Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
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ISBN: 9781337888745
Author: SERWAY, Raymond A., Jewett, John W.
Publisher: Cengage Learning
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Chapter 25, Problem 47CP
Some physical systems possessing capacitance continuously distributed over space can be modeled as an infinite array of discrete circuit elements. Examples are a microwave waveguide and the axon of a nerve cell. To practice analysis of an infinite array, determine the equivalent capacitance C between terminals X and Y of the infinite set of capacitors represented in Figure P25.47. Each capacitor has capacitance C0. Suggestions: Imagine that the ladder is cut at the line AB and note that the equivalent capacitance of the infinite section to the right of AB is also C.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
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[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
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[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 25 Solutions
Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
Ch. 25.1 - A capacitor stores charge Q at a potential...Ch. 25.2 - Many computer keyboard buttons are constructed of...Ch. 25.3 - Two capacitors are identical. They can be...Ch. 25.4 - You have three capacitors and a battery. In which...Ch. 25.5 - If you have ever tried to hang a picture or a...Ch. 25 - (a) When a battery is connected to the plates of a...Ch. 25 - Two conductors having net charges of +10.0 C and...Ch. 25 - When a potential difference of 150 V is applied to...Ch. 25 - An air-filled parallel-plate capacitor has plates...Ch. 25 - A variable air capacitor used in a radio tuning...
Ch. 25 - Review. A small object of mass m carries a charge...Ch. 25 - Find the equivalent capacitance of a 4.20-F...Ch. 25 - Why is the following situation impossible? A...Ch. 25 - A group of identical capacitors is connected first...Ch. 25 - Three capacitors are connected to a battery as...Ch. 25 - Four capacitors are connected as shown in Figure...Ch. 25 - (a) Find the equivalent capacitance between points...Ch. 25 - Find the equivalent capacitance between points a...Ch. 25 - You are working at an electronics fabrication...Ch. 25 - Two capacitors give an equivalent capacitance of...Ch. 25 - Two capacitors give an equivalent capacitance of...Ch. 25 - A 3.00-F capacitor is connected to a 12.0-V...Ch. 25 - Two capacitors, C1 = 18.0 F and C2 = 36.0 F, are...Ch. 25 - Two identical parallel-plate capacitors, each with...Ch. 25 - Two identical parallel-plate capacitors, each with...Ch. 25 - Two capacitors, C1 = 25.0 F and C2 = 5.00 F, are...Ch. 25 - A parallel-plate capacitor has a charge Q and...Ch. 25 - Consider two conducting spheres with radii R1 and...Ch. 25 - A supermarket sells rolls of aluminum foil,...Ch. 25 - Determine (a) the capacitance and (b) the maximum...Ch. 25 - The voltage across an air-filled parallel-plate...Ch. 25 - A commercial capacitor is to be constructed as...Ch. 25 - Each capacitor in the combination shown in Figure...Ch. 25 - A 2.00-nF parallel-plate capacitor is charged to...Ch. 25 - An infinite line of positive charge lies along the...Ch. 25 - A small object with electric dipole moment p is...Ch. 25 - The general form of Gausss law describes how a...Ch. 25 - You are working in a laboratory, using very...Ch. 25 - Four parallel metal plates P1, P2, P3, and P4,...Ch. 25 - A uniform electric field E = 3 000 V/m exists...Ch. 25 - Two large, parallel metal plates, each of area A,...Ch. 25 - A parallel-plate capacitor with vacuum between its...Ch. 25 - Why is the following situation impossible? A...Ch. 25 - Two square plates of sides are placed parallel to...Ch. 25 - (a) Two spheres have radii a and b, and their...Ch. 25 - Assume that the internal diameter of the...Ch. 25 - A parallel-plate capacitor of plate separation d...Ch. 25 - To repair a power supply for a stereo amplifier,...Ch. 25 - Example 25.1 explored a cylindrical capacitor of...Ch. 25 - You are part of a team working in a machine parts...Ch. 25 - Consider two long, parallel, and oppositely...Ch. 25 - Some physical systems possessing capacitance...Ch. 25 - A parallel-plate capacitor with plates of area LW...Ch. 25 - A capacitor is constructed from two square,...Ch. 25 - This problem is a continuation of Problem 45. You...
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