Test 5 Due: 11:59pm on Sunday, April 10, 2011 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy [ Switch to Standard Assignment View] Exercise 24.49 A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant . The magnitude of the charge on each plate is . Each plate has area , and the distance between the plates is . Part A Use Gauss's law to calculate the magnitude of the electric field in the dielectric. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Part B Use the electric field determined in part A to calculate the potential difference between the two plates. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Part C Use the result of part B to determine the capacitance of the capacitor. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Problem 24.73 Capacitors in networks cannot always be grouped into simple series or parallel combinations. As an example, the figure (a) shows three capacitors , and in a delta network, so called because of its triangular MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... 1 of 17 5/12/2011 8:11 PM
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Test 5Due: 11:59pm on Sunday, April 10, 2011
Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy
[Switch to Standard Assignment View]
Exercise 24.49A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant . The
magnitude of the charge on each plate is . Each plate has area , and the distance between the plates is
.
Part A
Use Gauss's law to calculate the magnitude of the electric field in the dielectric.
Express your answer in terms of the given quantities and appropriate constants.
ANSWER: =
Correct
Part B
Use the electric field determined in part A to calculate the potential difference between the two plates.
Express your answer in terms of the given quantities and appropriate constants.
ANSWER: =
Correct
Part C
Use the result of part B to determine the capacitance of the capacitor.
Express your answer in terms of the given quantities and appropriate constants.
ANSWER: =
Correct
Problem 24.73Capacitors in networks cannot always be grouped into simple series or parallel combinations. As an example,the figure (a) shows three capacitors , and
in a delta network, so called because of its triangular
shape. This network has three terminals a, b, and cand hence cannot be transformed into a singleequivalent capacitor. It can be shown that as far asany effect on the external circuit is concerned, a deltanetwork is equivalent to what is called a Y network. Forexample, the delta network of the figure (a) can bereplaced by the Y network of the figure (b). (The name"Y network" also refers to the shape of the network.)The transformation equations that give , , and
in terms of , and , and are
.
Part A
For the network shown in the figure (c), determine the equivalent capacitance between the terminals at theleft end of the network. (Hint: Use the delta-Y transformation derived in the introduction. Use points a, b,and c to form the delta, and transform the delta into a Y. The capacitors can then be combined using therelationships for series and parallel combinations of capacitors.)
ANSWER: = 14.0Correct
Part B
Determine the charges of, and the potential differences across, each capacitor in the figure (c).
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
ANSWER: My Answer:
Part C
Suppose that before the slab is moved by , the plates are disconnected from the battery, so that the
charges on the plates remain constant. Determine the magnitude of the charge on each plate.
Express your answer in terms of the given quantities and appropriate constants.
ANSWER: =
Correct
Part D
Show that when the slab is moved farther into the space between the plates, the stored energy changes
by an amount that is the negative of the expression for given in part B.
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
ANSWER: My Answer:
Part E
If is the force exerted on the slab by the charges on the plates, then should equal the work done
against this force to move the slab a distance . Thus . Show that applying this expression to
the result of part B suggests that the electric force on the slab pushes it out of the capacitor, while theresult of part D suggests that the force pulls the slab into the capacitor.
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
ANSWER: My Answer:
Part F
Figure24.16 in the textbook shows that the force in fact pulls the slab into the capacitor. Explain why theresult of part B gives an incorrect answer for the direction of this force.
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
Calculate the magnitude of the force. (This method does not require knowledge of the nature of the fringingfield.)
Express your answer in terms of the given quantities and appropriate constants.
ANSWER:
=
Correct
Exercise 24.11A cylindrical capacitor has an inner conductor with a radius of 1.3 and an outer conductor with a radius of3.3 . The two conductors are separated by vacuum, and the entire capacitor has a length of 3.0 .
Part A
What is the capacitance per unit length?
Express your answer using two significant figures.
ANSWER: = 6.0×10−11
Correct
Part B
The potential of the inner conductor relative to that of the outer conductor is 350 . Find the charge
(magnitude and sign) on both conductors.
Enter your answers numerically separated by a comma. Express your answers using twosignificant figures.
ANSWER: = 6.3×10−11,−6.3×10−11
Correct
Exercise 24.13A spherical capacitor contains a charge of 3.50 when connected to a potential difference of 230 . If its
plates are separated by vacuum and the inner radius of the outer shell is 5.00 .
Using the equation for the current in a discharging capacitor, derive an expression for the
instantaneous power dissipated in the resistor.
Express your answer in terms of the variables , , and .
ANSWER:
=
Correct
Part B
Integrate the expression for to find the total energy dissipated in the resistor.
Express your answer in terms of the variables , , and .
ANSWER:
=
Correct
Part C
Show that the total energy dissipated in the resistor is equal to the total energy initially stored in thecapacitor.
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
ANSWER: My Answer:
Problem 26.90: A Capacitor Burglar AlarmThe capacitance of a capacitor can be affected by dielectric material that, although not inside the capacitor, isnear enough to the capacitor to be polarized by the fringing electric field that exists near a charged capacitor.This effect is usually of the order of picofarads ( ), but it can be used with appropriate electronic circuitry to
detect a change in the dielectric material surrounding the capacitor. Such a dielectric material might be thehuman body, and the effect described above might be used in the design of a burglar alarm. Consider thesimplified circuit shown in the figure . The voltagesource has emf = 1000 , and the capacitor has
capacitance 10.0 . The electronic circuitry for
detecting the current, represented as an ammeter inthe diagram, has negligible resistance and is capableof detecting a current that persists at a level of at least1.00 for at least 200 after the capacitance has
designed to be activated if the capacitance changes by10%.
Part A
Determine the charge on the 10.0- capacitor when it is fully charged.
ANSWER: = 1.00×10−8
Correct
Part B
If the capacitor is fully charged before the intruder is detected, assuming that the time taken for thecapacitance to change by 10% is short enough to be ignored, derive an equation that expresses the currentthrough the resistor as a function of the time since the capacitance has changed.
Express your answer in terms of the variables , , , ( ) and .
ANSWER: =
All attempts used; correct answer displayed
Part C
Determine the range of values of the resistance that will meet the design specifications of the burglar
alarm. (Hint: You will not be able to solve this part analytically but must use numerical methods. Express
as a logarithmic function of plus known quantities. Use a trial value of and calculate from the
expression a new value. Continue to do this until the input and output values of agree to within three
significant figures.)
Enter your answers numerically separated by a comma.
ANSWER: , = 7.15×106,7.01×107
Correct
Part D
What happens if is too small? Too large?
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
Exercise 26.45In the circuit shown in the figure each capacitor initiallyhas a charge of magnitude 3.20 on its plates.
Part A
After the switch is closed, what will be the current in the circuit at the instant that the capacitors have lost
80.0% of their initial stored energy?
ANSWER: = 12.4Correct
Exercise 31.7In each circuit described next, an ac voltage source producing a current is connected to an
additional circuit element.
Part A
The ac source is connected across a resistor . Sketch graphs of the current in the circuit and the
potential difference across the resistor as functions of time, covering one cycle of oscillation. Put bothgraphs on the same set of axes so you can compare them.
