Monday, December 6, 2010
Final solutions: problems 5-8, 5d
Friday, December 3, 2010
Review tomorrow: Saturday, 12:30 - 2:00 PM
Also, i added an additional final practice problem in the Transient Circuits Lab post below.
Photosynthesis: can you live with it?
I know some of you have mixed feelings about photosynthesis. You like the oxygen, but you are worried that a question about an oscillating electric field initiating photosynthesis might be bad for your health.
To the right is a poll regarding photosynthesis. What it asks about is how you would feel about a supplemental extra-credit question; so you wouldn't have to do it at all if you don't want to, and you could get extra credit if you did do it. It would focus on the physics part of photosynthesis --the very beginning, in which an electric field helps an electron get into an excited state
Here are my thoughts on the initial part of the photosynthesis process. The part where a “photon” is absorbed and an electron makes a quantum leap from its ground state to an excited state. I won't use the word photon, because: 1) we haven't defined that, and 2) it is actually not helpful for describing transitions or calculating their rates. I will describe the initiation of photosynthesis in terms of electric fields pushing on electric charges. These are things we have been studying this quarter.
An electric field comes from the sun. It propagates across millions of miles of empty space using the magic of induction to transform its energy into a magnetic form and then back again trillions and trillions of times. (This is the nature of light. It is composed of oscillating electric and magnetic fields.)
* This is the essentially a quantum measurement process and so it has a probabilistic aspect to it. You do not need to worry too much about that unless it is something that particularly interests you.
To the right is a poll regarding photosynthesis. What it asks about is how you would feel about a supplemental extra-credit question; so you wouldn't have to do it at all if you don't want to, and you could get extra credit if you did do it. It would focus on the physics part of photosynthesis --the very beginning, in which an electric field helps an electron get into an excited state
Here are my thoughts on the initial part of the photosynthesis process. The part where a “photon” is absorbed and an electron makes a quantum leap from its ground state to an excited state. I won't use the word photon, because: 1) we haven't defined that, and 2) it is actually not helpful for describing transitions or calculating their rates. I will describe the initiation of photosynthesis in terms of electric fields pushing on electric charges. These are things we have been studying this quarter.
At the Mg2+ site, before any light arrives, the electrons are sitting quietly in their ground state. This is a very stable state--a neon-like closed shell (2s2, 2p6). The electrons are quiet and happy. They see no reason to change.
An electric field comes from the sun. It propagates across millions of miles of empty space using the magic of induction to transform its energy into a magnetic form and then back again trillions and trillions of times. (This is the nature of light. It is composed of oscillating electric and magnetic fields.)
When the electric field, which has the wave-like form which we discussed in class, passes through the chlorophyll it exerts a force on the electrons in the Mg2+. One electron in particular will begin to oscillate due to the influence of the electric field wave. It moves up and down in the same way that a floating buoy in the ocean moves up and down when ocean waves pass by it. The force on the electron is given by qE(t), where q is the charge of the electron and E(t) is the electric field of the light wave.
In this oscillating phase, the electron is in a superposition state, in which it is partially in an excited state and partially still in the ground state. After a little while, the ligands began to notice this oscillating, partially excited electron. They grab for the excited electron. Their chance* of success is not 100%, but if they are successful they will spirit the excited electron away and use its energy to initiate a complex chemical and biological process (6H2O + 6CO2 --> …..).
From a physics point of view, the key step is the transfer of energy from the electric field to the electron. This occurs via the qE interaction which gets the oscillatory movement of the electron started. The force on a charge due to an electric field, qE, was one of the first things we learned about this quarter.
* This is the essentially a quantum measurement process and so it has a probabilistic aspect to it. You do not need to worry too much about that unless it is something that particularly interests you.
Thursday, December 2, 2010
Some things to consider in preparing for your final.
Here is a preview summary of what you could choose to focus on for the final. (I will add more later.) These will be the things that I will emphasize in composing the final. The purpose of the final is to help you solidify your understanding of the most important aspects of this class in a way that will enable you to remember them for longer than usual.
First, it is useful to be able to quickly sketch electric fields due to two or three charges. This sort of skill helps you visualize electric fields, for example, especially those emanating from an oscillating electric dipole which plays an important role in our understanding of electromagnetic radiation generation.
Second, you would wish to be able to analyze the currents and voltages (voltage differences) in simple circuits with a few resistors. In my opinion, the key to understanding circuits is to understand current. In a simple loop circuit, with no bifurcations, the current is and must be the same everywhere along the circuit path. Additionally, current divides and recombines at simple bifurcating junctions in a simple way: if the there is a bifurcation (fork) where in the upper half the resistance is 1 Ohm and in the lower half resistance is 2 Ohms, then the current through the upper half will be twice as large as the current through the lower half. This implies that two thirds of the total current goes through the upper half and one third through the lower half. If you understand this intuitively you'll be able to do every problem. You did not need any formula other than V=IR. V=IR tells you the voltage drop across any particular resistor in terms of I. Tto find the current, I, however, you need to analyze the entire circuit as a system. You cannot look at just one part and tell what I is. That is what it means to say that the current is a property of the entire system not of an individual part.
Third, think about circuits which include capacitors and inductors --can you confidently articulate the behavior of circuits with capacitors and inductors. We describe the behavior of circuits in three ways: with equations, with graphs, and with words. All three are important. I hope you will be comfortable with all 3 modes of communicating and understanding circuits.
Circuits with capacitors and inductors exhibit time dependence. Why is that? Think about that for a while. That is a good practice problem. Why do circuits with capacitors or inductors exhibit time-dependent? (There are two different answers, one for capacitors on for inductors. Feel free to post your thoughts on that here.)
Understanding LRC circuits is also a point of emphasis for us. Our focus, is on LRC circuits that are similar to LC circuits --the current oscillates, the charge on the capacitor oscillates -- however, they lose a little energy in each cycle. What part of the circuit causes that energy loss? How and when does it happen?
In general for LRC circuits, the key things to understand are: charge (in the capacitor), as function of time, current as a function of time, what their graphs look like, how to calculate them, and everything having to do with energy. Energy can be stored in some parts of the circuit --and you want to understand that and its time dependence. Energy can also be lost in one part of the circuit. Losing energy is a bit different from storing energy. Understand the rate of energy loss and how that relates to other things and how it adds up over time is a good thing.
Other things that are important to understand and remember include the essential nature of E&M radiation, how photosynthesis gets started, how an oscillating electric dipole can generate an electric field wave...
anything i have left out?
Your input. comments and questions are welcome.
First, it is useful to be able to quickly sketch electric fields due to two or three charges. This sort of skill helps you visualize electric fields, for example, especially those emanating from an oscillating electric dipole which plays an important role in our understanding of electromagnetic radiation generation.
Second, you would wish to be able to analyze the currents and voltages (voltage differences) in simple circuits with a few resistors. In my opinion, the key to understanding circuits is to understand current. In a simple loop circuit, with no bifurcations, the current is and must be the same everywhere along the circuit path. Additionally, current divides and recombines at simple bifurcating junctions in a simple way: if the there is a bifurcation (fork) where in the upper half the resistance is 1 Ohm and in the lower half resistance is 2 Ohms, then the current through the upper half will be twice as large as the current through the lower half. This implies that two thirds of the total current goes through the upper half and one third through the lower half. If you understand this intuitively you'll be able to do every problem. You did not need any formula other than V=IR. V=IR tells you the voltage drop across any particular resistor in terms of I. Tto find the current, I, however, you need to analyze the entire circuit as a system. You cannot look at just one part and tell what I is. That is what it means to say that the current is a property of the entire system not of an individual part.
Third, think about circuits which include capacitors and inductors --can you confidently articulate the behavior of circuits with capacitors and inductors. We describe the behavior of circuits in three ways: with equations, with graphs, and with words. All three are important. I hope you will be comfortable with all 3 modes of communicating and understanding circuits.
Circuits with capacitors and inductors exhibit time dependence. Why is that? Think about that for a while. That is a good practice problem. Why do circuits with capacitors or inductors exhibit time-dependent? (There are two different answers, one for capacitors on for inductors. Feel free to post your thoughts on that here.)
Understanding LRC circuits is also a point of emphasis for us. Our focus, is on LRC circuits that are similar to LC circuits --the current oscillates, the charge on the capacitor oscillates -- however, they lose a little energy in each cycle. What part of the circuit causes that energy loss? How and when does it happen?
In general for LRC circuits, the key things to understand are: charge (in the capacitor), as function of time, current as a function of time, what their graphs look like, how to calculate them, and everything having to do with energy. Energy can be stored in some parts of the circuit --and you want to understand that and its time dependence. Energy can also be lost in one part of the circuit. Losing energy is a bit different from storing energy. Understand the rate of energy loss and how that relates to other things and how it adds up over time is a good thing.
Other things that are important to understand and remember include the essential nature of E&M radiation, how photosynthesis gets started, how an oscillating electric dipole can generate an electric field wave...
anything i have left out?
Your input. comments and questions are welcome.
Sunday, November 21, 2010
Transient Circuits lab discussion and related final practice problem
This lab is more aligned with what we have been emphasizing in class and will allow you to see the time-dependent behavior of circuits. It is very important to notice and understand that the duration of each square wave is much longer than the characteristic time scale associated with your circuits in this lab. Thus each square wave functions as essentially a DC voltage; the beginning of each square wave "on-cycle" is essentially equivalent to the closing of a switch and the application of a DC voltage. You will look at the time-dependent response after the switch is closed.
*In this context, transient circuit analysis means analysis of the time-dependent response of the circuit to a sudden change in voltage, which we have discussed quite a bit in class and on HW.
Please feel free to post your comments and questions here.
added Friday, Dec 3
Here is a new practice problem:
Saturday, November 20, 2010
Other things you would like to learn about.
Before our class is over, I would like to ask if there any other topics or issues, related to electricity and magnetism, you would like to learn more about? Please feel free to post comments and thoughts on that here (or to email me if you prefer). zacksc@gmail.com
Friday, November 19, 2010
Everything you always wanted to know about oscillating circuits and more.
LCR circuits might seem daunting; I would suggest viewing them as LC circuits with a small resistor tacked on. As we learned earlier, the LC combination produces oscillations! The inductor (L) stores energy -in its magnetic (B) field- when there is any current in the circuit; while the capacitor, on the other hand, stores energy -in its charge and the associated E field- when the current in the circuit is zero.... There is always energy somewhere, and it transfers back-and-forth, from the inductor to the capacitor, in an oscillatory fashion.
A small resistor adds a third element which transfers energy out of the circuit, e.g., into light and/or heat. We can regard the resistor as a small perturbation that gradually diminishes the energy in the circuit; with each oscillation the peak values of the charge and the current are a little less than they were the time before.
Below are some notes -calculations- which show a fundamental model equation for an LCR circuit and its solution in terms of Q(t). The main things you need to know are:
1) what the equation for Q(t) is; what its graph looks like -in detail-; and how its parameters and behavior depend on L, C and R.
2) same thing for the current, I(t). Additionally, the relationship, graphical and in equation form, between I(t) and Q(t) is important.
3) how to calculate energy from I(t) and Q(t).
4) how to calculate w, T and tau from L, C and R, and what they are and what role they play in Q, I, V and all related energies.
and additionally,
4) to have an intuitive feel for and understanding of the characteristic time scales-- tau and T -- and to understand what it means for tau to be much greater than T.
Your comments and questions are welcome!
A small resistor adds a third element which transfers energy out of the circuit, e.g., into light and/or heat. We can regard the resistor as a small perturbation that gradually diminishes the energy in the circuit; with each oscillation the peak values of the charge and the current are a little less than they were the time before.
Below are some notes -calculations- which show a fundamental model equation for an LCR circuit and its solution in terms of Q(t). The main things you need to know are:
1) what the equation for Q(t) is; what its graph looks like -in detail-; and how its parameters and behavior depend on L, C and R.
2) same thing for the current, I(t). Additionally, the relationship, graphical and in equation form, between I(t) and Q(t) is important.
3) how to calculate energy from I(t) and Q(t).
4) how to calculate w, T and tau from L, C and R, and what they are and what role they play in Q, I, V and all related energies.
and additionally,
4) to have an intuitive feel for and understanding of the characteristic time scales-- tau and T -- and to understand what it means for tau to be much greater than T.
Your comments and questions are welcome!
Thursday, November 18, 2010
Review: Saturday December 4, 12:30 - 2:00 PM
We'll have a review scheduled on Saturday Dec 4, at:
12:30 PM
in (our regular classroom)
Thimann 3
12:30 PM
in (our regular classroom)
Thimann 3
Tuesday, November 16, 2010
Homework practice problems for this week. *new 7 added on Dec 1
Thursday 1 PM: I did some minor edits.
(Instead of an online homework assignment this week, the class chose to instead work on some written practice/homework problems. Here they are. Feel free and encouraged to post any questions or comments here.)
PS. Even when the questions do not ask for graphs, i would strongly encourage you to graph everything you can think of, e.g., I v t, Q v t, tau v R, T v C, etc. Familiarity with graphs and their meanings is highly valued here. (I'll add that in now.)
1. In a series LRC circuit --which starts out with a charged capacitor -- which of the following statements is true:
a) the current starts out from the capacitor, then flows through the inductor and then through the resistor.
b) Current can flow either clockwise or counterclockwise, and it can change as a function of time, but at any given moment the current is the same everywhere in the circuit so it is not useful or helpful to talk about where it goes first.
---------------
2.
a) What is an Ohm in terms of Coulombs, Volts and seconds?
b) What is a Farad in terms of Coulombs, Volts and seconds?
c) What is a Henry in terms of Coulombs, Volts and seconds?
----------------
3. Consider a series LRC circuit with L= 1 H, R= 1 Ohm and C= 10^-2/(2*pi)^2 F*. Suppose that at t=0 the current is zero and the charge on the capacitor is 0.002 Coulombs.
(* This was 10^-6/(2*pi)^2 F earlier this week...)
a) What is tau? What is T? What is tau/T?
b) Write an equation for the charge on the capacitor as a function of time. (graph it)
c) At what time is the charge on the capacitor zero? What is the current in the circuit at that time? (graph it (current))
d) xc. why do you think i made C much smaller than R and L?
----------
4. Referring to the same circuit and initial conditions as in problem #3:
a) at the time when the charge on the capacitor has reached zero, where is the energy in the circuit and how much (energy) is there?
b) has any energy been lost? If so where did it go?
c) xc. draw a picture, a graph, which illustrates the lost energy as the area under a "curve". Describe in words what your picture represents and means.
5. Referring to the same circuit and initial conditions as in problem #3:
a) at approximately what time, after t=0, does the current return to zero? (graph it)
b) at that time, what is the energy stored in the inductor and in the capacitor respectively. (graph the energies as a function of time.)
c) has much energy been lost? how much? How does that compare to your result for energy lost from 4b?
6. Referring to the same circuit and initial conditions as in problem #3:
a) what is the voltage across the capacitor at t =0?
b) what is the voltage across the inductor at t = 0?
c) graph both voltages as a function of time.
7. a) Graph tau vs R.
b) Graph tau vs L.
c) Graph w vs C
d) Graph T vs C
e) extreme extra credit: graph T vs R. what is the range and domain that makes sense to you and why?
I realize these problems may be difficult. If you get stuck at any point, please ask questions with a comment here. Probably some other people are stuck on the same thing? For 3a), do you know what T refers to and how to calculate it? What equation do you use for w? You can ask very simple questions. For example: what is T?, how do we calculate w and tau??, how do you calculate the current, I(t)?, etc.
(Instead of an online homework assignment this week, the class chose to instead work on some written practice/homework problems. Here they are. Feel free and encouraged to post any questions or comments here.)
PS. Even when the questions do not ask for graphs, i would strongly encourage you to graph everything you can think of, e.g., I v t, Q v t, tau v R, T v C, etc. Familiarity with graphs and their meanings is highly valued here. (I'll add that in now.)
1. In a series LRC circuit --which starts out with a charged capacitor -- which of the following statements is true:
a) the current starts out from the capacitor, then flows through the inductor and then through the resistor.
b) Current can flow either clockwise or counterclockwise, and it can change as a function of time, but at any given moment the current is the same everywhere in the circuit so it is not useful or helpful to talk about where it goes first.
---------------
2.
a) What is an Ohm in terms of Coulombs, Volts and seconds?
b) What is a Farad in terms of Coulombs, Volts and seconds?
c) What is a Henry in terms of Coulombs, Volts and seconds?
----------------
3. Consider a series LRC circuit with L= 1 H, R= 1 Ohm and C= 10^-2/(2*pi)^2 F*. Suppose that at t=0 the current is zero and the charge on the capacitor is 0.002 Coulombs.
(* This was 10^-6/(2*pi)^2 F earlier this week...)
a) What is tau? What is T? What is tau/T?
b) Write an equation for the charge on the capacitor as a function of time. (graph it)
c) At what time is the charge on the capacitor zero? What is the current in the circuit at that time? (graph it (current))
d) xc. why do you think i made C much smaller than R and L?
----------
4. Referring to the same circuit and initial conditions as in problem #3:
a) at the time when the charge on the capacitor has reached zero, where is the energy in the circuit and how much (energy) is there?
b) has any energy been lost? If so where did it go?
c) xc. draw a picture, a graph, which illustrates the lost energy as the area under a "curve". Describe in words what your picture represents and means.
5. Referring to the same circuit and initial conditions as in problem #3:
a) at approximately what time, after t=0, does the current return to zero? (graph it)
b) at that time, what is the energy stored in the inductor and in the capacitor respectively. (graph the energies as a function of time.)
c) has much energy been lost? how much? How does that compare to your result for energy lost from 4b?
6. Referring to the same circuit and initial conditions as in problem #3:
a) what is the voltage across the capacitor at t =0?
b) what is the voltage across the inductor at t = 0?
c) graph both voltages as a function of time.
7. a) Graph tau vs R.
b) Graph tau vs L.
c) Graph w vs C
d) Graph T vs C
e) extreme extra credit: graph T vs R. what is the range and domain that makes sense to you and why?
Monday, November 15, 2010
Online homework poll
Please see the online homework poll to the right. Please feel free to comment here and suggest other questions and perspectives about the homework issue or anything related to that.
Sunday, November 14, 2010
Homework 7: comments here
Note added: homework 7 is canceled. I will post some potentially important and hopefully interesting practice problems instead.
HW #7 includes questions about circuits with L, C and R type elements. Please feel free to comment if some of these problems see impossible to do with what we have covered and emphasized in class. I will modify the HW later if that seems like a good idea.
In order for you to understand the nature oscillating LC circuits and LCR circuits, it is critically important for you to be quite familiar with sine and cosine functions, as well as exponential functions.
What does cos(wt) look like from wt=0 to pi/2 ?
What does sin(wt) look like from wt=0 to pi/2 ?
Why does it seem reasonable, looking at the graphs, that the derivative of cos(wt) is -wsin(wt)?
etc...
If you can achieve that familiarity, then you will be able to visualize, understand and discuss the behavior of circuits, which will be a major point of emphasis for he final.
Consider the function: sin(wt), where w has units of 1/seconds, also known as frequency and t is time. What is its value at t=0? Can you graph this function? What is its highest value? What is its lowest value? What is its period? These questions are best answered by looking at a graph and seeing and understanding what the function looks like -- how it goes up and down and repeats as a function of time.
The function, cos(wt), is equally important. Unlike the sine function it starts out at 1, at t=0, but just like the sine function, it oscillates up and down and repeats as a function of time. What does cos(wt) look like when it is multiplied by exp{-t/tau}...
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