College Physics (10th Edition)
10th Edition
ISBN: 9780321902788
Author: Hugh D. Young, Philip W. Adams, Raymond Joseph Chastain
Publisher: PEARSON
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Textbook Question
Chapter 18, Problem 37P
A disk-shaped parallel-plate capacitor has a capacitance C. In terms of C, what would the capacitance be if the radius of each plate were increased by a factor of 3?
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A parallel plate capacitor is made up of two conducting square plates of side length L = 4.3 cm. The distance between the plates is d = 9.2 mm. A dielectric with dielectric constant κ=88 and thickness 9.2 mm is inserted between the plates. The dielectric is L wide and L/2 long, what is the capacitance of this capacitor? Express your answer in farads to 3 significant figures.
Fifty parallel plate capacitors are connected in series. The distance between the plates is d for the first capacitor, 2d for the second capacitor, 3d for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set-in terms of C1 (the capacitance of the first capacitor).
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q.
The electric field E at a radial distance r from the central axis is given by the function:
E = ae Trao + B/r + bo
where alpha (a), beta (ß), ao and bo are constants. Find an expression for its capacitance.
First, let us derive the potential difference ab between the two conductors. The potential difference is related to the electric field by:
Vob =
- S *Edr= - ["Edr
Calculating the antiderivative or indefinite integral,
Vab = (-aage"
o-r/ao + B
+ bo
By definition, the capacitance C is related to the charge and potential difference by:
C =
Evaluating with the upper and lower limits of integration for Vab, then simplifying:
C = Q/(
(erb/ao - eralao) + ß In(
) + bo (
))
Chapter 18 Solutions
College Physics (10th Edition)
Ch. 18 - Why must electric field lines be perpendicular to...Ch. 18 - Which way do electric field lines point, from high...Ch. 18 - If the electric field is zero throughout a certain...Ch. 18 - The potential (relative to a point at infinity)...Ch. 18 - A capacitor is charged by being connected to a...Ch. 18 - A capacitor is charged by being connected to a...Ch. 18 - Two parallel-plate capacitors, identical except...Ch. 18 - The two plates of a capacitor are given charges Q,...Ch. 18 - Liquid dielectrics having polar molecules (such as...Ch. 18 - To store the maximum amount of energy in a...
Ch. 18 - You have two capacitors and want to connect them...Ch. 18 - You have three capacitors, not necessarily equal,...Ch. 18 - A surface will be an equipotential surface if...Ch. 18 - In Figure 18.31, point P is equidistant from both...Ch. 18 - For the capacitor network shown in Figure 18.32, a...Ch. 18 - Two charges are placed on the x axis. A charge of...Ch. 18 - Two point charges with charge +q are initially...Ch. 18 - If the potential (relative to infinity) due to a...Ch. 18 - If the electric potential energy of two point...Ch. 18 - An electron is released between the plates of a...Ch. 18 - The plates of a parallel-plate capacitor are...Ch. 18 - When a certain capacitor carries charge of...Ch. 18 - Two large metal plates carry equal and opposite...Ch. 18 - The electric potential (relative to infinity) due...Ch. 18 - A charge of 28.0 nC is placed in a uniform...Ch. 18 - Two very large charged parallel metal plates are...Ch. 18 - How far from a 7.20 C point charge must a +2.30 C...Ch. 18 - A point charge q1 = +2 40 C is held stationary at...Ch. 18 - Two stationary point charges of +3.00 nC and +2.00...Ch. 18 - A set of point charges is held in place at the...Ch. 18 - Three equal 1.20 C point charges are placed at the...Ch. 18 - When two point charges are a distance R apart,...Ch. 18 - Two large metal parallel plates carry opposite...Ch. 18 - A potential difference of 4.75 kV is established...Ch. 18 - BIO Axons. Neurons are the basic units of the...Ch. 18 - BIO Electrical sensitivity of sharks. Certain...Ch. 18 - A particle with a charge of +4 20 nC is in a...Ch. 18 - Two very large metal parallel plates are 20.0 cm...Ch. 18 - A uniform electric field has magnitude E and is...Ch. 18 - A point charge is sitting at the origin. The...Ch. 18 - An electron is to be accelerated from 3.00 108...Ch. 18 - A small particle has charge 5.00 C and mass 2.00 ...Ch. 18 - Two point charges q1 = +2.40 nC and q2 = 6.50 nC...Ch. 18 - A point charge Q = +4.00 C is held fixed al the...Ch. 18 - Two protons are released from rest when they are...Ch. 18 - x-ray tube. An x-ray tube is an evacuated glass...Ch. 18 - A parallel-plate capacitor having plates 6.0 cm...Ch. 18 - Two very large metal parallel plates that are 25...Ch. 18 - (a) A +5.00 C charge is located on a sheet of...Ch. 18 - A +1.50 C point charge is sitting at the origin....Ch. 18 - Dipole. A dipole is located on a sheet of paper....Ch. 18 - (a) You find that if you place charges of 1.25 C...Ch. 18 - The plates of a parallel-plate capacitor are 3.28...Ch. 18 - The plates of a parallel-plate capacitor are 2.50...Ch. 18 - A parallel-plate air capacitor has a capacitance...Ch. 18 - Suppose you were to design a 1 F parallel-plate...Ch. 18 - A 10.0 F parallel-plate capacitor with circular...Ch. 18 - A 10.0 F parallel-plate capacitor is connected to...Ch. 18 - You make a capacitor by cutting the...Ch. 18 - A 5.00 pF parallel-plate air-filled capacitor with...Ch. 18 - A disk-shaped parallel-plate capacitor has a...Ch. 18 - A parallel-plate capacitor C is charged up to a...Ch. 18 - For the system of capacitors shown in Figure...Ch. 18 - Electric eels. Electric eels and electric fish...Ch. 18 - In Figure 18.39, C1 = 6.00 f, C2 = 3.00 F. and C3...Ch. 18 - You are working on an electronics pro.ect that...Ch. 18 - In Figure 18 39, C1 = 3.00 F anri Vab = 120 V. The...Ch. 18 - A 4.00 F and a 6.00 F capacitor are wired in...Ch. 18 - In the circuit shown in Figure 18.40, the...Ch. 18 - In Figure 18.41 each capacitor has C = 4.00 f and...Ch. 18 - Figure 18.42 shows a system of four capacitors...Ch. 18 - For the system of capacitors shown in Figure...Ch. 18 - How much charge does a 12 V battery have to supply...Ch. 18 - A 5.80 F parallel-plate air capacitor has a plate...Ch. 18 - (a) How much charge does a battery have to supply...Ch. 18 - In the text, it was shown that the energy stored...Ch. 18 - A parallel-plate vacuum capacitor has 8.38 J of...Ch. 18 - A 5.00 nF parallel-plate capacitor contains 25.0 J...Ch. 18 - For the capacitor network shown in Figure 18.44,...Ch. 18 - For the capacitor network shown in Figure 18.45,...Ch. 18 - For the capacitor network shown in Figure 18.46,...Ch. 18 - A parallel-plate air capacitor has a capacitance...Ch. 18 - Cell membranes. Cell membranes (the walled...Ch. 18 - A parallel-plate capacitor is to be constructed by...Ch. 18 - A 12.5 F capacitor is connected to a power supply...Ch. 18 - The paper dielectric in a paper-and-foil capacitor...Ch. 18 - A constant potential difference of 12 V is...Ch. 18 - (a) If a spherical raindrop of radius 0.650 mm...Ch. 18 - At a certain distance from a point charge, the...Ch. 18 - Two oppositely charged identical insulating...Ch. 18 - A positive point charge Q is placed at a position...Ch. 18 - An alpha particle with a kinetic energy of 10.0...Ch. 18 - In the Bohr model of the hydrogen atom, a single...Ch. 18 - A proton and an alpha particle are released from...Ch. 18 - A parallel-plate air capacitor is made from two...Ch. 18 - In the previous problem, suppose the battery...Ch. 18 - A capacitor consists of two parallel plates, each...Ch. 18 - Electronic flash units for cameras contain a...Ch. 18 - In Figure 18.49, each capacitance C1 is 6.9 F and...Ch. 18 - Prob. 76PPCh. 18 - A helium ion (He++) that comes within about 10 fm...Ch. 18 - The maximum voltage at the center of a typical...Ch. 18 - How many moles of Na+ must move per unit area of...Ch. 18 - Prob. 80PPCh. 18 - Suppose that the change in Vm was caused by the...Ch. 18 - What is the minimum amount of work that must be...
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