COLLEGE PHYSICS (LL W/WEBASSIGN)
11th Edition
ISBN: 9781337741644
Author: SERWAY
Publisher: CENGAGE L
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Chapter 17, Problem 36P
If electrical energy costs $0.12 per kilowatt-hour, how much does it cost to (a) burn a 100-W lightbulb for 24 h? (b) Operate an electric oven for 5.0 h if it carries a current of 20.0 A at 220 V?
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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 17 Solutions
COLLEGE PHYSICS (LL W/WEBASSIGN)
Ch. 17.1 - Consider positive and negative charges all moving...Ch. 17.2 - Suppose a current-carrying wire has a...Ch. 17.3 - Look at the four circuits shown in Figure 17.6 and...Ch. 17.4 - Prob. 17.4QQCh. 17.4 - All electric devices are required to have...Ch. 17.4 - Suppose an electrical wire is replaced with one...Ch. 17.6 - Prob. 17.7QQCh. 17.6 - For the two resistors shown in Figure 17.12, rank...Ch. 17.6 - Two resistors, A and B, are connected in a series...Ch. 17.6 - The diameter of wire A is greater than the...
Ch. 17 - We have seen that an electric field must exist...Ch. 17 - A 12-V battery is connected across a device with...Ch. 17 - Prob. 3CQCh. 17 - In an analogy between traffic flow and electrical...Ch. 17 - Two copper wires A and B have the same length and...Ch. 17 - Two lightbulbs are each connected to a voltage of...Ch. 17 - Newspaper articles often have statements such as...Ch. 17 - There is an old admonition given to experimenters...Ch. 17 - What could happen to the drift velocity of the...Ch. 17 - Power P0 = I0 V0 is delivered to a resistor of...Ch. 17 - When is more power delivered to a lightbulb,...Ch. 17 - Prob. 1PCh. 17 - A copper wire has a circular cross section with a...Ch. 17 - In the Bohr model of the hydrogen atom, an...Ch. 17 - A typical lightning bolt may last for 0.200 s and...Ch. 17 - Prob. 5PCh. 17 - Prob. 6PCh. 17 - A 2.0 102-km-long high-voltage transmission line...Ch. 17 - An aluminum wire having a cross-sectional area of...Ch. 17 - An iron wire has a cross-sectional area of 5.00 ...Ch. 17 - Prob. 10PCh. 17 - Prob. 11PCh. 17 - Germanium is a semiconducting metal with a...Ch. 17 - Prob. 13PCh. 17 - Prob. 14PCh. 17 - Nichrome wire of cross-sectional radius 0.791 mm...Ch. 17 - Prob. 16PCh. 17 - A potential difference of 12 V is found to produce...Ch. 17 - The current supplied by a battery in a portable...Ch. 17 - A wire 50.0 m long and 2.00 mm in diameter is...Ch. 17 - Prob. 20PCh. 17 - Prob. 21PCh. 17 - The human body can exhibit a wide range of...Ch. 17 - Starting from Ohms law, show that E = J, where E...Ch. 17 - Prob. 24PCh. 17 - Prob. 25PCh. 17 - Prob. 26PCh. 17 - Prob. 27PCh. 17 - At what temperature will aluminum have a...Ch. 17 - At 20.0C, the carbon resistor in an electric...Ch. 17 - Prob. 30PCh. 17 - Prob. 31PCh. 17 - An engineer needs a resistor with a zero overall...Ch. 17 - In one form of plethysmograph (a device for...Ch. 17 - Prob. 34PCh. 17 - A 5.00-V power supply provides a maximum current...Ch. 17 - If electrical energy costs 0.12 per kilowatt-hour,...Ch. 17 - Residential building codes typically require the...Ch. 17 - A portable coffee heater supplies a potential...Ch. 17 - The heating element of a coffeemaker operates at...Ch. 17 - A typical cell phone consumes an average of about...Ch. 17 - Lightbulb A is marked 25.0 W 120. V, and lightbulb...Ch. 17 - Prob. 42PCh. 17 - A copper cable is designed to carry a current of...Ch. 17 - Batteries are rated in terms of ampere-hours (A ...Ch. 17 - The potential difference across a resting neuron...Ch. 17 - The cost of electricity varies widely throughout...Ch. 17 - An electric utility company supplies a customers...Ch. 17 - An office worker uses an immersion heater to warm...Ch. 17 - Two wires A and B made of the same material and...Ch. 17 - Prob. 50PCh. 17 - If a battery is rated at 60.0 A h, how much total...Ch. 17 - A car owner forgets to turn off the headlights of...Ch. 17 - Prob. 53APCh. 17 - A given copper wire has a resistance of 5.00 at...Ch. 17 - Prob. 55APCh. 17 - Birds resting on high-voltage power lines are a...Ch. 17 - Prob. 58APCh. 17 - You are cooking breakfast for yourself and a...Ch. 17 - The current in a conductor varies in time as shown...Ch. 17 - A 120.-V motor has mechanical power output of 2.50...Ch. 17 - Prob. 62APCh. 17 - A length of metal wire has a radius of 5.00 103 m...Ch. 17 - In a certain stereo system, each speaker has a...Ch. 17 - A resistor is constructed by forming a material of...Ch. 17 - When a straight wire is heated, its resistance...Ch. 17 - An x-ray tube used for cancer therapy operates at...Ch. 17 - A man wishes to vacuum his car with a canister...
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Ohm's law Explained; Author: ALL ABOUT ELECTRONICS;https://www.youtube.com/watch?v=PV8CMZZKrB4;License: Standard YouTube License, CC-BY