The Plan

1. The Plan • dielectrics, quickly • current & resistance • HW3 hints after the break (& in lab) • time permitting, some of dc circuits

2. 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.

8. not so funny now.

12. battery = pump voltage = pressure current = flow resistor = constriction capacitor = diaphragm / flexible reservoir diode = check valve inductor = paddle wheel

21. with the time left ... let’s get a jump on dc circuits

22. real battery = ideal battery + R

23. actual circuit has a parasitic r

24. real current sources

25. series resistors: conservation of energy Req R1 R2 a b c a c I I - + - + ∆V ∆V THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

26. R2 voltage divider Vout = Vin R1+R2 R1 signal in Vin Vout R1 signal out R2 volume R2 THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

27. 1 1 1 parallel resistors: conservation of charge = + Req R1 R2 ∆V1=∆V2=∆V R2 Req I1 R1 a b I2 I - + - + ∆V ∆V current divider THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

28. more complex arrangements THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

29. measuring voltage

30. real voltmeters

31. measuring current

32. a simple ammeter

33. V (open circuit) Thévenin equivalents Rth = I (closed circuit) Vth = V (open circuit) any weird combinations of R’s and V’s is equivalent to a SINGLE R and V (or a single I source in parallel with R) THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

34. so what? V E I R R real sources = ideal sources + R real meter = ideal meter with R THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

35. V source loading ∆Vload = V - Ir for r ≪ Rload, ∆Vload ≈ V V Rload r I V source wants R high one easy solution: large resistor in parallel with load source like a battery THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

36. r Iload = I r+R I source loading Rload r for Rload≪r, Iload ≈ I I Ip 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

37. R I I measuring the meter V 1+R/r r Rload Req V real meter ideal meter ∆Vload = IReq = Rload≪r, ∆Vload ≈ IR I THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

38. 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

39. Sourcing current This is what a hand meter does. Why is it no good? Rwires I V Rthing Rwires Vmeter = I(Rthing + 2Rwires) THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

40. Sourcing current, properly Rwires V I Rthing Rthing≪ Rinternal or add buffer Rwires 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

41. Sourcing voltage Rwires V Rthing Vs 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

42. Sourcing voltage II V Rwires Vs Rthing Rs Rpar Ι Ι Rwires = R = ∆V / I Note we need 4 wires again current meter - not hard still problems? Rprecise V THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

43. 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

44. what if I want to measure a *really* high R? V Ι Rwires Vs Rthing Rp Ι Rwires = = source voltage Rp has same voltage as Rthing Rs has same current have done >1010 Ohm Rs≪ Rthing V THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

45. what if I want to measure a *really* low R? Rwires V I Rthing 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

46. what if I want to measure a small change in R? R2 = R1 R3 ≈ R3 V Vs R2 Rx+dR balance bridge to V=0 detect small changes from null make R1-R3 about the same trimming resistor on R2 = dR THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

47. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

48. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center