18-1 (SJP, Phys 2020) Giancoli Ch 18: Electric Currents So far, we’ve considered electrostatics, charges which (pretty much) stay put. In the demos of sparking Van de Graafs, or discharging capacitors, we’ve seen the (important) effects of charges moving, which leads us to discuss the flow of charges: electric currents. This is where the action is, this is what household electronics is all about! Electric Currents: Whenever charges are free to move (e.g. in conductors), if you apply an E field, they will move. (After all, F = qE => acceleration!) Imagine a wire, pick some spot, and ask yourself How much charge passes by that spot each second? That’s the current. Current is called I = ΔQΔt , it's the (amount of charge passing) per sec. (Often written Q/t for short). The units of current are Coulombs/sec = C/s = 1 Ampere = 1 A. So if I = 1 A, that means 1 Coulomb flows by each second. That's a lot! Current has a direction. If the current is to the right, there’s a net flow of charge to the right. This could occur in one of two ways: It could mean “+”’s physically moving to the right OR it could mean “-”’s physically moving to the left. There’s (almost) no difference, in terms of “flow of charge”. Think about this, it’s an important point. Convince yourself! Negatives moving left are in most ways equivalent to positives moving right. The flow of charge is the same in either case. + + - -18-2 (SJP, Phys 2020) Here’s another way to think about this. Start with two neutral plates. Now, you could EITHER move some “-” charges down, OR move some “+” charges up, but either way, the final situation is the same. Our convention is always to define current I as the flow of imaginary “+” charges. (Even if in reality it’s really negatives going the other way. In most conductors, it really is negative electrons flowing opposite the current.) What makes currents flow? Generally, electric fields make charges move. You can also think of current as arising from changes in electric potential energy: a change in potential energy means you can convert potential energy into kinetic energy (motion), like a hill makes water flow down it... Batteries: Zinc ions (+ charged) get pulled off by chemistry (we won’t go into the details!) into the acid bath, leaving behind a residual “-” charge on the Zn rod (terminal, electrode). Meanwhile, electrons (- charged) are pulled off the carbon rod into the acid bath, leaving a residual + charge on the Carbon side. That means the carbon side is now at a higher potential, VA > VB. (Right? It's always higher voltage near the + charges, remember that?) This potential builds up, but if VA gets too high, the acid can’t pull electrons off any more (the electrostatic attraction of e-’s back onto the + carbon rod will equal the chemical attraction of the e-’s into the acid) So you reach an equilibrium with ΔV = VAB = VA - VB = some fixed value depending on the chemicals. People usually drop the Δ, and just talk about “V”, the battery’s voltage. (Too bad, remember they really mean the difference in voltage between the two electrodes.) Carbon ZincBattery, or electric cell. VA VB Acid18-3 (SJP, Phys 2020) In diagrams, we use a symbol for batteries: The “+” and “-“ are often left off: the longer line always represents the “+” side. It’s a little like the symbol for capacitors, except the lines are different length. Capacitors and batteries have some common aspects, but they are still very different. Capacitors don’t spontaneously build up a ΔV, like batteries do, and they don’t always have the same value of ΔV. You might expect that the “+” charges at the top of the C electrode would want to go over to the “-” post. They are attracted. The +’s would drop in energy, ΔPE = qΔV: they’d like that, like rolling down a hill. They can’t go through the acid, though: the chemical reactions are stopping them. But what if you let them go some other way, outside of the acid? E.g.: Symbol for ideal wire: Symbol for chunk of material that allows current through: Now we’ve provided an outside path, a conducting path, or circuit, for charges to flow from the + to - sides of the battery like they want to. There is a current flowing continuously through the circuit.. This is a simple electric circuit. This is NOT like discharging a capacitor (where the flow is quick, and then stops when the capacitor is discharged). The battery keeps maintaining a constant voltage difference, the current is continuous. (As long as the chemical reactions inside keep doing their thing, anyway!) Example: A bike light’s battery drives 2A of current through the bulb. How much charge has flowed in one hour?18-4 (SJP, Phys 2020) Answer: I = Q/t, so Q = I*t = (2 A)* (3600 sec) = 7200 C This corresponds to 7200 C / (1.6E-19 C/electron) = 5E22 electrons have flowed through the bulb! (Sounds like a lot, although 2 A really isn’t an unusual current. Electrons are small. If 7200 Coulombs all piled up in one spot, THAT would be a lot, but this kind of FLOW is normal) Some important concepts to be aware of: 1) In “ideal wires”, electrons are free to roam around. In good (perfectly) conducting metal it takes zero work to move electrons around. Metals like to be at an equipotential throughout, if they can. There is no voltage drop along ideal wires. This is funny, think about it! 2) Charge is conserved. In steady state circuits, that means there is no buildup of charge anywhere. Whatever charge comes in to some point must go right on by, and out the other side. (This too requires thought!) In that last example: Current (I) is the same everywhere along this circuit. That means = I through the wires = = I through the “chunk of material” = = I through the battery = = I passing by point A (IA) = = IB = IC = ID. Also, VA= VB (because, there is no voltage change along ideal wires!) VC= VD (again, because there is no voltage change along ideal wires.) However, VA-VD = “V of battery” is fixed, V>0. Look at the picture and convince yourself that this means VB-VC= VA-VD=V (of battery) also. The order of those terms matters: VB is higher than VC Everything I said above will make sense when you've thought about it, but you can't memorize this sort of thing. You have to see it, you have to figure out a way to understand it all. Walk
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