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 acid bath leaving behind a residual charge the Zn rod terminal electrode Meanwhile electrons charged are pulled off carbon rod into the acid bath leaving a residual charge on the C terminal Battery or electric cell VA VB Zinc Carbon Acid the on the 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 V VAB VA VB some fixed value depending on the chemicals People usually drop the 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 31 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 V like batteries do and they don t always have the same value of V 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 PE q V 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 ideal wire Symbol for ideal chunk of material e g metal Battery wire Symbol for chunk of material that allows current through ideal wire 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 I 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 31 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 I through the battery D C 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 A B However VA VD V of battery which we REALLY should call V 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 V The order of those terms matters VB is higher than VC 31 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 Flat smooth top of hill Switch gate open Ski Lift Flat smooth bottom of hill Moguls Steep downhill 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 Switch go UP the lift every hour as go DOWN the run every gate closed hour Ski Lift The ski lift is a pump a battery giving skiers potential energy keeping the current flowing If dies the flow of skiers halts the lift 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 top or bottom with no change in energy 31 5 SJP Phys 1120 Lots of bumps in the mogul means lots of resistance People ski slowly Only a small number of people can go down the hill every hour So only an equal small number of people can go up They better not let any more people on the lift …
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