrm{~mm}$ from the negative plate of a pair of parallel plates separated by $20.0 \mathrm{~mm}$ and connected to a 24 -V battery.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:15

Problem 23

Relative to the positive plate in Exercise $22,$ where is the point with a potential of $14 \mathrm{~V} ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:49

Problem 24

If the radius of the equipotential surface of a point charge is $10.5 \mathrm{~m}$ and is at a potential of $+2.20 \mathrm{kV}$ (compared to zero at infinity), what are the magnitude and sign of the point charge?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:35

Problem 25

(a) The equipotential surfaces in the neighborhood of a positive point charge are spheres. Which sphere is associated with the higher electric potential: (1) the smaller one, (2) the larger one, or (3) they are associated with the same potential? (b) Calculate the amount of work (in electron-volts) it would take to move an electron from $12.6 \mathrm{~m}$ to $14.3 \mathrm{~m}$ away from $\mathrm{a}+3.50-\mu \mathrm{C}$ point charge.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:49

Problem 26

The potential difference between the cloud and ground in a typical lightning discharge may be up to 100 MV (million volts). What is the gain in kinetic energy of an electron accelerated through this potential difference? Give your answer in both electron-volts and joules. (Assume that there are no collisions.)

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:33

Problem 27

In a typical Van de Graaff linear accelerator, protons are accelerated through a potential difference of $20 \mathrm{MV}$. What is their kinetic energy if they started from rest? Give your answer in (a) $\mathrm{eV},$ (b) $\mathrm{keV},$ (c) $\mathrm{MeV}$, (d) $\mathrm{GeV},$ and (e) joules.

Shahab Ullah
Shahab Ullah
Numerade Educator
03:26

Problem 28

In Exercise $27,$ how do your answers change if a doubly charged $(+2 e)$ alpha particle is accelerated instead? (An alpha particle consists of two neutrons and two protons.)

Shahab Ullah
Shahab Ullah
Numerade Educator
03:19

Problem 29

In Exercises 27 and 28 , compute the speed of the proton and alpha particle after being accelerated.

Shahab Ullah
Shahab Ullah
Numerade Educator
05:53

Problem 30

Calculate the voltage required to accelerate a beam of protons initially at rest, and calculate their speed if they have a kinetic energy of (a) $3.5 \mathrm{eV},$ (b) $4.1 \mathrm{keV}$, and (c) $8.0 \times 10^{-16} \mathrm{~J}$

Shahab Ullah
Shahab Ullah
Numerade Educator
06:37

Problem 31

Repeat the calculation in Exercise 30 for electrons instead of protons.

Vishal Gupta
Vishal Gupta
Numerade Educator
07:07

Problem 32

Two large parallel plates are separated by $3.0 \mathrm{~cm}$ and connected to a 12-V battery. Starting at the negative plate and moving $1.0
\mathrm{~cm}$ toward the positive plate at a $45^{\circ}$ angle (vFig. 16.27 ), (a) what value of potential would be reached, assuming the negative plate were defined as zero potential? (b) Repeat part (a) except move $1.0 \mathrm{~cm}$ directly toward the positive plate. Explain why your answers to
(a) and (b) are different. (c) After the movement in (b), suppose you moved $0.50 \mathrm{~cm}$ parallel to the plane of the plates. What would be the electric potential value then?

Vishal Gupta
Vishal Gupta
Numerade Educator
07:32

Problem 33

Consider a point midway between the two large charged plates in Fig. 16.27 . Compute the change in electric potential if from there you moved (a) $1.0 \mathrm{~mm}$ toward the positive plate, (b) $1.0 \mathrm{~mm}$ toward the negative plate, and
(c) $1.0 \mathrm{~mm}$ parallel to the plates. What do your answers tell you about the direction of the electric field in that region?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:54

Problem 34

Repeat Exercise 33 if the plates are instead connected to a 24-V battery. Also determine the electric field (direction and magnitude) at the midway point between the plates. Compare your answers to Exercise 33 and comment on the source of any differences.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:32

Problem 35

How much charge flows through a 12-V battery when a $2.0-\mu \mathrm{F}$ capacitor is connected across its terminals?

Shahab Ullah
Shahab Ullah
Numerade Educator
01:56

Problem 36

A parallel plate capacitor has a plate area of $0.525 \mathrm{~m}^{2}$ and a plate separation of $2.15 \mathrm{~mm}$. What is its capacitance?

Shahab Ullah
Shahab Ullah
Numerade Educator
01:55

Problem 37

What plate separation is required for a parallel plate capacitor to have a capacitance of $9.00 \mathrm{nF}$ if the plate area is $0.425 \mathrm{~m}^{2}$ ?

Shahab Ullah
Shahab Ullah
Numerade Educator
02:56

Problem 38

(a) For a parallel plate capacitor with a fixed plate separation distance, a larger plate area results in (1) a larger capacitance value, (2) an unchanged capacitance value, (3) a smaller capacitance value. (b) A 2.50 -nF parallel plate capacitor has a plate area of $0.514 \mathrm{~m}^{2}$. If the plate area is doubled, what is the new capacitance value?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
03:31

Problem 39

A 12.0 -V battery remains connected to a parallel plate capacitor with a plate area of $0.224 \mathrm{~m}^{2}$ and a plate separation of $5.24 \mathrm{~mm}$. (a) What is the charge on the capacitor? (b) How much energy is stored in the capacitor? (c) What is the electric field between its plates?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:56

Problem 40

If the plate separation of the capacitor in Exercise 39 changed to $10.48 \mathrm{~mm}$ after the capacitor is disconnected from the battery, how do your answers change?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:34

Problem 41

Current state-of-the-art capacitors are capable of storing many times the energy of older ones. Such a capacitor, with a capacitance of $1.0 \mathrm{~F}$, is able to light a small 0.50 - $W$ bulb at steady full power for 5.0 s before it quits. What is the terminal voltage of the battery that charged the capacitor?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
08:04

Problem 42

$\mathrm{A}$ 1.50-F capacitor is connected to a 12.0 for a long time, and then is disconnected. The capacitor briefly runs a 1.00-W toy motor for $2.00 \mathrm{~s}$. After this time, (a) by how much has the energy stored in the capacitor decreased? (b) What is the voltage across the plates?
(c) How much charge is stored on the capacitor? (d) How much longer could the capacitor run the motor, assuming the motor ran at full power until the end?

Vishal Gupta
Vishal Gupta
Numerade Educator
09:03

Problem 43

Two parallel plates have a capacitance value of $0.17 \mu \mathrm{F}$ when they are $1.5 \mathrm{~mm}$ apart. They are connected permanently to a 100 -V power supply. If you pull the plates out to a distance of $4.5 \mathrm{~mm},$ (a) what is the electric field between them? (b) By how much has the capacitor's charge changed? (c) By how much has its energy storage changed? (d) Repeat these calculations assuming the power supply is disconnected before you pull the plates further apart.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:13

Problem 44

A capacitor has a capacitance of $50 \mathrm{pF}$, which increases to $150 \mathrm{pF}$ when a dielectric material is between its plates. What is the dielectric constant of the material?

Shahab Ullah
Shahab Ullah
Numerade Educator
02:08

Problem 45

A 50 -pF capacitor is immersed in silicone oil, which has a dielectric constant of $2.6 .$ When the capacitor is connected to a 24 - $V$ battery, $($ a) what will be the charge on the capacitor? (b) How much energy is stored in the capacitor?

Shahab Ullah
Shahab Ullah
Numerade Educator
03:47

Problem 46

The dielectric of a parallel plate capacitor is to be a slab of glass that completely fills the volume between the plates. The area of each plate is $0.50 \mathrm{~m}^{2}$. (a) What thickness should the glass have if the capacitance is to be $0.10 \mu \mathrm{F} ?$ (b) What is the charge on the capacitor if it is connected to a 12-V battery? (c) How much more energy is stored in this capacitor compared to an identical one without the dielectric insert?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:08

Problem 47

co A parallel plate capacitor has a capacitance of $1.5 \mu \mathrm{F}$ with air between the plates. The capacitor is connected to a 12-V battery and charged. The battery is then removed. When a dielectric is placed between the plates, a potential difference of $5.0 \mathrm{~V}$ is measured across the plates. (a) What is the dielectric constant of the material?
(b) What happened to the energy storage in the capacitor: (1) it increased, (2) it decreased, or (3) it stayed the same? (c) By how much did the energy storage of this capacitor change when the dielectric was inserted?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
07:04

Problem 48

An air-filled parallel plate capacitor has rectangular plates with dimensions of $6.0 \mathrm{~cm} \times 8.0 \mathrm{~cm} .$ It is connected to a 12-V battery. While the battery remains connected, a sheet of 1.5 -mm-thick Teflon (dielectric constant of 2.1 ) is inserted and completely fills the space between the plates. (a) While the dielectric was being inserted, (a) charge flowed onto the capacitor, (2) charge flowed off the capacitor, (3) no charge flowed. (b) Determine the change in the charge storage of this capacitor because of the dielectric insertion. (c) Determine the change in energy storage in this capacitor because of the dielectric insertion. (d) By how much was the battery's stored energy changed?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:03

Problem 49

What is the equivalent capacitance of two capacitors with capacitances of $0.40 \mu \mathrm{F}$ and $0.60 \mu \mathrm{F}$ when they are connected (a) in series and (b) in parallel?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:59

Problem 50

Two identical capacitors are connected in series and their equivalent capacitance is $1.0 \mu \mathrm{F}$. What is each one's capacitance value? Repeat the calculation if, instead, they were connected in parallel.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:44

Problem 51

(a) Two capacitors can be connected to a battery in either a series or parallel combination. The parallel combination will require (1) more, (2) equal, (3) less energy from a battery than the series combination. Why?
(b) Two uncharged capacitors, one with a capacitance of $0.75 \mu \mathrm{F}$ and the other with that of $0.30 \mu \mathrm{F}$ are connected in series to a 12-V battery. Then the capacitors are disconnected, discharged, and reconnected to the same battery in parallel. Calculate the energy loss of the battery in both cases.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
01:36

Problem 52

For the arrangement of three capacitors in $v$ Fig. 16.28 , what value of $\mathrm{C}_{1}$ will give a total equivalent capacitance of $1.7 \mu \mathrm{F} ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
02:11

Problem 53

(a) Three capacitors of equal capacitance are connected in parallel to a battery, and together they acquire a certain total charge $Q$ from that battery. Will the charge on each capacitor be $(1) Q,(2) 3 Q,$ or $(3) Q / 3 ?$
(b) Three capacitors of $0.25 \mu \mathrm{F}$ each are connected in parallel to a 12-V battery. What is the charge on each capacitor?
(c) How much total charge was acquired from the battery?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
07:32

Problem 54

(a) If you are given three identical capacitors, you can obtain (1) three, (2) five, (3) seven different capacitance values. (b) If the three capacitors each have a capacitance of $1.0 \mu \mathrm{F}$, what are the different values of equivalent capacitance?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:17

Problem 55

What are the maximum and minimum equivalent capacitances that can be obtained by combinations of three capacitors of $1.5 \mu \mathrm{F}, 2.0 \mu \mathrm{F},$ and $3.0 \mu \mathrm{F} ?$

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:10

Problem 56

If the capacitance of $C_{1}$ is $0.10 \mu \mathrm{F},$ (a) what is the charge on each of the capacitors in the circuit in Fig. $16.28 ?$ (b) How much energy is stored in each capacitor?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
08:02

Problem 57

Four capacitors are connected in a circuit as illustrated in $v$ Fig. $16.29 .$ Find the charge on, the voltage difference across, and the energy stored for each of the capacitors.

Vishal Gupta
Vishal Gupta
Numerade Educator
10:21

Problem 58

A tiny dust particle in the form of a long thin needle has charges of $\pm 7.14 \mathrm{pC}$ on its ends. The length of the particle is $3.75 \mu \mathrm{m}$. (a) Which location is at a higher potential: (1) $7.65 \mu \mathrm{m}$ above the positive end,
(2) $5.15 \mu \mathrm{m}$ above the positive end, or (3) both locations are at the same potential? (b) Compute the potential at the two points in part (a). (c) Use your answer from part (b) to determine the work needed to move an electron from the near point to the far point.

Linda Winkler
Linda Winkler
Numerade Educator
07:40

Problem 59

A vacuum tube has a vertical height of $50.0 \mathrm{~cm}$. An electron leaves from the top at a speed of $3.2 \times 10^{6} \mathrm{~m} / \mathrm{s}$ downward and is subjected to a "typical" Earth field of $150 \mathrm{~V} / \mathrm{m}$ downward. (a) Use energy methods to determine whether it reaches the bottom surface of the tube.
(b) If it does, with what speed does it hit? If not, how close does it come to the bottom surface? (c) How does the gravitational force on the electron compare to the electric force on it, both in magnitude and in direction?

Vishal Gupta
Vishal Gupta
Numerade Educator
10:52

Problem 60

A helium atom with one electron already removed (a positive helium ion) consists of a single orbiting electron and a nucleus of two protons. The electron is in its minimum orbital radius of $0.027 \mathrm{nm}$. (a) What is the potential energy of the system? (b) What is the centripetal acceleration of the electron? (c) What is the total energy of the system? (d) What is the minimum energy required to "ionize" this atom, in other words, to cause the electron to leave completely?

Linda Winkler
Linda Winkler
Numerade Educator
07:39

Problem 61

Suppose that the three capacitors in Figure 16.22 have the following values: $C_{1}=0.15 \mu \mathrm{F}, C_{2}=0.25 \mu \mathrm{F},$ and $C_{3}=0.30 \mu \mathrm{F} .$ (a) What is the equivalent capacitance of this arrangement? (b) How much charge will be drawn from the battery? (c) What is the voltage across each capacitor? (d) What is the energy storage in each capacitor?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:59

Problem 62

Two very large horizontal parallel plates are separated by $1.50 \mathrm{~cm} .$ An electron is to be suspended at rest in midair between them. (a) The top plate should be at (1) a higher potential, (2) an equal potential, (3) a lower potential compared with the bottom plate. Explain.
(b) What voltage across the plates is required? (c) Does the electron have to be positioned midway between the plates, or is any location between the plates just as good?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:33

Problem 63

(Before attempting this one, see Insight 16.1, Electric Potential and Nerve Signal Transmission and Learn by Drawing 16.2 on graphical relationships between $\overrightarrow{\mathbf{E}}$ and V.) Suppose an (axon) cell membrane is experiencing the end of a stimulus event and the voltage across the cell membrane is instantaneous at $30 \mathrm{mV}$. Assume the membrane is $10 \mathrm{nm}$ thick. At this point the $\mathrm{Na} / \mathrm{K}$ -ATPase molecular pump starts to move the excess $\mathrm{Na}^{+}$ ions back to the exterior. (a) How much work does it take for the pump to move the first sodium ion? (b) Estimate the electric field (including direction) in the membrane under these conditions. (c) Estimate the force on that first sodium ion. (d) What is the electric field (including direction) under normal conditions when the voltage across the membrane is $-70 \mathrm{mV}$ ?

Shoukat Ali
Shoukat Ali
Other Schools
03:19

Problem 64

In Exercise $63,$ assume that the inside and outside surfaces of the axon membrane act like a parallel plate capacitor with an area of $1.1 \times 10^{-9} \mathrm{~m}^{2}$. (a) Estimate the capacitance of an axon's membrane, assuming it is filled with lipids with a dielectric constant of $3.0 .$ (b) How much charge would be on each surface under resting potential conditions? (c) How much electrostatic energy would be stored in this axon under resting potential conditions?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:48

Problem 65

Two parallel plates, $9.25 \mathrm{~cm}$ on a side, are separated by $5.12 \mathrm{~mm} .$ (See r Fig. 16.30a.) (a) Determine their capacitance if the volume from one plate to midplane is filled with a material of dielectric constant 2.55 and the rest is filled with a different material of dielectric constant $4.10 .$ (b) If these plates are connected to a 12-V battery, what is the electric field strength in each dielectric region? [Hint: Do you see two capacitors in series?]

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:35

Problem 66

Repeat Exercise 65 except fill the volume from one edge to the middle with the same two materials. (See Figure 16.30b.) (Do you see two capacitors in parallel?)

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
05:49

Problem 67

A capacitor $(5.70 \mu \mathrm{F})$ is connected in a series arrangement with a second capacitor $(2.30 \mu \mathrm{F})$ and a $12-\mathrm{V}$ battery. (a) How much charge is stored on each capacitor? (b) What is the voltage drop across each capacitor? The battery is then removed, leaving the two capacitors isolated. (c) If the smaller capacitor's capacitance is now doubled, by how much does the charge on each and the voltage across each change?

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator
04:52

Problem 68

Repeat Exercise 67 assuming, instead, that the capacitors are, instead, connected in parallel.

Mirza Aslam Beig
Mirza Aslam Beig
Numerade Educator