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Chapter 31

Chapter 31. Fundamentals of Circuits. Circuits. potential field current. Kirchoff ’ s rules. KLR: Kirchoff ’ s loop rule (conservation of energy). KJR: Kirchoff ’ s junction rule (conservation of charge). Always true!. Ohm ’ s Law. --Recall lab: rheostat (resistor), tungsten, carbon.

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Chapter 31

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

  2. Circuits potentialfield current Phys 133 -- Chapter 31

  3. Kirchoff’s rules KLR: Kirchoff’s loop rule (conservation of energy) KJR: Kirchoff’s junction rule (conservation of charge) Always true! Phys 133 -- Chapter 31

  4. Ohm’s Law --Recall lab: rheostat (resistor), tungsten, carbon Phys 133 -- Chapter 31

  5. 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 Phys 133 -- Chapter 31

  6. Ideal wire: --no potential difference (“no voltage drop”) --all potential difference across resistors Phys 133 -- Chapter 31

  7. Circuit elements: real and schematic Phys 133 -- Chapter 31

  8. I (+) ≈0 ≈0 Basic circuit + - Phys 133 -- Chapter 31

  9. Problem A • --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. Phys 133 -- Chapter 31

  10. I (+) V 6 V 3 V r Draw a schematic of this circuit. Choose a direction of positive current Indicate the high and low side of the resistor. + - Problem A (ans) Apply Kirchoff’s law Phys 133 -- Chapter 31

  11. Do Workbook 31.6 • Iout ? Iin • < • > • = • b) R1 ? R2 ? R3 • R1 > R2 > R3 • R3 > R1 > R2 • R1 = R2 = R3 • R2 > R1 > R3 • c) E ? • Right • Left • E = 0 Phys 133 -- Chapter 31

  12. Do Workbook 31.9 • DV12 = ? • 0V • 3V • <3V Phys 133 -- Chapter 31

  13. In general Resistors-series Currents are the same Phys 133 -- Chapter 31

  14. Determine the current through R1 and R2? Determine the potential difference ∆V1 and ∆V2? Problem B Phys 133 -- Chapter 31

  15. I Problem B (ans) R1 & R2 in series + - R1 & R2 in series Phys 133 -- Chapter 31

  16. Voltage in a circuit The light bulb in this circuit has a resistance of 1 W. What are the values of: DV12 DV23 DV34 Suppose the bulb is removed from its socket. Then what are values of DV12 DV23 DV34 • Answers: • 0V • 1V • 2V • 3V Phys 133 -- Chapter 31

  17. In general Resistors-parallel Potential differences are the same Phys 133 -- Chapter 31

  18. Determine the current through R1 and R2? Determine the potential difference ∆V1 and ∆V2? Problem C c) What fraction of the current goes through R1? What happens to this fraction if the value of R2 is increased? Phys 133 -- Chapter 31

  19. I R1 & R2 in parallel Problem C (ans) + - R1 & R2 in parallel Phys 133 -- Chapter 31

  20. Power and energy For battery For resistor Phys 133 -- Chapter 31

  21. Problem D How much power is dissipated by each resistor? How much power is provided by each battery? Series Parallel Phys 133 -- Chapter 31

  22. Parallel Series Problem D (ans) Phys 133 -- Chapter 31

  23. Real batteries: ideal emf and internal resistance Phys 133 -- Chapter 31

  24. Compared to an ideal battery, by what percentage does the battery’s internal resistance reduce the potential difference across the 30  resistor? Problem E Phys 133 -- Chapter 31

  25. 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) Phys 133 -- Chapter 31

  26. 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 = B = C • B = C > A • A > B = C • A > B > C *RTP Lab 3 Homework Phys 133 -- Chapter 31

  27. Conceptual 2 A wire is connected from the battery terminal at point 1 to point 4 What happens to the potential difference across bulb B? Explain. What happens to the potential difference across bulb C? Explain. What happens to the potential difference between points 1 and 5? Explain your reasoning. What happens to the brightness of each of the three bulbs? Explain. What happens to the current through point 3? Explain. *RTP Lab 3 Homework Phys 133 -- Chapter 31

  28. Resistors Phys 133 -- Chapter 31

  29. General relationships Phys 133 -- Chapter 31

  30. Problem 31.67 Find the current through and potential difference across each resistor. (Hint: Collapse and expand.) Phys 133 -- Chapter 31

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

  32. Problem: Multi-loop circuit Find the current (I) and potential difference (V) across each resistor. (Hint: use KLR and KJR.) Phys 133 -- Chapter 31

  33. Circuit problemstrategy --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 Phys 133 -- Chapter 31

  34. 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) Phys 133 -- Chapter 31

  35. + - + - I3 I2 + - I1 Apply KLR abcea: Problem F (ans) abcdea: Apply KJR Junction c: ecde: Junction e: 5 equations, 3 unknowns Choose 3, and solve Phys 133 -- Chapter 31

  36. Grounding: convention/safety Phys 133 -- Chapter 31

  37. Do Workbook 31.32 Phys 133 -- Chapter 31

  38. Problem 31.34 Determine the potential at points a through d. Phys 133 -- Chapter 31

  39. + - 7 V 9 V 0 V 4 V - + Problem 31.34 (ans) Determine the potential at points a through d. Phys 133 -- Chapter 31

  40. RC circuits: discharge Before the switch closes Apply KLR After the switch is closed Phys 133 -- Chapter 31

  41. RC circuits: discharge Phys 133 -- Chapter 31

  42. RC circuits: charging Phys 133 -- Chapter 31

  43. 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? Phys 133 -- Chapter 31

  44. Problem G (ans) Close switch at t=0, then Find t when Q(t)=20µC Phys 133 -- Chapter 31

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