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Introductory Circuit Analysis

Robert L. Boylestad

Chapter 10

Capacitors - all with Video Answers

Educators

Chapter Questions

01:48

Problem 1

a. Find the electric field strength at a point $2 \mathrm{~m}$ from a charge of $4 \mu \mathrm{C}$.
b. Find the electric field strength at a point $1 \mathrm{~mm}$ from the same charge as part (a) and compare results.

Nishant Kumar
Nishant Kumar
Numerade Educator
01:21

Problem 2

The electric field strength is 72 newtons/coulomb $(\mathrm{N} / \mathrm{C})$ at a point $r$ meters from a charge of $2 \mu \mathrm{C}$. Find the distance $r$.

Nishant Kumar
Nishant Kumar
Numerade Educator
00:56

Problem 3

Find the capacitance of a parallel plate capacitor if $1200 \mu \mathrm{C}$ of charge are deposited on its plates when $10 \mathrm{~V}$ are applied across the plates.

Dading Chen
Dading Chen
Numerade Educator
00:55

Problem 4

How much charge is deposited on the plates of $0.15 \mu \mathrm{F}$ capacitor if $45 \mathrm{~V}$ are applied across the capacitor?

Dading Chen
Dading Chen
Numerade Educator
01:10

Problem 5

Find the electric field strength between the plates of a parallel plate capacitor if $100 \mathrm{mV}$ are applied across the plates and the plates are $2 \mathrm{~mm}$ apart.

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Charles Magnusen
Numerade Educator
01:29

Problem 6

Repeat Problem 5 if the plates are separated by 10 mils.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:50

Problem 7

A $4 \mu \mathrm{F}$ parallel plate capacitor has $160 \mu \mathrm{C}$ of charge on its plates. If the plates are $5 \mathrm{~mm}$ apart, find the electric field strength between the plates.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
00:50

Problem 8

Find the capacitance of a parallel plate capacitor if the area of each plate is $0.1 \mathrm{~m}^2$ and the distance between the plates is $2 \mathrm{~mm}$. The dielectric is air.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
07:25

Problem 9

Repeat Problem 8 if the dielectric is paraffin-coated paper.

kj
Karl Jacob
Numerade Educator
03:16

Problem 10

Find the distance in mils between the plates of a $2 \mu \mathrm{F}$ capacitor if the area of each plate is $0.15 \mathrm{~m}^2$ and the dielectric is transformer oil.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:46

Problem 11

The capacitance of a capacitor with a dielectric of air is $1200 \mathrm{pF}$. When a dielectric is inserted between the plates, the capacitance increases to $6 \mathrm{nF}$. Of what material is the dielectric made?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:23

Problem 12

The plates of a parallel plate air capacitor are $0.2 \mathrm{~mm}$ apart and have an area of $0.08 \mathrm{~m}^2$, and $200 \mathrm{~V}$ are applied across the plates.
a. Determine the capacitance.
b. Find the electric field intensity between the plates.
c. Find the charge on each plate if the dielectric is air.

Linda Winkler
Linda Winkler
Numerade Educator
04:23

Problem 13

A sheet of Bakelite $0.2 \mathrm{~mm}$ thick having an area of $0.08 \mathrm{~m}^2$ is inserted between the plates of Problem 12.
a. Find the electric field strength between the plates.
b. Determine the charge on each plate.
c. Determine the capacitance.

Linda Winkler
Linda Winkler
Numerade Educator
02:31

Problem 14

A parallel plate air capacitor has a capacitance of $5 \mu \mathrm{F}$. Find the new capacitance if:
a. The distance between the plates is doubled (everything else remains the same).
b. The area of the plates is doubled (everything else remains the same as for the $5 \mu \mathrm{F}$ level).
c. A dielectric with a relative permittivity of 20 is inserted between the plates (everything else remains the same as for the $5 \mu \mathrm{F}$ level).
d. A dielectric is inserted with a relative permittivity of 4 , and the area is reduced to $1 / 3$ and the distance to $1 / 4$ of their original dimensions.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:21

Problem 15

Find the maximum voltage that can be applied across a parallel plate capacitor of $6 \mathrm{nF}$ if the area of one plate is $0.02 \mathrm{~m}^2$ and the dielectric is mica. Assume a linear relationship between the dielectric strength and the thickness of the dielectric.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:23

Problem 16

Find the distance in micrometers between the plates of a parallel plate mica capacitor if the maximum voltage that can be applied across the capacitor is $1200 \mathrm{~V}$. Assume a linear relationship between the breakdown strength and the thickness of the dielectric.

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:05

Problem 17

A $22 \mu \mathrm{F}$ capacitor has $-200 \mathrm{ppm} /{ }^{\circ} \mathrm{C}$ at room temperature of $20^{\circ} \mathrm{C}$. What is the capacitance if the temperature increases to $100^{\circ} \mathrm{C}$, the boiling point of water?

Mayukh Banik
Mayukh Banik
Numerade Educator
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Problem 18

What is the capacitance of a small teardrop capacitor labeled $40 \mathrm{~J}$ ? What is the range of expected values as established by the tolerance?

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 19

A large, flat, mica capacitor is labeled $220 \mathrm{M}$. What are the capacitance and the expected range of values guaranteed by the manufacturer?

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 20

A small flat disc ceramic capacitor is labeled $333 \mathrm{~K}$. What are the capacitance level and the expected range of values?

Victor Salazar
Victor Salazar
Numerade Educator

Problem 21

For the circuit in Fig. 10.87, composed of standard values:
a. Determine the time constant of the circuit.
b. Write the mathematical equation for the voltage $v_c$ following the closing of the switch.
c. Determine the voltage $v_c$ after one, three, and five time constants.
d. Write the equations for the current $i_C$ and the voltage $v_R$.
e. Sketch the waveforms for $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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01:08

Problem 22

Repeat Problem 21 for $R=1 \mathrm{M} \Omega$, and compare the results.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator

Problem 23

For the circuit in Fig. 10.88, composed of standard values:
a. Determine the time constant of the circuit.
b. Write the mathematical equation for the voltage $v_C$ following the closing of the switch.
c. Determine $v_c$ after one, three, and five time constants.
d. Write the equations for the current $i_C$ and the voltage $v_R$ -
e. Sketch the waveforms for $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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Problem 24

For the circuit in Fig. 10.89, composed of standard values;
a. Determine the time constant of the circuit.
b. Write the mathematical equation for the voltage $v_c$ following the closing of the switch.
c. Write the mathematical expression for the current $i_C$ following the closing of the switch.
d. Sketch the waveforms of $v_C$ and $i_C$.

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09:08

Problem 25

Given the voltage $v_C=60 \mathrm{mV}\left(1-e^{-n S m s}\right)$ :
a. What is the time constant?
b. What is the voltage at $t=2 \mathrm{~ms}$ ?
c. What is the voltage at $t=100 \mathrm{~ms}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
07:09

Problem 26

The voltage across a $10 \mu \mathrm{F}$ capacitor in a series $R-C$ circuit is $v_C=12 \mathrm{~V}\left(1-e^{-1 / 40 \mathrm{mc}}\right)$.
a. On a practical basis, how much time must pass before the charging phase has passed?
b. What is the resistance of the circuit?
c. What is the voltage at $t=20 \mathrm{~ms}$ ?
d. What is the voltage at 10 time constants?
e. Under steady-state conditions, how much charge is on the plates?
f. If the leakage resistance is $1000 \mathrm{M} \Omega$, how long will it take (in hours) for the capacitor to discharge if we assume that the discharge rate is constant throughout the discharge period?

Vishal Gupta
Vishal Gupta
Numerade Educator

Problem 27

For the $R$-C circuit in Fig. 10.90, composed of standard values:
a. Determine the time constant of the circuit when the switch is thrown into position 1.
b. Find the mathematical expression for the voltage across the capacitor and the current after the switch is thrown into position 1 .
c. Determine the magnitude of the voltage $v_C$ and the current $i_C$ the instant the switch is thrown into position 2 at $t=1 \mathrm{~s}$.
d. Determine the mathematical expression for the voltage $v_C$ and the current $i_C$ for the discharge phase.
e. Plot the waveforms of $v_C$ and $i_C$ for a period of time extending from 0 to $2 \mathrm{~s}$ from when the switch was thrown into position 1 .
(FIGURE CAN'T COPY)

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Problem 28

For the network in Fig. 10.91, composed of standard values:
a. Write the mathematical expressions for the voltages $v_C$. and $v_{R_1}$ and the current $i_C$ after the switch is thrown into position 1 .
b. Find the values of $v_C, v_{R_1}$, and $i_C$ when the switch is moved to position 2 at $t=100 \mathrm{~ms}$.
c. Write the mathematical expressions for the voltages $v_C$ and $v_{R_2}$ and the current $i_C$ if the switch is moved to position 3 at $t=200 \mathrm{~ms}$.
d. Plot the waveforms of $v_C, v_{R_2}$, and $i_C$ for the time period extending from 0 to $300 \mathrm{~ms}$.
(FIGURE CAN'T COPY)

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04:02

Problem 29

Repeat Problem 28 for a capacitance of $20 \mu \mathrm{F}$ assuming that the leakage resistance of the capacitor is $\infty \Omega$.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 30

For the network in Fig. 10.92, composed of standard values:
a. Find the mathematical expressions for the voltage $v_C$ and the current $i_c$ when the switch is thrown into position 1 .
b. Find the mathematical expressions for the voltage $v_c$ and the current $i_C$ if the switch is thrown into position 2 at a time equal to five time constants of the charging circuit.
c. Plot the waveforms of $v_C$ and $i_c$ for a period of time extending from 0 to $30 \mu \mathrm{s}$.
(FIGURE CAN'T COPY)

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09:08

Problem 31

The $1000 \mu \mathrm{F}$ capacitor in Fig. 10.93 is charged to $6 \mathrm{~V}$. To discharge the capacitor before further use, a wire with a resistance of $2 \mathrm{~m} \Omega$ is placed across the capacitor.
a. How long will it take to discharge the capacitor?
b. What is the peak value of the current?
c. Based on the answer to part (b), is a spark expected when contact is made with both ends of the capacitor?
(FIGURE CAN'T COPY)

Vishal Gupta
Vishal Gupta
Numerade Educator

Problem 32

The capacitor in Fig. 10.94 is initially charged to $10 \mathrm{~V}$ with the polarity shown.
a. Write the expression for the voltage $v_c$ after the switch is closed.
b. Write the expression for the current $i_C$ after the switch is closed.
c. Plot the results of parts (a) and (b).
(FIGURE CAN'T COPY)

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Problem 33

The capacitor in Fig. 10.95 is initially charged to $40 \mathrm{~V}$ before the switch is closed. Write the expressions for the voltages $v_C$ and $v_R$ and the current $i_C$ following the closing of the switch. Plot the resulting waveforms.
(FIGURE CAN'T COPY)

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Problem 34

The capacitor in Fig. 10.96 is initially charged to $20 \mathrm{~V}$ with the polarity shown. Write the expressions for the voltage $v_c$ and the current $i_C$ following the closing of the switch. Plot the resulting waveforms.
(FIGURE CAN'T COPY)

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Problem 35

The capacitor in Fig. 10.97 is initially charged to $12 \mathrm{~V}$ with the polarity shown.
(FIGURE CAN'T COPY)
a. Find the mathematical expressions for the voltage $v_c$ and the current $i_C$ when the switch is closed.
b. Sketch the waveforms of $v_C$ and $i_C$.

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Problem 36

Given the expression $v_C=12 \mathrm{~V}\left(1-e^{-d 210 \mu c}\right)$ :
a. Determine $v_C$ at $t=10 \mu \mathrm{s}$.
b. Determine $v_C$ at $t=10 \tau$.
c. Find the time $t$ for $v_c$ to reach $6 \mathrm{~V}$.
d. Find the time $t$ for $v_C$ to reach $11.98 \mathrm{~V}$.

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04:17

Problem 37

For the network in Fig. 10.98, $V_L$ must be $8 \mathrm{~V}$ before the system is activated. If the switch is closed at $t=0 \mathrm{~s}$, how long will it take for the system to be activated?
(FIGURE CAN'T COPY)

Kajal Gautam
Kajal Gautam
Numerade Educator

Problem 38

Design the network in Fig. 10.99 such that the system turns on $10 \mathrm{~s}$ after the switch is closed.
(FIGURE CAN'T COPY)

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Problem 39

For the circuit in Fig. 10.100:
a. Find the time required for $v_C$ to reach $60 \mathrm{~V}$ following the closing of the switch.
(FIGURE CAN'T COPY)
b. Calculate the current $i_C$ at the instant $v_C=60 \mathrm{~V}$.
c. Determine the power delivered by the source at the instant $t=2 \tau$.

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Problem 40

For the network in Fig. 10.101:
a. Calculate $v_C, i_C$, and $v_{R_1}$ at $0.5 \mathrm{~s}$ and $1 \mathrm{~s}$ after the switch makes contact with position 1 .
b. The network sits in position $110 \mathrm{~min}$ before the switch is moved to position 2 . How long after making contact with position 2 will it take for the current $i_C$ to drop to $8 \mu \mathrm{A}$ ? How much longer will it take for $v_c$ to drop to $10 \mathrm{~V}$ ?
(FIGURE CAN'T COPY)

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Problem 41

For the system in Fig. 10.102 , using a DMM with a $10 \mathrm{M} \Omega$ intemal resistance in the voltmeter mode:
a. Determine the voltmeter reading one time constant after the switch is closed.
b. Find the current $i_C$ two time constants after the switch is closed.
c. Calculate the time that must pass after the closing of the switch for the voltage $v_c$ to be $50 \mathrm{~V}$.
(FIGURE CAN'T COPY)

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Problem 42

For the circuit in Fig. 10.103:
(FIGURE CAN'T COPY)
a. Find the mathematical expressions for the transient behavior of the voltage $v_C$ and the current $i_C$ following the closing of the switch.
b. Sketch the waveforms of $v_C$ and $i_C$.

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Problem 43

The capacitor in Fig. 10.104 is initially charged to $2 \mathrm{~V}$ with the polarity shown.
a. Write the mathematical expressions for the voltage $v_C$ and the current $i_C$ when the switch is closed.
b. Sketch the waveforms of $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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Problem 44

The capacitor in Fig. 10.105 is initially charged to $4 \mathrm{~V}$ with the polarity shown.
a. Write the mathematical expressions for the voltage $v_c$ and the current $i_C$ when the switch is closed.
b. Sketch the waveforms of $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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Problem 45

For the circuit in Fig. 10.106:
a. Find the mathematical expressions for the transient behavior of the voltage $v_C$ and the current $i_C$ following the closing of the switch.
b. Sketch the waveforms of $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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Problem 46

The capacitor in Fig. 10.107 is initially charged to $3 \mathrm{~V}$ with the polarity shown.
a. Write the mathematical expressions for the voltage $v_C$ and the current $i_C$ when the switch is closed.
b. Sketch the waveforms of $v_C$ and $i_C$.
(FIGURE CAN'T COPY)

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Problem 47

For the system in Fig. 10.108 , using a DMM with a $10 \mathrm{M} \Omega$ internal resistance in the voltmeter mode:
a. Determine the voltmeter reading four time constants after the switch is closed.
b. Find the time that must pass before $i_C$ drops to $3 \mu \mathrm{A}$.
c. Find the time that must pass after the closing of the switch for the voltage across the meter to reach $10 \mathrm{~V}$.
(FIGURE CAN'T COPY)

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03:46

Problem 48

Find the waveform for the average current if the voltage across the $2 \mu \mathrm{F}$ capacitor is as shown in Fig. 10.109.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:46

Problem 49

Find the waveform for the average current if the voltage across the $4.7 \mu \mathrm{F}$ capacitor is as shown in Fig. 10.110.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:19

Problem 50

Given the waveform in Fig. 10.111 for the current of a $20 \mu \mathrm{F}$ capacitor, sketch the waveform of the voltage $v_C$ across the capacitor if $v_C=0 \mathrm{~V}$ at $t=0 \mathrm{~s}$.
(FIGURE CAN'T COPY)

Amit Srivastava
Amit Srivastava
Numerade Educator
02:03

Problem 51

Find the total capacitance $C_T$ for the circuit in Fig. 10.112.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:03

Problem 52

Find the total capacitance $C_T$ for the circuit in Fig. 10.113.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:49

Problem 53

Find the voltage across and the charge on each capacitor for the circuit in Fig. 10.114.
(FIGURE CAN'T COPY)

Shoukat Ali
Shoukat Ali
Other Schools
02:48

Problem 54

Find the voltage across and the charge on each capacitor for the circuit in Fig. 10.115.
(FIGURE CAN'T COPY)

Dading Chen
Dading Chen
Numerade Educator
02:48

Problem 55

For the configuration in Fig. 10.116, determine the voltage across each capcitor and the charge on each capacitor.
(FIGURE CAN'T COPY)

Dading Chen
Dading Chen
Numerade Educator

Problem 56

For the configuration in Fig. 10.117, determine the voltage across each capacitor and the charge on each capacitor.
(FIGURE CAN'T COPY)

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01:07

Problem 57

Find the energy stored by a $120 \mathrm{pF}$ capacitor with $12 \mathrm{~V}$ across its plates.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:37

Problem 58

If the energy stored by a $6 \mu \mathrm{F}$ capacitor is $1200 \mathrm{~J}$, find the charge $Q$ on each plate of the capacitor.

Shahab Ullah
Shahab Ullah
Numerade Educator
05:03

Problem 59

For the network in Fig. 10.118:
a. Determine the energy stored by each capacitor under steady-state conditions.
b. Repeat part (a) if the capacitors are in series.
(FIGURE CAN'T COPY)

Abhishek Jana
Abhishek Jana
Numerade Educator
02:02

Problem 60

An electronic flashgun has a $1000 \mu \mathrm{F}$ capacitor that is charged to $100 \mathrm{~V}$.
a. How much energy is stored by the capacitor?
b. What is the charge on the capacitor?
c. When the photographer takes a picture, the flash fires for $1 / 2000 \mathrm{~s}$. What is the average current through the flashtube?
d. Find the power delivered to the flashtube.
e. After a picture is taken, the capacitor has to be recharged by a power supply that delivers a maximum current of $10 \mathrm{~mA}$. How long will it take to charge the capacitor?

DM
Delete Me
Numerade Educator

Problem 61

Using PSpice or Multisim, verify the results in Example 10.6.

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Problem 62

Using the initial condition operator, verify the results in Example 10.8 for the charging phase using PSpice or Multisim.

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Problem 63

Using PSpice or Multisim, verify the results for $v_C$ during the charging phase in Example 10.11.

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Problem 64

Using PSpice or Multisim, verify the results in Problem 48.

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