1. Phys 133 -- Chapter 311 Chapter 31 Fundamentals of Circuits

2. Phys 133 -- Chapter 312 Circuits potential  field  current

3. Phys 133 -- Chapter 313 KLR: Kirchoff’s loop rule (conservation of energy) Kirchoff’s rules KJR: Kirchoff’s junction rule (conservation of charge) Always true!

4. Phys 133 -- Chapter 314 --Recall lab: rheostat (resistor), tungsten, carbon Ohm’s Law

5. Phys 133 -- Chapter 315 Question A typical resistance value is 1Ω. A typical copper wire has a radius of 0.5 mm. How long must the typical copper wire be so that it has a 1Ω resistance?  copper = 1.7 x 10 -8 Ωm

6. Phys 133 -- Chapter 316 --no potential difference (“no voltage drop”) --all potential difference across resistors Ideal wire:

7. Phys 133 -- Chapter 317 Circuit elements: real and schematic

8. Phys 133 -- Chapter 318 ≈0 Basic circuit +-+- I (+)

9. Phys 133 -- Chapter 319 - -Find the magnitude and direction of the current through the 18  resistor. On your way to the solution: Draw a schematic of this circuit. Choose a direction of positive current Indicate the high and low side of the resistor. Apply Kirchoff’s law --Draw a graph of the potential as a function of the clockwise distance around the circuit. Start with V=0 at lower left corner. Problem A

10. Phys 133 -- Chapter 3110 Problem A (ans) I (+) + - Apply Kirchoff’s law Draw a schematic of this circuit.Choose a direction of positive currentIndicate the high and low side of the resistor. 6 V 3 V V r

11. Phys 133 -- Chapter 3111 Do Workbook 31.6 a)I out ? I in A.< B.> C.= b) R 1 ? R 2 ? R 3 A.R 1 > R 2 > R 3 B.R 3 > R 1 > R 2 C.R 1 = R 2 = R 3 D.R 2 > R 1 > R 3 c) E ? A.Right B.Left C.E = 0

12. Phys 133 -- Chapter 3112 Do Workbook 31.9  V 12 = ? A.0V B.3V C.<3V

13. Phys 133 -- Chapter 3113 Resistors-series Currents are the same In general

14. Phys 133 -- Chapter 3114 a)Determine the current through R 1 and R 2 ? b)Determine the potential difference ∆V 1 and ∆V 2 ? Problem B

15. Phys 133 -- Chapter 3115 Problem B (ans) R 1 & R 2 in series I +-+-

16. Phys 133 -- Chapter 3116 Voltage in a circuit The light bulb in this circuit has a resistance of 1 . What are the values of:  V 12  V 23  V 34 Suppose the bulb is removed from its socket. Then what are values of  V 12  V 23  V 34 A n s w e r s : A.0 V B.1 V C.2 V D.3 V

17. Phys 133 -- Chapter 3117 Resistors-parallel Potential differences are the same In general

18. Phys 133 -- Chapter 3118 Problem C a)Determine the current through R 1 and R 2 ? b)Determine the potential difference ∆V 1 and ∆V 2 ? c) What fraction of the current goes through R 1 ? What happens to this fraction if the value of R 2 is increased?

19. Phys 133 -- Chapter 3119 Problem C (ans) R 1 & R 2 in parallel I +-+-

20. Phys 133 -- Chapter 3120 Power and energy For battery For resistor

21. Phys 133 -- Chapter 3121 a)How much power is dissipated by each resistor? b)How much power is provided by each battery? Problem D Series Parallel

22. Phys 133 -- Chapter 3122 Problem D (ans) Series Parallel

23. Phys 133 -- Chapter 3123 Real batteries: ideal emf and internal resistance

24. Phys 133 -- Chapter 3124 Compared to an ideal battery, by what percentage does the battery’s internal resistance reduce the potential difference across the 30  resistor? Problem E

25. Phys 133 -- Chapter 3125 Compared to an ideal battery, by what percentage does the battery’s internal resistance reduce the potential difference across the 30  resistor? Problem E (ans)

26. Phys 133 -- Chapter 3126 Conceptual 1 In the circuit below, the battery maintains a constant potential difference between its terminals at points 1 and 2 (i.e., the internal resistance of the battery is considered negligible). The three light bulbs, A, B, and C are identical. How do the brightnesses of the three bulbs compare to each other? A.A = B = C B.B = C > A C.A > B = C D.A > B > C *RTP Lab 3 Homework

27. Phys 133 -- Chapter 3127 Conceptual 2 A wire is connected from the battery terminal at point 1 to point 4 a)What happens to the potential difference across bulb B? Explain. b)What happens to the potential difference across bulb C? Explain. c)What happens to the potential difference between points 1 and 5? Explain your reasoning. d)What happens to the brightness of each of the three bulbs? Explain. e)What happens to the current through point 3? Explain. *RTP Lab 3 Homework

28. Phys 133 -- Chapter 3128 seriesparallel VV  V 1 +  V 2 =  V eq V1=V2V1=V2 II 1 =I 2 I 1 +I 2 = I eq Resistors

29. Phys 133 -- Chapter 3129 SeriesParallel VV addsame Q, Isameadd General relationships

30. Phys 133 -- Chapter 3130 Find the current through and potential difference across each resistor. (Hint: Collapse and expand.) Problem 31.67

31. Phys 133 -- Chapter 3131 Problem 31.67 (ans)

32. Phys 133 -- Chapter 3132 Find the current (I) and potential difference (  V) across each resistor. (Hint: use KLR and KJR.) Problem: Multi-loop circuit

33. Phys 133 -- Chapter 3133 --draw currents (any direction), split at each junction --use KJR at junction(s) --using KLR, go around a loop (any direction) Battery--  V increases going (-  +) of battery --  V decreases going (+  -) of battery Resistor--  V increases upstream (against current) --  V decreases downstream (with current) --solve equations for unknown currents Circuit problem strategy

34. Phys 133 -- Chapter 3134 Find the current (I) and potential difference (  V) across each resistor. (Hint: use KLR and KJR.) Problem F --draw currents (any direction), split at each junction --use KJR at junction(s) --using KLR, go around a loop (any direction)

35. Phys 133 -- Chapter 3135 Problem F (ans) + - I1I1 +-+- I3I3 +-+- I2I2 Apply KLR Apply KJR abcea: abcdea: ecde: Junction c: Junction e: 5 equations, 3 unknowns Choose 3, and solve

36. Phys 133 -- Chapter 3136 Grounding: convention/safety

37. Phys 133 -- Chapter 3137 Do Workbook 31.32

38. Phys 133 -- Chapter 3138 Determine the potential at points a through d. Problem 31.34

39. Phys 133 -- Chapter 3139 Determine the potential at points a through d. Problem 31.34 (ans) + - - + 0 V 4 V 7 V 9 V

40. Phys 133 -- Chapter 3140 RC circuits: discharge Before the switch closes After the switch is closed Apply KLR

41. Phys 133 -- Chapter 3141 RC circuits: discharge

42. Phys 133 -- Chapter 3142 RC circuits: charging

43. Phys 133 -- Chapter 3143 A 20  F capacitor initially charged to 40  C is discharged through a 5.0 k  resistor. Problem G How long does it take to reduce the capacitor’s charge to 10  C? What is the initial current through the resistor?

44. Phys 133 -- Chapter 3144 Problem G (ans) Close switch at t=0, then Find t when Q(t)=20µC