PHYSICS:F/SCI.+ENGRS-W/WEBASSIGN
10th Edition
ISBN: 9781337888479
Author: SERWAY
Publisher: CENGAGE L
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Chapter 27, Problem 38AP
Why is the following situation impossible? A battery has an emf of ε = 9.20 V and an internal resistance of r = 1.20 Ω. A resistance R is connected across the battery and extracts from it a power of P = 21.2 W.
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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,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 27 Solutions
PHYSICS:F/SCI.+ENGRS-W/WEBASSIGN
Ch. 27.1 - To maximize the percentage of the power from the...Ch. 27.2 - With the switch in the circuit of Figure 27.4a...Ch. 27.2 - With the switch in the circuit of Figure 27.6a...Ch. 27.2 - Prob. 27.4QQCh. 27.4 - Consider the circuit in Figure 27.17 and assume...Ch. 27 - Two 1.50-V batterieswith their positive terminals...Ch. 27 - As in Example 27.2, consider a power supply with...Ch. 27 - Figure P27.3 shows the interior of a three-way...Ch. 27 - Prob. 4PCh. 27 - Consider the two circuits shown in Figure P27.5 in...
Ch. 27 - Consider strings of incandescent lights that are...Ch. 27 - You are working at an electronics fabrication...Ch. 27 - In your new job at an engineering company, your...Ch. 27 - A battery with = 6.00 V and no internal...Ch. 27 - A battery with emf and no internal resistance...Ch. 27 - Todays class on current and resistance is about to...Ch. 27 - Why is the following situation impossible? A...Ch. 27 - Calculate the power delivered to each resistor in...Ch. 27 - For the purpose of measuring the electric...Ch. 27 - Four resistors are connected to a battery as shown...Ch. 27 - You have a faculty position at a community college...Ch. 27 - The circuit shown in Figure P27.17 is connected...Ch. 27 - The following equations describe an electric...Ch. 27 - Taking R = 1.00 k and = 250 V in Figure P27.19,...Ch. 27 - In the circuit of Figure P27.20, the current I1 =...Ch. 27 - (a) Can the circuit shown in Figure P27.21 be...Ch. 27 - For the circuit shown in Figure P27.22, we wish to...Ch. 27 - An uncharged capacitor and a resistor are...Ch. 27 - Show that the time constant in Equation 27.20 has...Ch. 27 - In the circuit of Figure P27.25, the switch S has...Ch. 27 - In the circuit of Figure P27.25, the switch S has...Ch. 27 - A 10.0-F capacitor is charged by a 10.0-V battery...Ch. 27 - Show that the integral 0e2t/RCdtin Example 27.11...Ch. 27 - You and your roommates are studying hard for your...Ch. 27 - Prob. 30PCh. 27 - Turn on your desk lamp. Pick up the cord, with...Ch. 27 - Four resistors are connected in parallel across a...Ch. 27 - Find the equivalent resistance between points a...Ch. 27 - The circuit in Figure P27.34a consists of three...Ch. 27 - The circuit in Figure P27.35 has been connected...Ch. 27 - The resistance between terminals a and b in Figure...Ch. 27 - (a) Calculate the potential difference between...Ch. 27 - Why is the following situation impossible? A...Ch. 27 - When two unknown resistors are connected in series...Ch. 27 - When two unknown resistors are connected in series...Ch. 27 - The circuit in Figure P27.41 contains two...Ch. 27 - Two resistors R1 and R2 are in parallel with each...Ch. 27 - A power supply has an open-circuit voltage of 40.0...Ch. 27 - A battery is used to charge a capacitor through a...Ch. 27 - An ideal voltmeter connected across a certain...Ch. 27 - (a) Determine the equilibrium charge on the...Ch. 27 - In Figure P27.47, suppose the switch has been...Ch. 27 - Figure P27.48 shows a circuit model for the...Ch. 27 - The student engineer of a campus radio station...Ch. 27 - A voltage V is applied to a series configuration...Ch. 27 - The switch in Figure P27.51a closes when Vc23Vand...
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