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The Plan • • • • dielectrics, quickly current & resistance HW3 hints after the break (& in lab) time permitting, some of dc circuits • • • • Exam 1 Right here, 3pm Thursday - electric forces & fields electrical potential & energy current & resistance NO RELATIVITY study quick quizzes, example probs our HW and quizzes problems in notes relax. it will be ok. not so funny now. battery = pump voltage = pressure current = flow resistor = constriction capacitor = diaphragm / flexible reservoir diode = check valve inductor = paddle wheel with the time left ... let’s get a jump on dc circuits real battery = ideal battery + R actual circuit has a parasitic r real current sources series resistors: conservation of energy a R1 b R2 c a Req c I I + ∆V THE UNIVERSITY OF ALABAMA + ∆V CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center voltage divider Vin R1 Vout R2 signal in R1 volume R2 signal out R2 Vout = Vin R1+R2 THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center parallel resistors: conservation of charge ∆V1=∆V2=∆V I1 a I 1 = 1 1 + Req R1 R2 Req R2 R1 b I2 + ∆V + ∆V current divider THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center more complex arrangements THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center measuring voltage real voltmeters measuring current a simple ammeter Thévenin equivalents Vth = V (open circuit) Rth = any weird combinations of R’s and V’s is equivalent to a SINGLE R and V THE UNIVERSITY OF ALABAMA V (open circuit) I (closed circuit) (or a single I source in parallel with R) CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center so what? E I R V R real sources = ideal sources + R THE UNIVERSITY OF ALABAMA real meter = ideal meter with R CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center V source loading ∆Vload = V - Ir V Rload for r ≪ Rload, ∆Vload ≈ V r source like a battery I V source wants R high one easy solution: large resistor in parallel with load THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center I source loading r Iload = I r+R r Ip I Rload for Rload ≪ r, Iload ≈ I Iload source I source wants R low sourcing currents at high Rload is hard THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center measuring the meter I Rload I r V real meter ∆Vload = R IReq = 1+R/r I THE UNIVERSITY OF ALABAMA Req V ideal meter Rload ≪ r, ∆Vload ≈ IR CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center summary voltmeter wants R low! can use a buffer/follower I source wants R low transformer pre-amp consider sourcing V V source wants R high large series + parallel resistors present large R THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing current This is what a hand meter does. Why is it no good? Rwires I V Rthing Rwires THE UNIVERSITY OF ALABAMA Vmeter = I(Rthing + 2Rwires) CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing current, properly Rwire I s Rthin V g Rwires Rthing ≪ Rinternal or add buffer No problem. You just need four wires. What is still wrong? THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage Rwires Rthing Vs V Rwires Still have to measure voltage on device the wires still use up some of V What about current? THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage II Rwires Vs Rs Rthing Rpar Ι Rwires R = ∆V / I V Ι = Rprecise Note we need 4 wires again current meter - not hard still problems? THE UNIVERSITY OF ALABAMA V CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center source/meter resistances voltmeter wants R low but V source wants R high need buffer/amp on V meter resistor in parallel with source if V source is problem, R is too low consider sourcing I THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a *really* high R? Vs Ι Rwires Rthing V Rp Rwires source voltage Rp has same voltage as Rthing Rs has same current have done >1010 Ohm THE UNIVERSITY OF ALABAMA Ι = Rs ≪ Rthing V CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a *really* low R? Rwire I s Rthin V g Rwires this works just fine ... so long as your V meter is good v. good amp / part of a bridge THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a small change in R? R1 R3 V Vs R2 THE UNIVERSITY OF ALABAMA balance bridge to V=0 detect small changes from null R2 = Rx+dR R3same make R1-R3 about≈the trimming resistor on R2 = dR CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center