Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 27, Problem 87PQ
A Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A camera flash circuit consisting of 3 AA batteries in series, a capacitor and a flash bulb is shown in the figure.
The parallel-plate capacitor is made from 2 circular plates with a radius of 0.25cm and separated by a distance
of 1mm. The AA batteries provide a voltage of 1.5V each. While charging the
capacitor, switch A is closed and switch B is open.
B
a. What is the capacitance of the capacitor?
b. What is the voltage across the capacitor and what is the charge stored on the capacitor when it is fully
charged?
c. How much energy is stored on the capacitor when it is fully charged?
d. After the capacitors are fully charged, switch A is opened. To use the flash once, you close and then open
switch B. After one flash, the energy is reduced by 50%. What is the voltage across the capacitor after one
flash?
e. If you were to add a second (identical) capacitor to the circuit, how would you connect it so that you
increase the total energy available for the flash bulb? Draw your new…
A combination of series and parallel connections of capacitors is shown in the figure. The sizes of these capacitors are given by the follow data:
C1 = 4.8 μFC2 = 3.8 μFC3 = 8.9 μFC4 = 2.2 μFC5 = 1.3 μFC6 = 16.5 μF
Find the total capacitance of the combination of capacitors in microfarads.
Three capacitors are connected as shown in the figure. C1 = 6.6 μF, C2 = 9.2 μF, C3 = 6.7 μF. The voltage on the battery is 12 V.
Part a Express the equivalent capacitance of the two capacitors C1 and C2 in terms of the variables given in the problem statement.
Part b Using the above result, express the total capacitance in terms of C12 and C3.
Part c Calculate the numerical value of the total capacitance in μF.
Part d Express the charge Q stored in the circuit in terms of capacitance C and the potential difference ΔV across the battery.
Part e Calculate the numerical value of Q in μC.
Part f Express the energy stored in a capacitor in terms of capacitance C and the potential difference ΔV.
Part g Calculate the numerical value of U in μJ.
Chapter 27 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 27.1 - CASE STUDY How Big a Spring? Imagine the ring in...Ch. 27.2 - Consider two different capacitors, A and B. Figure...Ch. 27.2 - a. If capacitor B in Figure 27.8 has a charge of...Ch. 27.3 - Explain why electrons stop flowing when the...Ch. 27.3 - A large parallel-plate capacitor is attached to a...Ch. 27.4 - CASE STUDY Capacitors for a Thompson coil The...Ch. 27.7 - An X-ray tube at a dentists office produces X-rays...Ch. 27 - CASE STUDY Concept Exercise 27.1 (page 829), we...Ch. 27 - Prob. 2PQCh. 27 - In Franklins time, a device for storing electric...
Ch. 27 - The first Leyden jar was probably discovered by a...Ch. 27 - Prob. 5PQCh. 27 - According to UE=12C(V)2 (Eq. 27.3), a greater...Ch. 27 - In Figure P27.7, capacitor 1 (C1 = 20.0 F)...Ch. 27 - Prob. 8PQCh. 27 - A 4.50-F capacitor is connected to a battery for a...Ch. 27 - Prob. 10PQCh. 27 - Prob. 11PQCh. 27 - Prob. 12PQCh. 27 - Prob. 13PQCh. 27 - When a Leyden jar is charged by a hand generator...Ch. 27 - Prob. 15PQCh. 27 - A 6.50-F capacitor is connected to a battery. What...Ch. 27 - A pair of capacitors with capacitances CA = 3.70 F...Ch. 27 - Two 1.5-V batteries are required in a flashlight....Ch. 27 - Two capacitors have capacitances of 6.0 F and 3.0...Ch. 27 - Prob. 20PQCh. 27 - Calculate the equivalent capacitance between...Ch. 27 - Prob. 22PQCh. 27 - Given the arrangement of capacitors in Figure...Ch. 27 - An arrangement of capacitors is shown in Figure...Ch. 27 - Prob. 25PQCh. 27 - Prob. 26PQCh. 27 - Find the equivalent capacitance for the network...Ch. 27 - Prob. 28PQCh. 27 - The capacitances of three capacitors are in the...Ch. 27 - For the four capacitors in the circuit shown in...Ch. 27 - The separation between the 4.40-cm2 plates of an...Ch. 27 - A spherical capacitor is made up of two concentric...Ch. 27 - A Derive an expression for the capacitance of an...Ch. 27 - Prob. 34PQCh. 27 - Prob. 35PQCh. 27 - Prob. 36PQCh. 27 - Prob. 37PQCh. 27 - Prob. 38PQCh. 27 - Review One of the plates of a parallel-plate...Ch. 27 - Prob. 40PQCh. 27 - Prob. 41PQCh. 27 - A 56.90-pF cylindrical capacitor carries a charge...Ch. 27 - Prob. 43PQCh. 27 - Prob. 44PQCh. 27 - Prob. 45PQCh. 27 - Prob. 46PQCh. 27 - The plates of an air-filled parallel-plate...Ch. 27 - Prob. 48PQCh. 27 - Prob. 49PQCh. 27 - Prob. 50PQCh. 27 - Prob. 51PQCh. 27 - Prob. 52PQCh. 27 - Prob. 53PQCh. 27 - A parallel-plate capacitor with an air gap has...Ch. 27 - A parallel-plate capacitor with plates of area A =...Ch. 27 - Prob. 56PQCh. 27 - Prob. 57PQCh. 27 - Prob. 58PQCh. 27 - Prob. 59PQCh. 27 - Prob. 60PQCh. 27 - Find an expression for the electric field between...Ch. 27 - An air-filled parallel-plate capacitor is charged...Ch. 27 - Two Leyden jars are similar in size and shape, but...Ch. 27 - Prob. 64PQCh. 27 - Nerve cells in the human body and in other animals...Ch. 27 - Prob. 66PQCh. 27 - Prob. 67PQCh. 27 - Prob. 68PQCh. 27 - Prob. 69PQCh. 27 - Prob. 70PQCh. 27 - What is the maximum charge that can be stored on...Ch. 27 - Prob. 72PQCh. 27 - In a laboratory, you find a 9.00-V battery and a...Ch. 27 - Prob. 74PQCh. 27 - Figure P27.75 shows four capacitors with CA = 4.00...Ch. 27 - Prob. 76PQCh. 27 - Prob. 77PQCh. 27 - A parallel-plate capacitor with plates of area A...Ch. 27 - Prob. 79PQCh. 27 - Prob. 80PQCh. 27 - A 90.0-V battery is connected to a capacitor with...Ch. 27 - Consider an infinitely long network with identical...Ch. 27 - Prob. 83PQCh. 27 - What is the equivalent capacitance of the five...Ch. 27 - The circuit in Figure P27.85 shows four capacitors...Ch. 27 - Prob. 86PQCh. 27 - A Pairs of parallel wires or coaxial cables are...Ch. 27 - A parallel-plate capacitor has square plates of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Consider an infinitely long network with identical capacitors arranged as shown in Figure P27.82. Determine the equivalent capacitance of such a network. Each capacitor has a capacitance of 1.00 F.arrow_forwardThe circuit in Figure P27.85 shows four capacitors connected to a battery. The switch S is initially open, and all capacitors have reached their final charge. The capacitances are C1 = 6.00 F, C2 = 12.00 F, C3 = 8.00 F, and C4 = 4.00 F. a. Find the potential difference across each capacitor and the charge stored in each. b. The switch is now closed. What is the new final potential difference across each capacitor and the new charge stored in each? Figure P27.85arrow_forwardFigure P27.75 shows four capacitors with CA = 4.00 F, CB = 8.00 F. CC = 6.00 F. and CD = 5.00 F connected across points a and b, which have potential difference Vab = 12.0 V. a. What is the equivalent capacitance of the four capacitors? b. What is the charge on each of the four capacitors?arrow_forward
- For the four capacitors in the circuit shown in Figure P27.30, CA = 1.00 F, CB = 4.00 F, CC = 2.00 F, and CD = 3.00 F. What is the equivalent capacitance between points a and b? Figure P27.30arrow_forwardA pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?arrow_forwardFind the equivalent capacitance for the network shown in Figure P27.26 if C1 = 1.00 F, C2 = 2.00 F, C3 = 3.00 F, C4 = 4.00 F, and C5 = 5.00 F. FIGURE P27.26 Problems 26 and 27.arrow_forward
- A spherical capacitor is made up of two concentric spherical conductors. The inner sphere has positive charge +Q, and the outer sphere has negative charge Q. The radius of the inner sphere is rin, and the radius of the outer sphere is rout. Show that its capacitance is C = 40[rinrout/(rout rin)].arrow_forwardThe circuit in Figure P21.59 has been connected for a long time. (a) What is the potential difference across the capacitor? (b) If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?arrow_forwardThe capacitances of three capacitors are in the ratio 1:2:3. Their equivalent capacitance when all three are in parallel is 120.0 pF greater than when all three are in series. Determine the capacitance of each capacitor.arrow_forward
- A Derive an expression for the capacitance of an isolated sphere of radius r by taking the limit of C = 40[rinrout/(rout rin)] (see Problem 32) as rout approaches infinity.arrow_forward(a) On a particular day, it takes 9.60103 J of electrical energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V. (b) What is unreasonable about this result? (c) Which assumptions are responsible?arrow_forwardA parallel-plate capacitor has square plates of side s = 2.50 cm and plate separation d = 2.50 mm. The capacitor is charged by a battery to a charge Q = 4.00 C, after which the battery is disconnected. A porcelain dielectric ( = 6.5) is then inserted a distance y = 1.00 cm into the capacitor (Fig. P27.88). Hint: Consider the system as two capacitors connected in parallel. a. What is the effective capacitance of this capacitor? b. How much energy is stored in the capacitor? c. What are the magnitude and direction of the force exerted on the dielectric by the plates of the capacitor? Figure P27.88arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
DC Series circuits explained - The basics working principle; Author: The Engineering Mindset;https://www.youtube.com/watch?v=VV6tZ3Aqfuc;License: Standard YouTube License, CC-BY