31-1 (SJP, Phys 1120) Electrical Circuits: Most electrical phenomena (everything from light bulbs to toaster ovens to computer screens to lightning bolts..) involve the flow of current. Flow happens when you have a source of potential difference, and a circuit, a closed path for current to flow. (Since charge is conserved, charges ultimately have to go around in a circuit for the flow to be sustainable!) Let's start by thinking about sources of potential difference. Knight call any such device an "emf" device, in Chapter 30. You could think of "emf" as a funny spelling of "oomph". It's what provides the oomph, the required potential difference to drive current. Examples: generators, solar panels, fuel cells, or batteries. Batteries will be our "typical" emf devices: Batteries: An example of an EMF device 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 C terminal. That means the carbon side is now at a higher potential, VA > VB. 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.) Some people will call this the EMF of the battery, using a curly E that I don't have in my fonts. EMF=work/charge, the electrical potential difference created. If there's no circuit, the two terminals are at some potential difference, but no current flows. If you connect something across them, current will flow, but the IDEAL battery maintains a constant voltage difference between the terminals! The EMF device provides energy to the charges moving around the circuit. Carbon ZincBattery, or electric cell. VA VB Acid31-2 (SJP, Phys 1120) 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. chunk ofmaterial, e.g.metal.ideal wireBatteryideal wire I31-3 (SJP, Phys 1120) Example: A bike light’s battery drives 2A of current through the bulb. How much charge has flowed in one hour? Answer: I = Q/t, so Q = I*t = (2 A)* (3600 sec) = 7200 C This corresponds to 7200 C / (1.6E19 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.) 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!) Be very clear: VA refers to the value of voltage at point A. It's a number. It doesn't refer to a difference. Similarly, VC= VD (again, because there is no voltage change, or voltage difference along ideal wires.) However, VA-VD = “V of battery” (which we REALLY should call ΔV, but people rarely do) is fixed, V>0. Look at the picture and convince yourself that this means VB-VC= VA-VD=V (of battery) (which we should really call ΔV!) The order of those terms matters: VB is higher than VC. I A C BD31-4 (SJP, Phys 1120) There are several analogies that might help you think intuitively about V, I, and R in circuits. Analogy #1: Voltage tells about electrical potential energy, so think of gravitational potential energy instead, as the analogue. • Think of flowing charges as people sliding around at a ski area. • Think of batteries (which lift charges up to high voltage) as chair lifts that lift people up to high (gravitational) potential. • Think of resistors (which allow current flow, but eat up energy) as bumpy mogul runs, which let people ski past, but slow you down. I added a new circuit element here, a switch. As shown, it’s “don’t pass”, Unfortunately, this is called an “open switch”, (but that means the run is closed, no current can flow. ) As shown, we have an “open circuit”, the gate is forbidding flow: no flow of skiers, no current. (People will build up briefly at the top, but the lift operators will frantically call down and say “hold up, no more people!” and there’ll soon be no flow of skiers anywhere) When you close the switch (which unfortunately means “open the run”) skiers (current) flows. In steady state, equal numbers of skiers go UP the lift every hour as go DOWN the run every hour. The ski lift is a pump, a battery, giving skiers potential energy, keeping the current flowing. If the lift dies, the flow of skiers halts. The lift raises your potential energy. You’re not allowed to ride the lift DOWN, you have to ski. The “flat smooth” parts are ideal wires. Skiers can freely wander forwards or backwards at the
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