Your friendly neighbourhood webTA here wishing you good luck on your exam tomorrow! Wise advice from Douglas Adams and the Hitchiker's Guide to the Galaxy:
DON'T PANIC!
Relax, try to stay clear-headed, and don't stay up all night studying, get some sleep.
Good luck to you all.
16 April 2007
05 April 2007
Question: AC circuits and resonance
This question relates to Lab 6 but also to the lecture material (it was in the lab that I figured out that my understanding of the material was totally wrong).
It makes sense that in an A/C circuit the capacitor charges when there is a voltage and then discharges through the inductor when the voltage goes away. Also, it seems that the capacitor may or may not reach it's max charge depending of the frequency of the A/C generator (is that correct?). But why does the charging/discharging create a pattern with deteriorating voltage? It seems like the charge in the capacitor should just go up and down to the same extream values over and over. And how is this related to the resonance of the circuit at all? For some reason the frequency of these oscillations is the same as the resonance frequency, but it seems like this shouldn't be the case at all, I would have thought they would be very different values.
Let's see if I can help...
Your first comment is regarding the decay in the oscillations in the LC circuit. It's been awhile since I was a lab demonstrator, so I don't recall the setup exactly for this experiment, however, it sounds like there is a resistance in the circuit (whether there is a resistor there or not... it could be the fact that you have a "real" inductor which consists of a length of wire and will have some resistance). In that case, you have a damped harmonic oscillator system. The inductor and capacitor act as an oscillator (where the capacitor acts like a mass, and the inductor provides a restoring force like a spring), but the resistance provides a means for energy to leave the system, so the oscillations will decay. An analogous mechanical system would be a mass on a spring in molasses... for an entertaining visual. As for what you think it "should" do, you are correct, in that if you had a perfect capacitor and a perfect inductor with no resistances, the system would keep on oscillating forever.
As for resonance... this seems to confuse a lot of people every year. Here's a question and answer from a couple of years ago just to define what we are talking about:
Q: I am a little confused about frequency. What exactly is the resonant frequency and how and why does it effect the current compared to the frequency?
A: In an AC circuit, depending on the components in the circuit, the impedance (a sort of complex resistance) may depend on the frequency. Thus, if an oscillating voltage is applied, the amplitude of the current (peak amount of current that flows) may also depend on the frequency of the applied voltage. This is how the current depends on frequency.
In the case of an LRC circuit, there is a phenomenon called "resonance", whereby the amplitude response of the current has a maximum at the so-called "resonant frequency". Resonance is a common in oscillatory systems, where the amplitude response of the system, be it a mechanical system, or an electrical system, has a maximum at some frequency. At frequencies other than the resonance frequency the amplitude response of the system (the amplitude of the current in this case) will be smaller.
Now, in an electrical system, the resonance will be established by the capacitor and the inductor (the resistance provides the damping), and the values of these components will give the resonance frequency, which is the natural frequency at which the oscillating system operates at, and where it will have the greatest response if you drive it with a frequency. If you input an oscillating voltage to an LC circuit, the amplitude of the current should be very small until you get near the resonance frequency. However... I'm not sure if this is what you did?
If you input a square wave at a much much lower frequency than the resonance, then it will be like turning on and off the voltage, and you would see oscillations at the resonance frequency, which would decay until the next cycle when they would start again. Perhaps this is what you did in the lab.
I hope this is somewhat helpful. Without knowing what you did in lab, I can't be sure where the confusion lies. Please do comment (click the # comment link below... or email if that doesn't work) to follow up!
It makes sense that in an A/C circuit the capacitor charges when there is a voltage and then discharges through the inductor when the voltage goes away. Also, it seems that the capacitor may or may not reach it's max charge depending of the frequency of the A/C generator (is that correct?). But why does the charging/discharging create a pattern with deteriorating voltage? It seems like the charge in the capacitor should just go up and down to the same extream values over and over. And how is this related to the resonance of the circuit at all? For some reason the frequency of these oscillations is the same as the resonance frequency, but it seems like this shouldn't be the case at all, I would have thought they would be very different values.
Let's see if I can help...
Your first comment is regarding the decay in the oscillations in the LC circuit. It's been awhile since I was a lab demonstrator, so I don't recall the setup exactly for this experiment, however, it sounds like there is a resistance in the circuit (whether there is a resistor there or not... it could be the fact that you have a "real" inductor which consists of a length of wire and will have some resistance). In that case, you have a damped harmonic oscillator system. The inductor and capacitor act as an oscillator (where the capacitor acts like a mass, and the inductor provides a restoring force like a spring), but the resistance provides a means for energy to leave the system, so the oscillations will decay. An analogous mechanical system would be a mass on a spring in molasses... for an entertaining visual. As for what you think it "should" do, you are correct, in that if you had a perfect capacitor and a perfect inductor with no resistances, the system would keep on oscillating forever.
As for resonance... this seems to confuse a lot of people every year. Here's a question and answer from a couple of years ago just to define what we are talking about:
Q: I am a little confused about frequency. What exactly is the resonant frequency and how and why does it effect the current compared to the frequency?
A: In an AC circuit, depending on the components in the circuit, the impedance (a sort of complex resistance) may depend on the frequency. Thus, if an oscillating voltage is applied, the amplitude of the current (peak amount of current that flows) may also depend on the frequency of the applied voltage. This is how the current depends on frequency.
In the case of an LRC circuit, there is a phenomenon called "resonance", whereby the amplitude response of the current has a maximum at the so-called "resonant frequency". Resonance is a common in oscillatory systems, where the amplitude response of the system, be it a mechanical system, or an electrical system, has a maximum at some frequency. At frequencies other than the resonance frequency the amplitude response of the system (the amplitude of the current in this case) will be smaller.
Now, in an electrical system, the resonance will be established by the capacitor and the inductor (the resistance provides the damping), and the values of these components will give the resonance frequency, which is the natural frequency at which the oscillating system operates at, and where it will have the greatest response if you drive it with a frequency. If you input an oscillating voltage to an LC circuit, the amplitude of the current should be very small until you get near the resonance frequency. However... I'm not sure if this is what you did?
If you input a square wave at a much much lower frequency than the resonance, then it will be like turning on and off the voltage, and you would see oscillations at the resonance frequency, which would decay until the next cycle when they would start again. Perhaps this is what you did in the lab.
I hope this is somewhat helpful. Without knowing what you did in lab, I can't be sure where the confusion lies. Please do comment (click the # comment link below... or email if that doesn't work) to follow up!
18 March 2007
Question: Induced EMF coil-solenoid; How do areas play a role?
If a coil is placed around a solenoid that has a fluctuating current, how do the radii of the coil and solenoid (so basically, the areas) affect the induced EMF in the coil? Thanks.
Thanks for your question.
The EMF induced in the outer coil is a result of the magnetic field produced in the solenoid.
First let's consider the magnetic field produced by the solenoid, which is given by:
B=μnl
where n is the number of turns/unit length. But wait! There's no mention of area here... in fact as long as the approximation that l>>r holds (and that you are not near the ends), the magnetic field generated by a solenoid is independent of the cross-sectional area.
So let's consider the EMF induced in the coil surrounding the solenoid. This is given by:
EMF=-ΔΦB/Δt=-AperpendicularΔB/Δt
So the cross-sectional area of the coil does enter into the induced EMF.
Hope that is helpful. For a related question check out: Question: Solenoid in a coil
Thanks for your question.
The EMF induced in the outer coil is a result of the magnetic field produced in the solenoid.
First let's consider the magnetic field produced by the solenoid, which is given by:
B=μnl
where n is the number of turns/unit length. But wait! There's no mention of area here... in fact as long as the approximation that l>>r holds (and that you are not near the ends), the magnetic field generated by a solenoid is independent of the cross-sectional area.
So let's consider the EMF induced in the coil surrounding the solenoid. This is given by:
EMF=-ΔΦB/Δt=-AperpendicularΔB/Δt
So the cross-sectional area of the coil does enter into the induced EMF.
Hope that is helpful. For a related question check out: Question: Solenoid in a coil
06 March 2007
Topic open: Magnetostatics
The following topic is now open for questions: Magnetostatics.
To pose a question, please post a comment to this post by clicking on the comments link below.
To pose a question, please post a comment to this post by clicking on the comments link below.
Topic open: Circuits
The following topic is now open for questions: Circuits. Anything about resistors, capacitors, RC, RL, RLC circuits.
To pose a question, please post a comment to this post by clicking on the comments link below.
To pose a question, please post a comment to this post by clicking on the comments link below.
31 January 2007
"Potential" for confusion: Electrostatic potential and potential energy
Let's start at the beginning:
Electric Potential Energy, like any other potential energy, is defined in relation to a conservative force: in this case, the electrostatic force. If one moves a charge from one point to another through an electric field, one must exert a force over this distance... hence work has been done, which corresponds to a difference in the potential energy.
The electric PE at a given point is generally defined relative to a point at infinity; ie. infinitely far away from the influence of any other charges. This is why we talk about "bringing charges in from infinity" to calculate the potential energy of an arrangement of charges.
One additional complication with electric potential energy compared to graviational potential energy is that charges have different signs. That means that the forces which lead to the potential energy can be either attractive or repulsive. It is perhaps worth drawing from the vector definintion of work:
which tells us that we consider only the contributions of the force which are parallel (or antiparallel) to the path. The result? If we are moving the particle on a path parallel to the force on that particle (the force is acting in the same direction we are moving the particle), the work done by the force will be positive, and the potential energy will decrease. Since we are starting at infinity where the PE is zero, this means we will end up with a negative PE. Conversely, if we are moving the particle in countering the force (the force and direction are anti-parallel) then the resulting PE will be positive.
In this way we can think of PE around charges as hills and valleys: if the force between the "active" particle and another in the arrangement is attractive we will have a potential energy valley, but if the force is repulsive we have a potential energy hill. Let's hold onto this landscape idea and revisit it in relation to electric potential.
Electric, or electrostatic, Potential is the electrostatic potential per unit charge. Think of it as: electric potiential is to electrostatic PE, as electric field is to electrostatic force. That means that the electric potential takes on all the same characteristics as the electrostatic potential: it is a scalar quantity, it can be positive or negative depending on whether the interaction is repulsive or attractive.
Like the electric field, the sign will be determined by considering a positive test charge. With electric field, the direction of the vector quantity is determined by the direction of a force on a positive test charge. Since electric potential doesn't have a direction, it is just the sign which is determined by the positive test charge.
Let's return to our landscape idea then... with PE, we have to consider the magnitude and sign of the charge we are describing, however, since electric potential is per unit charge, it will always remain the same (unless the charges defining the landscape move). Since the positive test charge will be attracted by negative charges, there will be "valleys", or regions of negative potential near these, and near positive charges there will be "hills", or regions of positive potential. In this way, electric potential is kind of a measure of the attractiveness and repulsiveness of a position... just remember that it will be opposite for a negative charge.
I hope I've helped, and not muddled the situation further. Please post a comment if you wish some clarification.
I have some other resources posted for you on the topic of electric potential and potential energy for further reading:
Electric Potential Energy, like any other potential energy, is defined in relation to a conservative force: in this case, the electrostatic force. If one moves a charge from one point to another through an electric field, one must exert a force over this distance... hence work has been done, which corresponds to a difference in the potential energy.
The electric PE at a given point is generally defined relative to a point at infinity; ie. infinitely far away from the influence of any other charges. This is why we talk about "bringing charges in from infinity" to calculate the potential energy of an arrangement of charges.
One additional complication with electric potential energy compared to graviational potential energy is that charges have different signs. That means that the forces which lead to the potential energy can be either attractive or repulsive. It is perhaps worth drawing from the vector definintion of work:
which tells us that we consider only the contributions of the force which are parallel (or antiparallel) to the path. The result? If we are moving the particle on a path parallel to the force on that particle (the force is acting in the same direction we are moving the particle), the work done by the force will be positive, and the potential energy will decrease. Since we are starting at infinity where the PE is zero, this means we will end up with a negative PE. Conversely, if we are moving the particle in countering the force (the force and direction are anti-parallel) then the resulting PE will be positive.
In this way we can think of PE around charges as hills and valleys: if the force between the "active" particle and another in the arrangement is attractive we will have a potential energy valley, but if the force is repulsive we have a potential energy hill. Let's hold onto this landscape idea and revisit it in relation to electric potential.
Electric, or electrostatic, Potential is the electrostatic potential per unit charge. Think of it as: electric potiential is to electrostatic PE, as electric field is to electrostatic force. That means that the electric potential takes on all the same characteristics as the electrostatic potential: it is a scalar quantity, it can be positive or negative depending on whether the interaction is repulsive or attractive.
Like the electric field, the sign will be determined by considering a positive test charge. With electric field, the direction of the vector quantity is determined by the direction of a force on a positive test charge. Since electric potential doesn't have a direction, it is just the sign which is determined by the positive test charge.
Let's return to our landscape idea then... with PE, we have to consider the magnitude and sign of the charge we are describing, however, since electric potential is per unit charge, it will always remain the same (unless the charges defining the landscape move). Since the positive test charge will be attracted by negative charges, there will be "valleys", or regions of negative potential near these, and near positive charges there will be "hills", or regions of positive potential. In this way, electric potential is kind of a measure of the attractiveness and repulsiveness of a position... just remember that it will be opposite for a negative charge.
I hope I've helped, and not muddled the situation further. Please post a comment if you wish some clarification.
I have some other resources posted for you on the topic of electric potential and potential energy for further reading:
23 January 2007
Topic open: Electric Potential and Potential Energy
The following topic is now open for questions: Electrostatic Potential and Potential Energy.
To pose a question, please post a comment to this post by clicking on the comments link below.
To pose a question, please post a comment to this post by clicking on the comments link below.
19 January 2007
Vector Addition
Since many of you seem a little uncertain about adding vectors, here's a quick review example:
The proceedure is the same when you have more than two vectors. Break down all the vectors into components relative to some coordinate system (note that you can choose this such that it is aligned with one of your vectors), add all the components and then using the pythagorean theorem find the magnitude of the resultant vector, and find the angle using trigonometry.
The proceedure is the same when you have more than two vectors. Break down all the vectors into components relative to some coordinate system (note that you can choose this such that it is aligned with one of your vectors), add all the components and then using the pythagorean theorem find the magnitude of the resultant vector, and find the angle using trigonometry.
09 January 2007
Topic open: Forces on charges and Electric fields
The following topic is now open for discussion: Forces on charges and Electric fields.
If you have a question regarding this topic, please post a comment to this post by clicking on the comment link below.
If you have a question regarding this topic, please post a comment to this post by clicking on the comment link below.
04 January 2007
Welcome to the physics 102 webTA blog: winter '07
This will be the second year of the webTA, so I hope that things will continue to improve and be more helpful for you all. There will be 3 parts of the "webTA" persona:
The static site will stay mostly the same as last year. I hope to add maybe one or two new examples written out in full, however, most new material will stay here on the blog.
The blog will be continually updated with answers to your questions. Old posts will never be taken down so that you can learn from the puzzlings of your predecessors. As I've upgraded to the newer version of blogger, there are now labels for all the topics so things should be easier to find. You can also use the blog search to in the toolbar at the top to search for more specific things within the blog site. I will periodically open the floor for questions via a "topic opening" post to which you can add a comment with your question on that topic. Until such time as it becomes a problem (and I hope it won't), you may post anonymously. I would most prefer you ask questions this way as this allows other students to see what others are finding difficult. Also please read these guidelines for posting questions.
I will also hopefully have access this year to the webCT discussions. This would allow me to pop in periodically and sort of "chat" with you and give me a better idea of where you need help, as well as allow me to give quick explanations to little things you have questions about. I won't be a moderator (I don't have that kind of time), but if I see inappropriate discussions I will have to mention it, so please moderate your selves and your peers. If I notice that lots of people are having the same problems I will likely write up a blog post here and direct you all to it. If I do get access to the discussions, I may set up some sort of "virtual office hours" where I will regularly log in, and try to make them outside of regular tutorial or office hours (say, for example, a weekend time).
You can also contact me by email (in the sidebar). I have a few requests however... first, please use a mcgill address for this (I want to know emails are from students in the class and not random people who found the site), second, it is quite unlikely I will be able to reply to each email individually. If you have a question, then it may be answered on the blog, and I will let you know when an answer is posted. If you have a technical question I will try to make sure it is resolved, and may ask you to try again.
A note on questions: not all will be answered. This depends highly on the volume of traffic and questions received, however, last year (especially at the end of term... hint, hint... don't wait!) I could not keep up entirely. Please be patient, as I might not get to them immediately, and I will give priority to groups of similar questions by many students. The "webTA" is one person (me) not a group of TA's, and as such there is a limit to the amount I can do and how fast I can do it. ;)
One last thing... I'd like the webTA sites to act as an additional resource for the class. Please make use of your tutorials; there's nothing like talking to a real person when you need help. With that, I hope you find the webTA project helpful, and I'm always listening for new suggestions!
Good luck!
- The static site
- The blog (right here)
- The WebCT discussion forum
The static site will stay mostly the same as last year. I hope to add maybe one or two new examples written out in full, however, most new material will stay here on the blog.
The blog will be continually updated with answers to your questions. Old posts will never be taken down so that you can learn from the puzzlings of your predecessors. As I've upgraded to the newer version of blogger, there are now labels for all the topics so things should be easier to find. You can also use the blog search to in the toolbar at the top to search for more specific things within the blog site. I will periodically open the floor for questions via a "topic opening" post to which you can add a comment with your question on that topic. Until such time as it becomes a problem (and I hope it won't), you may post anonymously. I would most prefer you ask questions this way as this allows other students to see what others are finding difficult. Also please read these guidelines for posting questions.
I will also hopefully have access this year to the webCT discussions. This would allow me to pop in periodically and sort of "chat" with you and give me a better idea of where you need help, as well as allow me to give quick explanations to little things you have questions about. I won't be a moderator (I don't have that kind of time), but if I see inappropriate discussions I will have to mention it, so please moderate your selves and your peers. If I notice that lots of people are having the same problems I will likely write up a blog post here and direct you all to it. If I do get access to the discussions, I may set up some sort of "virtual office hours" where I will regularly log in, and try to make them outside of regular tutorial or office hours (say, for example, a weekend time).
You can also contact me by email (in the sidebar). I have a few requests however... first, please use a mcgill address for this (I want to know emails are from students in the class and not random people who found the site), second, it is quite unlikely I will be able to reply to each email individually. If you have a question, then it may be answered on the blog, and I will let you know when an answer is posted. If you have a technical question I will try to make sure it is resolved, and may ask you to try again.
A note on questions: not all will be answered. This depends highly on the volume of traffic and questions received, however, last year (especially at the end of term... hint, hint... don't wait!) I could not keep up entirely. Please be patient, as I might not get to them immediately, and I will give priority to groups of similar questions by many students. The "webTA" is one person (me) not a group of TA's, and as such there is a limit to the amount I can do and how fast I can do it. ;)
One last thing... I'd like the webTA sites to act as an additional resource for the class. Please make use of your tutorials; there's nothing like talking to a real person when you need help. With that, I hope you find the webTA project helpful, and I'm always listening for new suggestions!
Good luck!
Subscribe to:
Posts (Atom)
