I inadvertently made number 6b a bit harder than I thought ...
For part b, if you are not able to prove the general result, it is sufficient to prove that a parallel combination has lower power consumption than a series combination. Full points if you can do this, five bonus points if you solve the question as asked.
If you want to prove the general result as the question asks, see HERE for a massive hint, along with smaller ones for other questions.
Overall, I was very pleased with homework 4. The average was 91.4% (std. dev. 8.2%), and most questions had an average of 90% or better:
Questions 2 and 8 caused some trouble though. Question 2 was difficult, I think, due to the unusual phrasing of the problem. This was intentional - you were given realistic data that one could easily measure, and asked to deduce something you can't easily measure. It is a conceptually tricky problem, I think it may be worth your time to read through the solution to this one.
Question 8 was also conceptually tricky. Definitely have a look at the solutions for this one. Briefly:
a) Charge carrier density in a metal is determined mainly just by how many atoms per unit volume there are. Each atom contributes a certain number of mobile electrons, like in problem 4.
b) Current density is just current per unit area - if one doubles, so does the other
c) Drift velocity is proportional to current and the electric field, if current doubles, so does drift velocity.
d) The collision time was assumed to be a constant for each material because it is primarily determined by the random thermal velocity, not the drift velocity. Chaotic thermal motion which gives no net displacement dominates the carrier motion, drift velocity is a tiny effect that gives a small net motion in one direction. In our simple model, collision time depends only on temperature and materials properties.
As I mentioned today, I'm out of town from Thursday morning (14th) until some time Sunday night (17th). Thursday you will do a lab with Mr. Hamner, and Friday a quiz + exam review.
I'll be around my office most of the day tomorrow, and most of this coming Monday though (18th).
Keep in mind that homework is due this coming Monday, 18 Feb.
We will investigate charging and discharging of RC circuits on Thursday. There will be no lecture, only the laboratory experiment. Thus, you should be done early ...
Here is the procedure.
Friday's quiz will be on dc circuits.
If one were interested in NASCAR, and had a physics paper to write, this might be interesting.
NY Times, free registration required.
[Reminder: paper topics are due Feb 29th.]
Enjoy.
I have not carefully proofread these yet, but all of the answers should at least be correct. I will post here if I find any major errors.
Here you go.
Solutions to homework 4 should be finished and online some time tomorrow.
