In my first year of graduate school (2008), i TA'd for an introductory electromagnetism class that turned out to be very difficult. Except for the difficulty, i liked a lot of things about the way the course was structured. This letter, then, is advice from a younger me to students dealing with professors like the one i am trying to be.
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Dear Section 2,
A number of you have asked me for study strategies and tips for the final exam. So far i've given only half-answers and promises to think about it. Unfortunately, the number of people i've blown off is slowly approaching the section size. So rather than track you all down with an answer, i'm going to do this all at once. I'm sure there is at least one person who has asked me about a specific situation
that isn't addressed by this e-mail. Whoever you are, i'm sorry, i've forgotten. Ask me again and i'll try to give you a straight answer.
Most of you seem to be having three basic problems:
First, in some instances you just can't get your head around a concept, even in theory. For many, this is your first experience studying phenomena of which you can't immediately form a mental picture, so you are much more scared than you need to be.
Second, you may understand a concept in theory, but don't know when to use it. This issue is characterized by staring blankly at problems while a thousand unusable or unrelated tidbits of information swim through your head.
Third, once you've figured out what concept to use, you discover that you don't really understand it well enough to implement it properly. On exams this tends to manifest itself as a half-credit solution in which you picked random areas, charges, currents, etc. and plugged them into your equation wherever they would fit (or not in some cases).
Finally, as a corollary, several students have complained that they do homework with a group, but on their own they can never reproduce the work. Or they could eventually flail their way to a mostly correct solution, but in an exam there isn't time. These are all problems that are common but somewhat unique to physics. Again, since you have relatively little experience with physics, you are probably more upset than the situation warrants. So calm down, take a deep breath...and let's talk about study strategies.
To start, it might be good to re-read the notes i sent out before the midterm. They contain some tips for right before and during the final that i won't reiterate here. If you need a copy, let me know.
The first problem can only be dealt with by another person. Assuming you've read the lecture notes and the book as they relate to a particular concept, reading them over and over again is unlikely to impart any sudden epiphany. Ask a friend to explain it to you. If that doesn't work, take your friend with you and ask a TA or the professor to explain. I'm always available by e-mail, but basic conceptual questions are much better addressed in person. (Note that you can still use e-mail to make an in-person appointment.) On the flip side, if someone asks you to explain a concept, please make every effort to do so. You might just discover that you don't know it as well as you thought you did. When explaining an equation, if you need math, you don't really understand it. By taking time to just review the theory of the class to each other, you insure yourselves against that sudden feeling of cluelessness when you open the exam.
There is still the question of which concepts in the course are fundamental. If there's a demand for it, i can put together a list, but the part of me that feels responsible doesn't want to risk leaving something off and the physicist in me says it's obvious. Please let me know if this is grossly incorrect. (Update: Nobody asked for this, partly because it was covered in the exam review. If its ever unclear which concepts in my courses are fundamental, please let me know!)
Problem two is basically an inability to DO physics, despite understanding it. The antidote, then, is obviously to do more physics. However it is possible to struggle through many problems without really getting at the underlying skill that makes them look easy in a physicists hands. I've stressed that you can learn faster by working in groups, but there is a danger that part of the group does problems while another part watches. Therefore it is best to work in smaller groups and stay engaged in your group. I've found 2-4 to be about right at this level. That is NOT to say that you can't have more people than that working together. I strongly suggest you make a party of it. Order food, find a place with lots of whiteboard space and invite everyone you know in the class to a physics party. That means someone has to step up and organize it, but you all have to learn the material anyway and this is so much faster and more fun. Some of the best times i had as an undergrad were with some subset of the two dozen people who were just as buried in physics as i was. (Yes, i'm a nerd, but that doesn't make me wrong.) Freshmen: you might even get an RA to organize something for everyone in your dorm.
Several of you have told me that you do practice problems, but they always seem to take forever and/or you're never sure you've got them right. Remember that problems are always written to test one or more of the fundamental concepts. Figure out what those concepts are and you're well on your way to solving the problem. Not by coincidence, the grading rubric usually starts with a couple points just for writing down the relevant concept, often directly from the equation sheet. So in studying and on the exam, start by writing down the concept you are going to use! This will give you something to break into manageable pieces and calm the flutter of other facts running through your head. Once you have a concept, break it down. If it's Gauss' Law, find an appropriate Gaussian surface, calculate it's area and count/calculate the charge it encloses. If you want to integrate the force on a wire from a magnetic field, draw dL and B at some point on your diagram and use the right hand rule to locate the dF vector. At this point, i always wave my hands at the board and say "Do math." From there, you will usually see an obvious, mostly mathematical, path to a solution. If your math skills are a little rusty, group study can be a good time to brush them up.
The third problem is less frightening but more insidious than the first two. It certainly claims the most points. When you understand an equation well enough to see that it applies to your problem, but don't really know what it means or where it came from, you produce a solution that graders politely refer to as 'creative'. This is one of the best reasons to check that you can explain the fundamentals of the course to a fellow student without breaking out any math. This is the reason, when studying, to break each equation into parts and make sure you know what each part is and what it means. This is why every problem should start with a concept, not just an equation. For example: If you know that the voltage around a moving loop is vlB but don't know why or when, you have no idea what length to use and have restricted your knowledge of moving wires to linearly translating loops entering magnetic fields (although you probably don't know that). V=vlB is an equation, Faraday's Law is a concept. The moving wire problem should start with Faraday's Law. The cure to Problem 3 is a combination of the cures to the first two problems. Working problems from their fundamentals will bring out those things that you don't quite understand fully. At that point, it's important not to be afraid of asking about a concept that you thought you had down. In a group, that means asking why the group did what it did. Alone, that means finding a friend or asking a TA. (When you e-mail a TA, remember to tell us what problem you are working on and what you've already done.) Some of you have asked about good problems to study. Obviously old midterm and practice midterms are good. It helps that you have the solution key. But you've seen them before, so they may not build your confidence about fresh problems. Problems from <textbook> are also good, but you don't necessarily have the solutions and they tend to be easier than exam problems. I assume <Head TA> will post practice finals on <course management website>. Those are probably the best material.
I think that covers most of the issues i promised to address. Again, let me know if i've left out something you asked me. Actually, feel free to bring any problems i haven't covered, but hopefully this gets most of them.
Ben
Thursday, July 31, 2014
Friday, March 21, 2014
Watts Up?
A while back i was adding instruments to a rack already loaded with sensitive equipment and started to worry about blowing a fuse in the middle of a delicate experiment. A colleague lent me a power monitor made by the Watts Up? Corporation. You plug it into an outlet, then plug your devices into it and it reads out statistics on your power consumption in Volts, Amps, Watts or Dollars. It does peak detection and a number of other sophisticated things, but i was struck by how little i actually know about grid power usage. I consider myself fairly well informed (i work with electronics for a living), but i did not know, for example, that my desktop draws 0.9 A at rest and 1.3 A when working hard. At 120 V, assuming a rate of $0.15/kWh, it costs $0.39/day to leave my computer running ($0.56 if i leave it running an experiment). Good to know.
I suspect i am in the American majority in having a vague sense that i should reduce my power consumption without really knowing how to effectively do that. I'm sure that some of the 'green consumer' advice we get is good and some of it is hogwash, but i've never taken a quiet stroll through the data to decide which is which.
I'll start at the small end. How important is it to unplug chargers when not in use? Any power 'wasted' by a device turns to heat. In the absence of cooling fins, all heat is radiated away. So if we know the surface area of a device and its temperature, we know how much heat is being wasted. In the extreme limit, a charger that was a 4 inch cube heated to the boiling point would be wasting 42 W. But that's unrealistic. My cell phone charger is about 2"x1"x1" and isn't warm to the touch. Even assuming it is 5 ˚C above room temperature, it wastes 0.18 W (costing me $0.24/year). Not worth the hassle of forgetting to plug it in even once a year.
Looking up, i see that each of my labs is lit by 16 32W fluorescent bulbs, or 512 W. This costs $0.61 per room each day if i work 8 hours (ha), and $1.22 per room if i forget to turn them off one night. That's starting to look like real money. Whatever the advertisers say, fluorescent bulbs don't last any longer than incandescents, but each of those 32 W fluorescents probably replaces a 100 W incandescent. Over the 1000 hr life of each bulb, that extra 68 W costs $10.20. So even though they cost a few bucks extra and are heavily over-advertised, i should probably replace my incandescents at home with compact fluorescents. (grumblegrumble)
A quick search of Energy Star ratings tells me that modern home refrigerators use 280-580 kWh/yr at a cost of $42-$87/yr. (1 kWh/yr = 0.114 W) This number does seem to be very time dependent. Refrigerators from the '90s routinely ran over 1000 kWh/yr or $150/yr. Since a new refrigerator can cost $500-$2000 and lasts 10-15 years, i'd say from a cost perspective its probably not worth replacing a nice refrigerator that isn't nearing the end of its life anyway. (Unless the price of electricity goes up.) On the other hand, my parents have an enormous deep freezer that has been in our basement for my entire life. When we become real people and have our own house, my wife and i definitely want one; but that might be a case where buying new actually is cheaper.
Frankly, i suspect all of this logic is wiped out by the cost of heating and cooling a home. The insulative power of materials is a tricky thing to measure, but the standard unit seems to be R-value measured in (m^2*K)/(W*in). This has the advantage that you add the R-values of multiple insulation layers, but its a weird unit to think about. Most decent insulation has an R-value of about 1, so 5 inches of decent insulation lets through about 0.2 W/(m^2*K), which is a nice physics unit that i'm used to. If we imagine a standard 2-story, square, 200 m^2 house with no windows, a flat roof and 2.5 meter ceilings, it would have 200 m^2 of wall and another 100 m^2 of roof. If you try to pull a 10 degC difference between inside and outside, you need to move 300 W of heat. Total cost: $394/year.
Huh. Actually, that's not bad. However...a single square meter of single-pane glass will cost you 70 W = $92/year under those conditions. Glass is effectively a conductor, but it does block convection. Even double-pane glass with radiation coatings only get this down to ~10 W/m^2 = $13/yr/m^2. If you've used fiberglass panels (R = 0.44) instead of, say, polyurethane foam (R ~ 1), you spend an extra $500/year. On the other hand, installing blown foam costs about $15/m^2, or $4500 for our fictitious house. You'd recover your investment in nine years in modest climes. Definitely worth it in extreme climates, but very geography-dependent. Same goes for double-pane windows. They range $200-$500/m^2 and may save around $80/m^2/year.
Of course, this assumes you're running an electric heater. Air conditioning is even trickier. First, cooling power is often rated in 'tons', which apparently means the same cooling power as 1 ton of ice melting over 1 day. This works out to 3517 W or $4620/yr if it ran continuously. Next is efficiency ratings. There seem to be at least four competing systems, most of which mix imperial and metric units. I like the Coefficient of Performance (COP), which is (Watts removed from house) / (Watts of power used). It seems that COP values of 2-5 are common for cooling systems. Of course, if you switch the input and output pipes on your AC, you could theoretically get that same boost to efficiency by 'cooling' the outdoors to warm your house. This arrangement is sold under the name 'heat pump', which i guess makes sense.
This is rapidly becoming too situation-dependent to carry further. The pattern here seems to be that most of the eco-friendly advice makes good economic sense most of the time, but a lot of it is in the margins and many power usage decisions are interlinked. You really can save money every year by installing better insulation, getting a newer fridge or switching to CPFs. But at current electricity prices, you won't recoup your investment for several years. As for the Watt's Up meters, they range $50-200. Its possible that having better information could help a homeowner save $200 in the course of a decade by making better choices. Probably not worth buying for an apartment-dweller.
I suspect i am in the American majority in having a vague sense that i should reduce my power consumption without really knowing how to effectively do that. I'm sure that some of the 'green consumer' advice we get is good and some of it is hogwash, but i've never taken a quiet stroll through the data to decide which is which.
I'll start at the small end. How important is it to unplug chargers when not in use? Any power 'wasted' by a device turns to heat. In the absence of cooling fins, all heat is radiated away. So if we know the surface area of a device and its temperature, we know how much heat is being wasted. In the extreme limit, a charger that was a 4 inch cube heated to the boiling point would be wasting 42 W. But that's unrealistic. My cell phone charger is about 2"x1"x1" and isn't warm to the touch. Even assuming it is 5 ˚C above room temperature, it wastes 0.18 W (costing me $0.24/year). Not worth the hassle of forgetting to plug it in even once a year.
Looking up, i see that each of my labs is lit by 16 32W fluorescent bulbs, or 512 W. This costs $0.61 per room each day if i work 8 hours (ha), and $1.22 per room if i forget to turn them off one night. That's starting to look like real money. Whatever the advertisers say, fluorescent bulbs don't last any longer than incandescents, but each of those 32 W fluorescents probably replaces a 100 W incandescent. Over the 1000 hr life of each bulb, that extra 68 W costs $10.20. So even though they cost a few bucks extra and are heavily over-advertised, i should probably replace my incandescents at home with compact fluorescents. (grumblegrumble)
A quick search of Energy Star ratings tells me that modern home refrigerators use 280-580 kWh/yr at a cost of $42-$87/yr. (1 kWh/yr = 0.114 W) This number does seem to be very time dependent. Refrigerators from the '90s routinely ran over 1000 kWh/yr or $150/yr. Since a new refrigerator can cost $500-$2000 and lasts 10-15 years, i'd say from a cost perspective its probably not worth replacing a nice refrigerator that isn't nearing the end of its life anyway. (Unless the price of electricity goes up.) On the other hand, my parents have an enormous deep freezer that has been in our basement for my entire life. When we become real people and have our own house, my wife and i definitely want one; but that might be a case where buying new actually is cheaper.
Frankly, i suspect all of this logic is wiped out by the cost of heating and cooling a home. The insulative power of materials is a tricky thing to measure, but the standard unit seems to be R-value measured in (m^2*K)/(W*in). This has the advantage that you add the R-values of multiple insulation layers, but its a weird unit to think about. Most decent insulation has an R-value of about 1, so 5 inches of decent insulation lets through about 0.2 W/(m^2*K), which is a nice physics unit that i'm used to. If we imagine a standard 2-story, square, 200 m^2 house with no windows, a flat roof and 2.5 meter ceilings, it would have 200 m^2 of wall and another 100 m^2 of roof. If you try to pull a 10 degC difference between inside and outside, you need to move 300 W of heat. Total cost: $394/year.
Huh. Actually, that's not bad. However...a single square meter of single-pane glass will cost you 70 W = $92/year under those conditions. Glass is effectively a conductor, but it does block convection. Even double-pane glass with radiation coatings only get this down to ~10 W/m^2 = $13/yr/m^2. If you've used fiberglass panels (R = 0.44) instead of, say, polyurethane foam (R ~ 1), you spend an extra $500/year. On the other hand, installing blown foam costs about $15/m^2, or $4500 for our fictitious house. You'd recover your investment in nine years in modest climes. Definitely worth it in extreme climates, but very geography-dependent. Same goes for double-pane windows. They range $200-$500/m^2 and may save around $80/m^2/year.
Of course, this assumes you're running an electric heater. Air conditioning is even trickier. First, cooling power is often rated in 'tons', which apparently means the same cooling power as 1 ton of ice melting over 1 day. This works out to 3517 W or $4620/yr if it ran continuously. Next is efficiency ratings. There seem to be at least four competing systems, most of which mix imperial and metric units. I like the Coefficient of Performance (COP), which is (Watts removed from house) / (Watts of power used). It seems that COP values of 2-5 are common for cooling systems. Of course, if you switch the input and output pipes on your AC, you could theoretically get that same boost to efficiency by 'cooling' the outdoors to warm your house. This arrangement is sold under the name 'heat pump', which i guess makes sense.
This is rapidly becoming too situation-dependent to carry further. The pattern here seems to be that most of the eco-friendly advice makes good economic sense most of the time, but a lot of it is in the margins and many power usage decisions are interlinked. You really can save money every year by installing better insulation, getting a newer fridge or switching to CPFs. But at current electricity prices, you won't recoup your investment for several years. As for the Watt's Up meters, they range $50-200. Its possible that having better information could help a homeowner save $200 in the course of a decade by making better choices. Probably not worth buying for an apartment-dweller.
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