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As for the other two questions!
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But yes, your intuition is pretty close to right. Electrons can only go where there's room for them. Metals make room very easily. Nonmetals hold on to their electrons firmly. Since it takes energy to displace an electron, that reduces the amount of energy available to continue propagating the current. |
There's a whole lot more factors to sound than I'd thought :o.
By sound reflecting, do you mean that when someone knocks on a door, the door also knocks on the person's bones and then the person's bones make the reflected sound..? I have heard of cold welding from class! But it was put in as an interesting side note and I forgot how it happened and didn't connect it with friction. But I'd though it only happened in space o_o |
It happens more easily in space because there's no air to GET in between, but it's totally possible to squeeze out all the air on the surface with some effort (or power tools).
And no, I mean that the atoms you knock on bounce forward to hit the atoms behind them, but they also bounce back and hit the air on the same side as you. (Yes, they also knock back on your knuckles, but that doesn't make a whole lot of sound because your knuckles don't have a whole lot of surface contact with the air.) |
Ohh, I hadn't realized that the atoms first hit would bounce back too, woops.
Is the fact that when an object hits another object of equal mass, it can either stop, bounce back, or roll forward too (but slower) just something I need to accept and remember? |
You already know enough about Newtonian physics to derive that result yourself, actually.
In the absence of friction, a perfectly rigid object in motion that strikes another perfectly rigid object at rest will transfer 100% of its kinetic energy. (Equivalently: in the absence of friction, two perfectly rigid objects exchange their kinetic energy when they collide. You can see this is equivalent by choosing different frames of reference for the same interaction.) But because real objects aren't perfectly rigid (this would imply an infinite speed of sound in that material), the transfer of energy happens through a finite impulse, and because most experiments you can run don't take place in outer space, there's going to be friction. There are also additional forces acting on the system that you might not be thinking about. Let's think of hockey pucks on a flat surface with low but nonzero friction. Why hockey pucks? Because balls roll, and spinning introduces angular momentum, which is conserved just like linear momentum is. In order for puck #1 to make puck #2 move, it has to exert enough force to overcome the friction keeping puck #2 where it is. That force is obviously going to apply an acceleration to puck #2, and the reaction force will apply a deceleration to puck #1. This means that the two pucks will be sliding together for some distance, remaining in contact with each other until puck #2's velocity exceeds puck #1's. In the case where puck #1 stops and puck #2 moves away at full speed, this means that the contact time was long enough for that impulse to transfer all of the momentum. In the case where puck #1 slows down but keeps going, that means that only some of the momentum was transferred before puck #2 was moving too fast to keep them in contact. The only remaining scenario to consider is bouncing back. I actually don't think this is possible in a sliding-only interaction in the absence of friction if the two objects are of equal mass. Without rolling or friction, bouncing back means that puck #2 would have to have more mass than puck #1, so that the reaction force would accelerate #1 backwards faster than #2 gets accelerated forward. The force of friction, though, shifts the balance. Static friction is greater than kinetic friction. So the reaction force has less resistance to pushing puck #1 backwards than the action force has to pushing puck #2 forwards. Over the span of the impulse, this could mean that puck #1 is accelerated enough faster than puck #2 to bounce back instead of stopping or proceeding forward. |
Objects being not perfectly rigid means the infinite speed of sound?
Is it something to do with how impulse requires time and if something's perfectly rigid it won't take any time? So..impulse is force in an amount of time, so that means it takes time for momentum to be transferred and that determines if puck #1 continues in the same direction or stops. I was pretty much guessing that an object of equal mass could bounce back because I wasn't certain what it could do '~'. So..with lots of friction or greater mass for puck #2, then because puck #2 with friction, or puck #2 with greater mass will push puck #1 the same, puck #1 will accelerate backwards? |
I mentioned a couple posts ago that the speed of sound is how fast forces can propagate through an object. A perfectly rigid object -- one that wouldn't deform at all when you push on it -- would therefore have to have an infinite speed of sound, in order to keep the far side of the object exactly the same distance from the near side of the object at all times.
It is indeed related to impulse taking time. Sounds like you've got a pretty good handle on this! |
Can synthetic division not be used for fractional rational roots?
(I was doing a problem to solve for all real roots of p(x) = 3x3 - 5x2 - 8x - 2 and I got -1/3 as a real root using rational roots theorem. Trying to find the rest of the roots by using synthetic division with -1/3 gave me a wrong answer, but long dividing the original 3x3 - 5x2 - 8x - 2 by 3x + 1 worked fine.) |
Erf. Geez. I haven't done synthetic division in like fifteen years, maybe longer. This is going to take research. ^^()
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If you don't want to research it, I can also ask a math teacher tomorrow xD
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Okay, so brushing up on the technique...
EDIT: Equivalently, x2 - 2x - 2, because we're finding roots; 0 * anything = 0 so we can multiply the whole thing by 1/3 and get the same results. EDIT 2: Which... um... I usually go for the quadratic formula here: (-(-2) +/- sqrt((-2)2 - 4*1*-2)) / (2*1) (2 +/- sqrt(4 + 8)) / 2 (2 +/- 2sqrt(3)) / 2 1 +/- sqrt(3) The remaining two roots are irrational -- (x - 1 - sqrt(3)) and (x - 1 + sqrt(3)). You CAN, theoretically, do synthetic division on one of those to get the other, but you'd be juggling those silly radicals through the whole thing and it's probably not worth the effort. |
By multiplying the whole thing by 1/3, do you mean multiplying the (x + 1/3) by 3 and multiplying (3x2 - 6x - 6) by 1/3 ?
Thanks for the explanations! EDIT: Uh, quadratic equations don't need equations to be simplified right? I think I just messed that part up (forgot to multiply the bottom of the fraction by 3 as part of 2a --> 2(3)) |
No, I mean multiply both sides of 0 = 3x2 - 6x - 6 by 1/3. Don't screw with the factor you've already pulled out; that one's already locked down.
The equation doesn't have to be simplified to use the quadratic formula. If you don't simplify it, then the /2a term will simplify it for you in the end. I was simplifying it to see if I could find the remaining factors by inspection. |
Ohh I see. Normally I'd simplify because of habit. I didn't because I forgot. Thankfully it seems okay to forget.
Oh! I see, so because in trying to find zeros for that, multiplying and dividing wouldn't affect anything! If I were trying to multiply the factors together to make the original equation, is it okay to screw with the factor..? |
If you're multiplying the factors together to get back the original equation, then you can always be off by a constant multiple. That is, (x2 - x) and (2x2 - 2x) have the same roots (x and (x-1)) but they differ by multiplying the entire expression by a constant.
If it matters, and you don't know, write k(x2 - x). If it matters and you need to find out, then you need at least one non-zero point on the curve and then you can plug that into the expression and solve for k. |
Ohh, I see!
I have another question, does it matter if I write a factor as (x + 1/3) or (3x + 1)? Is it more convenient or more proper to write it one way or the other? |
Doesn't make much difference. Whichever form is easier to manipulate with whatever technique you happen to be using at the time.
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Is there anything preventing objects from gaining even more electrons? (In class we're learning about positives and negatives and stuff making other things positive and negative. I noticed the more I rubbed plastic pens with fabric, the better it got at picking up pieces of paper. What keeps someone from charging something until, say, the pen could stick to a wall made of paper or something?)
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It might be possible to charge something as light as a pen enough that it can hold its own weight electrostatically against a wall. It's certainly possible to do that with an inflated balloon. (Try it! It's fun.)
A general principle in physics, that holds true at all scales, from subatomic to universal, is that processes by default proceed towards lower-energy states or more stable states. (Usually these are equivalent, but there are some cases where a stable state has more energy than an unstable state; the most common examples are endothermic chemical reactions, which absorb heat from the environment to make a final compound that's more stable than the reactants that went into it.) A ball at the top of a hill has more potential energy than a ball at the bottom of a hill, and it doesn't take much of a bump to cause that ball to proceed to a more stable, lower-energy state. To make a system move the other direction, you have to put energy in. It takes work to separate charges. The greater the difference already is, the more effort it takes to separate them further. You know that like charges repel, so as you get more negative charge gathered on one object, those charges try to push each other (and further negative charge) away. The same is true of positive charge. As you keep forcing charge in, the equilibrium will be such that even the air molecules bouncing off the surface of the object will have an easier time holding that charge than the object itself, so in effect the object bleeds off excess charge into the atmosphere. And you already know what happens when the potential difference between two surfaces gets too great -- the electrons will actually JUMP from one side to the other through whatever path they can find: sparks and lightning. |
I don't think I have the patience to try to see if a pen can stick to the wall, but in class we did stick a balloon to the wall. It wouldn't stick after rubbing it on cloth, but did stick with hair. I vaguely recall it was because hair let go of electrons more easily...? I stuck a bunch of balloons to the ceiling after they stopped flying by rubbing them on my shirt though. Is it because the balloons were lighter? Because maybe the rubber material was different?
So..eventually the electrons will just have too hard a time moving into an object or out of one and that's what decides the limit? ...if I had a cloth and was using it to stick helium balloons to a wall, would the cloth get less and less effective? |
Your body is a good electrical conductor, while the rubber of the balloon or the plastic of the pen is a good electrical insulator. Your own body ends up providing a connection between the cloth in your hand and the ground, so the cloth is able to drain off its excess charge THROUGH you.
In isolation -- say, if you used a pair of rubber tongs to manipulate the cloth... You might be right. EDIT: Your other questions! Yes, the buoyancy of balloons in the air helps. The pen doesn't have a lot of surface area to collect charge on, and it has more weight. And yes, that's the limit. It's not STRICTLY a limit, mind you; it's not some fixed measurable cap. It's just a question of how much work you want to apply to the task. Rubbing the objects together by hand within the atmosphere may simply not impart enough energy to go beyond the small effect you've seen. On the other hand, van der Graff generators can build up HUGE potentials because their parts are very well isolated from grounding. |
Ohh I didn't realize the cloth would regain electrons just by holding it with bare hands :/.
Are electrical conductors and heat conductors completely unrelated? So..a "ground" is anything that acts as a source of electrons..? Does a "potential" mean an object is more negative, or does it mean it's far from neutral? |
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Heat is the kinetic energy of the particles within an object. Electrons are particles, so electron motion contributes to heat motion. For metals, there's a relatively straightforward relationship between electrical and thermal conductivity. At a given temperature, the thermal conductivity is directly proportional to the electrical conductivity (that is, metals that are good electrical conductors are also good heat conductors), and raising the temperature causes electrical conductivity to go down and thermal conductivity to go up, and vice versa (that is, all metals transfer heat better when they're hot and transfer electricity better when they're cold). This is called the Wiedemann-Franz law, although I didn't actually KNOW that name until I went and looked it up just now. For nonmetals, the electrons still contribute to heat transfer, but the molecules as a whole have a greater impact on how fast or slow the heat is transferred, so the specific relationship isn't so cleanly predictable. It's still possible to figure out the relationship in a given substance, but there's a lot more that you have to take into account. Quote:
It's called a ground because the Earth itself is the biggest, most convenient ground available, so when you're wiring a house for electricity, you shove a big metal spike into the ground (or you use a big buried metal pipe) and connect stuff to it so that it's easier for the current to go through that route instead of through your body to the ground THAT way if you touch a bare piece of electrified metal by accident. Quote:
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Pushing electrons? As in moving them into the ground/earth..?
Why do colder metals transfer electricity better when cold? Because the protons are moving around and attracting electrons :/? Why do metals transfer heat better when hotter? Does that mean a hot metal pot gets hotter more easily than a cold metal pot :o? |
I mean that when you're dealing with chemical batteries or solar cells, you're getting a bunch of free electrons on one end of the circuit, and since like charges repel, they get pushed out as soon as there's a place where they can actually go. And they're not specifically looking for a positively-charged place to go; they're just looking for a less-negative place to go (because being less negative means it's going to push the electrons away less), and the Earth is so massive that you can add a whole lot of electrons to it without making a significant difference to its net charge, so it stays overall pretty neutral no matter how much you pump into it.
You CAN do it the other way. You CAN have a reaction that binds up electrons and leaves a positively-charged void that's desperately trying to attract electrons. That's a negative electric potential. It'll happily draw those electrons from the ground (because the Earth has so many electrons that it'll never miss a few) if there's no place better to get them from. Chemical batteries do this at the positive terminal, so given the choice to travel from the negative terminal to the ground or to the positive terminal, the positive terminal is twice as attractive of a destination. Solar cells are comparatively weak because the only force pulling electrons through the circuit load is the fact that, after a photon forces an electron to start moving down the wire, there's not an electron there anymore so there's room for another one to come in from the other side. You're not too far off when it comes to why colder metals conduct better. A hotter material has more random motion in it, the atoms in it are moving faster relative to each other, so electrons have to be moving faster in order to make the jump from atom to atom. A colder material keeps the atoms closer together. I don't completely understand the thermal conductivity thing myself. I know it because i read it. However, no, it doesn't mean that a hot metal pot will get hotter more easily. It means that the heat will spread out more evenly once it's gotten warmed up compared to at the beginning. Instead of a pot, think about a long metal pipe with a heat source at constant temperature at one end. If you draw a graph of the temperature of the other end of the pipe, then it'll be a curve going upward instead of a straight line -- the hotter the far end already is, the more rapidly it approaches the temperature of the heat source. If I had to take a guess as to why this is true: Imagine a billiards table. In a cold material, the balls are all close together, with some space between them. If you shoot the cue ball into the cluster of balls, the energy is going to get spread out pretty fast because each ball will bump into more balls as they start moving. But if the balls are more spread out, then when you shoot the cue ball, whatever it hits is going to immediately go zipping off because there's not as much in its way, and so it can transfer its energy to a place farther away on the table sooner. |
Err, so in a house or apartment, electricity comes from some..plant(?). Then that is continuously(?) running through the place and..then gets pushed down to the ground? And when someone plugs something into a power socket..they get access to that electricity and use its energy(?) to convert it into whatever the thing they plugged in does(?) (ex: to light up a light).
^I'm pretty much guessing most of that. How do power outlets work and where does the electricity come from to get pushed into the ground in the first place..? So...solar cells are parts of the solar panels? I found this little picture: Is it saying that normally, electrons are stuck around atoms, then the sunlight hits it --> an electron is freed from the atom --> electron attracted to bottom layer so it moves through a wire making it accessible to household appliances. I guess the layer separating them makes the electron just "know" the wire lets it get to that more electron attracting(?) layer? Furthermore, where how the electron get back after it reaches the bottom layer o_o? Isn't the top layer less attractive than the top one? What are all the middle layers supposed to do? Chemical batteries...so terminals are, I'm guessing, the + and the - labeled ends of a battery? Err is this about recharging batteries..? I'm not really sure how to picture what's happening. I think I didn't know the definition of conductivity o_o. So conductivity is how easily something spreads(?) throughout an object? Like heat throughout the whole length of a wooden spoon or electricity through a whole length of wire? ...Oh, actually, does thermal conductivity in metals decrease with temperatures normally? stainless steel is different though. But for nonmetals, conductivity does increase with temperature. But why? And what are the billiards balls representing? |
Overall, you're right on the money about how household power works.
More details: "Solar cell" specifically refers to a photoelectric or photovoltaic device, which is what your picture is of. "Solar panel" can also refer to solar heat storage (big tubes full of water set out to absorb sunlight; the hot water then gets stored in an insulated tank and it slowly lets the heat out into the house when it gets colder at night). That picture is misleading. This one is better: What happens is that the sunlight displaces an electron from inside the separation layer. The top silicon layer is "doped" with impurities that make it more likely for the displaced electron to flow that direction, while the bottom silicon layer is doped with a different kind of impurities that give it extra electrons to work with. When the electron moves out, it leaves a positively-charged "hole" behind and the bottom layer gives up an electron to fill it in, replacing it with an electron drawn from the circuit. The separation layer keeps the positive and negative sides from having a shortcut route for electrons to flow that isn't going through the circuit. Equivalently, since the top layer gained an electron and the bottom layer lost one, it creates a potential difference. Re: Thermal conductivity: I guess I misread things. That graph says I'm wrong for most metals. Like I said before, I actually DON'T know a whole lot about that and I was guessing. The billiard balls represent the atoms in the object. |
Err, do you mean the bottom layer has electrons that can move, and when a photon makes an electron move away, the electron in the bottom layer moves up--and because it moves it, it is now positive, attracting the electron that got knocked out by a photon? Aand somehow the middle layers only allow electron movement from the bottom to the top..?
And thank-you very much for that explanation on household power! |
Yep, that's a pretty good explanation of the phenomenon.
The middle layer is suuuuper interesting, actually. It's a pure (undoped) wafer of silicon crystal. Silicon has some WEIRD properties. Silicon is not exactly a metal, and it's not exactly a non-metal. It's a metalloid. It's not exactly an electrical conductor, but it's not exactly an electrical insulator. It's a semiconductor. You've probably heard that term before when talking about computers; well, you're about to learn what that actually means. Pure silicon crystal, with no impurities whatsoever, has a very neat arrangement of electrons. Every atom has exactly the number of electrons it wants to have, and it's energetically stable, so the electrons don't have much motivation to go anywhere. It acts as a weak insulator. But that's assuming that all of the electrons ARE where they belong. It takes more energy than a normal electric current to dislodge those electrons from their happy place of stability, but it doesn't take THAT much -- it takes less than an insulator would take. And conveniently, photons near the visible light spectrum have enough energy to do the job. And when the electron is forced out of place, if it has somewhere it can go -- such as into a circuit -- then it leaves a positively-charged hole behind. That hole is unstable. There's a pressure to pull another electron from nearby into the hole. But that means THAT electron leaves a hole behind that needs to be filled. So eventually that hole has to get filled by an electron from outside. But that's the behavior of pure silicon. If you mix in just a few atoms of phosphorus, then you have extra electrons. The region gains a small net positive charge, because those extra electrons will readily leave. If you mix in a few atoms of boron, then you have extra holes. The region gains a small net negative charge, because those holes will accept extra electrons readily. (Yes, it sounds a little bit counterintuitive that adding atoms with too many electrons will cause it to have a positive charge, and vice versa. This is because the phosphorus atom is neutrally-charged normally but when you mix it in, it loses the extra electron, thereby becoming positively-charged.) So by sandwiching undoped silicon between a negatively-doped ("n-type") region on top and a positively-doped ("p-type") region on the bottom, all of the mobile electrons or holes in the undoped silicon that MIGHT allow conducting electricity are pulled away into the doped regions -- the silicon is "depleted" (hence "depletion zone" in the picture) of charge carriers, leaving a potential difference that further resists electrons passing through. And if a loose electron DOES get in there (perhaps because it was hit by a photon, eh?), it follows the bias of the electric field. So the current can only flow one way through it. |
Err what does a semiconductor have to do with computers?
What's the difference between a semiconductor and a not-so-bad conductor? Or, why is it that being a semi-conductor is special? On second thought, what is the definition of a metal exactly? Of a metalloid o_o? What is the "bias of the electric field"? That current can flow only in one direction at a time..? Undoped silicon doesn't take much to give up electrons, and so its electrons get pulled into..either layer o_o? But maybe electrons can only flow one way(?) so it just goes to the top as the electrons on the n-layer move to the p-layer...? |
Computer chips are the most well-known use of semiconductors.
The thing that makes a semiconductor special is the ability to control WHEN it's a conductor. Metals just always conduct, even if the conductivity is low. Most elements (91 out of the 118 known elements) are metals. Metals characteristically lose their outermost electrons very easily, which means there's a free-flowing cloud of electrons inside the metal instead of a rigid electron structure. This is why they conduct heat and electricity so well. Metals are usually malleable (able to be pressed into shapes without breaking), ductile (able to be stretched into wires), and fusible (can be melted together). A nonmetal is anything that doesn't do these things. Metalloids have properties in between, though which elements are metalloids and which aren't isn't completely agreed upon (for example, some classifications say aluminum is a metalloid, most say it's a metal; some say carbon is a metalloid, most say it's a nonmetal). I'm not using "bias" in a jargon sense here. I just mean that having an electric field means that electrons will have a strong preference to move in one direction and not the other. I said "charge carriers," not "electrons." You can treat the absence of an electron as a mobile positive charge. THOSE have all gotten pulled out, too -- that is to say, all of the holes got filled up with electrons and there are no excess electrons hanging around either. |
Oh woops, I missed the "charge carriers." Basically that middle part is content to not have electrons moving through?
Back to this diagram: Is it that the sunlight hits the undoped silicon --> an electron now leaves that depletion zone and a hole is created there(?) (this part I'm confused about) and somehow it's the bottom p-type layer that now has a hole, maybe because it moved an electron up to the depletion zone because electrons prefer to move in one direction as the electrons from the N-type layer are attracted to the P-type layer? Why is it that there are two arrows coming out of the "Photon Absorbed in Depletion Zone Electron-hole Creation"? And..the photon just bypasses the N-layer and goes to the Depletion zone :o? Quote:
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Yep, the middle part has all of its electrons right where they want to be so it resists further movement.
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Photons with too low of energy to dislodge an electron end up just passing right through. Higher-energy photons are more likely to interact. Some energetic photons will get unlucky and hit an electron near the surface of the panel, sending an electron spinning around in the region where it's already happy to float around, and nothing significant happens except the panel gets a little bit warmer (like EVERYTHING does when you shine light on it). But since silicon is still somewhat transparent at those slightly-higher energies, some photons aren't going to bump into anything until they're deeper into the material, and those are the ones that make electricity. Your intuition might be saying this already, so let me validate it: Yes, solar cells are actually very inefficient, and most photons that land on them don't get converted into electricity. You need huge arrays of thousands of solar cells to generate enough energy to power a house. But we don't really care all that much about that inefficiency, because those photons weren't going to be doing us much good anyway. Quote:
"Chip" is slang for "integrated circuit," of which the most important one in your computer is the CPU (or "processor"). They're the (usually black) rectangular things stuck to circuit boards, and they're full of micro-printed silicon wafers to create complex circuits. I would recommend against digging any deeper into this at the moment because it spirals VERY VERY QUICKLY into mindboggling complexity. Suffice to say that modern technology is printing individual details only a few atoms wide and we're very very close to hitting fundamental quantum-scale limitations on how small we can make things and still have them work. |
I'll not ask about the last bit on computers, especially since I don't understand most of the words there ("integrated circuit," "CPU"/"processor," "circuit board," "silicon wafer," "fundamental quantum-scale limitations" [though for this one I guess I can just take away that modern technology is getting parts smaller and smaller and extremely close to some point where it can't work any smaller]).
I guess solar panels are only worth it with lots of space and lots of solar panels xD? ...do solar panels connect to the same power outlets that receive electricity from powerlines or whatever else is generating power from outside? Because if they do, doesn't that mean installing solar power means both a lack of access to those power lines and that those sockets can't be used if it's been cloudy for many days and power stored in batteries ran out (would running out happen? Although I guess this depends on how many solar panels a particular household has)? |
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Just a few bullet-point-sized definitions to help you round out some basic knowledge: * "Silicon wafer" is exactly what it sounds like -- a thin sheet of silicon. * An "integrated circuit" is a bunch of microscopic electronic components made from a single piece of silicon. It's called "integrated" because before they were invented you'd have a bunch of small parts (usually roughly cylindrical in shape) that you'd have to wire together. * A "CPU" is basically the brain of a computer. Every computer has to have one. To give you an idea of just how complex they are nowadays, the CPU in an iPhone 7 has 3 billion individual components printed into it (imagine how small an iPhone is -- and the CPU isn't even the only chip in it!), and the CPU in an Xbox One has 5 billion. Quote:
But yes, if you want to power something large, you need a lot of them. For large-scale solar electricity generation, it's more efficient to use mirrors to reflect sunlight to heat up water to spin a turbine. Quote:
But after that, yes, they do connect to the same outlets. However, it's actually not particularly difficult to combine multiple sources of electricity, so houses with both solar panels and city services electricity just have a power regulator that draws from the solar panels when the batteries have sufficient charge and smoothly transition over to city services otherwise. In especially sunny places such as southern California, solar panels can actually generate more power in the course of a day than the house will actually use (or at least, more than the batteries can store), so those houses can actually sell their generated power back to the electric company. |
Oh wow, I didn't know that there were traffic lights that used solar power! Nor did I know that mirrors were used for power.
What happens to the traffic lights if there's a long storm? Or do they store enough in batteries to make it through..? Actually, do traffic lights even use that much power? How does the solar power make its way to the electric company..? Does it even? |
I'm talking about single little warning flashers, not crossing lights. I would imagine those things draw so little power that they could run for a week without a recharge. I've also seen roadside speed indicators ("YOUR SPEED: ___ MPH") with a solar panel that I would guess to be about... oh, half a square meter? Big compared to the rest of the sign but not enormous. If one of those were to run dead, it wouldn't cause any trouble, so it's not a problem if it's cloudy for a few days.
It doesn't actually have to make it all the way back. Like I said, it's not all that hard to combine sources of electricity, so just pushing more current into the line instead of pulling it out is enough to share that energy for other nearby buildings. The power meter keeps track of how many kilowatt-hours you draw in compared to how many you push out and you get billed for the difference or get credit to your account. |
Oh! So there are power meters xD! Come to think of it, I've not thought about the fact that I didn't know how power bills were kept track of--or any other bills, for that matter.
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Why does this equation: Fe = (k|q1||q2|)/r2
Have absolute values around q1 and q2? Wouldn't it be easier to have if something turns out negative they attract and if something turns out positive they repel? Or is that actually more of a hassle than it is useful? Why does that equation use "r" for distance? |
To be honest? I don't know. I have a GUESS (using the absolute value means you could use vector quantities instead of scalar ones) but nothing concrete. Maybe it's just a question of consistency.
r is for radius; you can model such effects as a spherical field emanating from one of the point charges and then reason about the other point charge based on its distance from the center. |
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