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. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center series resistors: conservation of energy - + R2R2 I I ∆V∆V R1R1 acb R eq ∆V∆V ac - +

26. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center voltage divider R2R2 R1R1 V in V out V out = R2R2 R 1 +R 2 V in signal in signal out R1R1 R2R2 volume

27. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center parallel resistors: conservation of charge current divider I - + R1R1 ∆V∆V R2R2 ab I1I1 I2I2 ∆V 1 =∆V 2= ∆V - + R eq ∆V∆V R eq R 1 R 2 111 = +

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

29. measuring voltage

30. real voltmeters

31. measuring current

32. a simple ammeter

33. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Thévenin equivalents 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) V th = V (open circuit) R th = V (open circuit) I (closed circuit)

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

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

36. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center IpIp I source loading source R load I source wants R low sourcing currents at high R load is hard I r I load I load = I r r+R for R load ≪ r, I load ≈ I

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

38. THE UNIVERSITY OF ALABAMA 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

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

40. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing current, properly No problem. You just need four wires. What is still wrong? R wires R thin g I V R thing ≪ R internal or add buffer

41. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage R wires R thing VsVs Still have to measure voltage on device the wires still use up some of V What about current? V

42. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage II R = ∆V / I Note we need 4 wires again current meter - not hard still problems? R wires R thing VsVs V Ι Ι = R precise V R par RsRs

43. THE UNIVERSITY OF ALABAMA 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

44. 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? R wires R thing VsVs V Ι = R s ≪ R thing RpRp Ι = V source voltage R p has same voltage as R thing R s has same current have done >10 10 Ohm

45. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a *really* low R? R wires R thin g I V this works just fine... so long as your V meter is good v. good amp / part of a bridge

46. 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? V R1R1 R3R3 R2R2 R x +dR VsVs balance bridge to V=0 detect small changes from null make R 1 -R 3 about the same trimming resistor on R 2 = dR R 2 = ≈ R 3

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