Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 27.2, Problem 27.2QQ
With the switch in the circuit of Figure 27.4a closed, there is no current in R2 because the current has an alternate zero-resistance path through the switch. There is current in R1, and this current is measured with the ammeter (a device for measuring current) at the bottom of the circuit. If the switch is opened (Fig. 27.4b), there is current in R2. What happens to the reading on the ammeter when the switch is opened? (a) The reading goes up. (b) The reading goes down. (c) The reading does not change.
Figure 27.4 (Quick Quiz 27.2) What happens when the switch is opened?
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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]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 27 Solutions
Physics for Scientists and Engineers
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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