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Series and Parallel Circuits

Series and Parallel Circuits. Homework. Webassign!. Ohm’s law applies for each circuit element and for the circuit as a whole. Electrons have a choice about which path they follow. V. V. Electrons must all flow in the same path. V T. A. A. A. A. +. V. V. V 2, I 2. V. V.

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Series and Parallel Circuits

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  1. Series and Parallel Circuits

  2. Homework Webassign!

  3. Ohm’s law applies for each circuit element and for the circuit as a whole. Electrons have a choice about which path they follow. V V Electrons must all flow in the same path VT A A A A + V V V2, I2 V V V1, I1 R1 R2 IT V V V V Series Circuit Parallel Circuit

  4. Electrical Circuits In a series electric circuit, the voltage drops as it flows through each resistive circuit element

  5. Resistors in Series: Building Analogy R1 = Lamp 6 steps R1 R2 = Lamp Elevator (battery) 11 steps R3 = Lamp R2 3 steps To go from the top to the bottom floor, all people must take the same path. So, by definition, the staircases are in series. With each flight people lose some of the potential energy given to them by the elevator, expending all of it by the time they reach the ground floor. So the sum of the V drops across the resistors the voltage of the battery. People lose more potential energy going down longer flights of stairs, so long stairways correspond to high resistance resistors. The double waterfall is like a pair of resistors in series because there is only one route for the water to take. The longer the fall, the greater the resistance.

  6. Diagramming circuits

  7. Kirchoff’s Loop Rule • Conservation of Energy • The sum of the changes in potential around any closed path (loop) of a circuit must be zero.

  8. Series Circuit • Current : One path for the flow of charge • It = I1 = I2 = I3 • Resistance must increase because length increases • Rt = R1 + R2 + R3 • Voltage must add to Zero • Vt - V1 - V2 - V3=0 Vt =V1 + V2 + V3

  9. Name:___________________________________________________ I1 = 1 A + V2 = V1 = 9 R2 = V V

  10. Name:___________________________________________________ VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … First, fill in all values of V and I. After review, fill in values of R. Assume all light bulbs have the same resistance. I1 = A + Vt = 4 V V A L1 V1 = I1= R1= P1 = V2= I2= R2= P2 = Vt = It= Rt= Pt= I2 = 2 L2 V V

  11. VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … First, fill in all values of V and I. After review, fill in values of R. Assume all light bulbs have the same resistance. IT = 1 V1 = I1 = R1 = A + VT = A V V A L1 I1 = V2 = 3 I2 = R2 = V V L2 V3 = I3 = R3 = I2 = V1 = I1= R1= P1 = V2= I2= R2= P2 = V3= I3= R3= P3= Vt= It= Rt= Pt= L3 V V

  12. VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … IT V1 = I1= R1= P1 = V2= I2= R2= P2 = V3= I3= R3= P3= Vt= It= Rt= Pt= V1 = I1 = R1 = 5W + VT V V Series Circuit Example A A V2 = I2 = 1A R2 = V V Given: Vt= 10V R1 = 5W I2 = 1A P3 = 2W V3 = I3 = R3 = V V

  13. VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … IT V1 = I1= R1= P1 = V2= I2= R2= P2 = V3= I3= R3= P3= Vt= It= Rt= Pt= V1 = I1 = R1 = 5W + VA V V Series Circuit Example A A V2 = I2 = 1A R2 = + VB V V Given: VA= 3V VB = 7V R1 = 5W I2 = 1A P3 = 2W V3 = I3 = R3 = V V

  14. VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … IT V1 = I1= R1= P1 = V2= I2= R2= P2 = V3= I3= R3= P3 = V4= I4= R4= P4 = Vt= It= Rt= Pt= V1 = I1 = R1 = 1W V V A V2 = I2 = R2 = 2W A A + VT V V I5 = V3 = 6V I3 = R3 = 3W V V I6 = V4 = I4 = R4 = 4W V V

  15. VT = V1 + V2 + V3 + … IT = I1 = I2 = I3 = … RT = R1 + R2 + R3 + … It = V1 = I1= R1= P1 = V2= I2= R2= P2 = V3= I3= R3= P3 = V4= I4= R4= P4 = Vt= It= Rt= Pt= V1 = 3 I1 = R1 = V V A V2 = I2 = R2 = 2W A A + Vt = V V I5 = V3 = 5V I3 = R3 = V V I6 = V4 = 4V I4 = R4 = 4W V V

  16. Questions What happens if we greatly increase the resistance? When else, besides electricity, do we see things like this? - Think about the effects on voltage (pressure), current (flow), and resistance (blockage)

  17. Tell me about heart bypassess…

  18. Tell me about heart bypassess…

  19. Parallel Circuit • More than one path for the flow of charge • More room for the flow of charge so Resistance goes down • Voltage must stay the same since all sections have the same drop

  20. Series and Parallel Circuits L Series: Single Path, high effective resistance a L A Parallel: Multiple Paths, low effective resistance

  21. Parallel Circuit: • Voltmeters are parallel to the circuit How do the sum of I1, I2, and I3 relate to IT? Hint: What is current? What is it made up of? A A A IT IT A A I2 + I3 I1 R3 R1 R2 V1 V2 V3 V V V V V V IT

  22. Parallel Circuit: • Voltmeters are parallel to the circuit IT = I1 + I2 + I3 by Conservation of charge (conservation of matter) A IT IT A I2 + I3 I1 R3 R1 R2 V1 V2 V3 V V V V V V IT

  23. Kirchoff’s Junction Rule • Conservation of charge

  24. Parallel Equations • It = I1 + I2 + I3 + … • Vt = V1 = V2 = V3 = How do we find the equivalent or total resistance?

  25. Parallel Equations • It = I1 + I2 + I3 + … So • It/Vt = I1/Vt + I2/Vt + I3/Vt … But • Vt = V1 = V2 = V3 =, implying • It/Vt = I1/V1 + I2/V2 + I3/V3 … Or, by Ohm’s law, • 1/Rt = 1/R1 + 1/R2 + 1/R3 + …

  26. Parallel Circuit Rules • VT = V1 = V2 = V3 = … • IT = I1 + I2 + I3 + … • 1/RT = 1/R1 + 1/R2 + 1/R3 + … Start here

  27. Parallel Circuit: • Follow the current • Now map the current flow for circuit 2 A A IT A R4 R5 R6 V2, I2 V3, I3 V1, I1 R3 R1 R2 IT Circuit 1 Circuit 2

  28. Parallel Circuit: • Follow the current • How does circuit 1 differ from circuit 2? A A IT A R4 R5 R6 V2, I2 V3, I3 V1, I1 R3 R1 R2 IT

  29. R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = VT V2 = RT = A V2, I2 V V V1, I1 R1 R2 IT IT = I1 = I2 =

  30. R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = R3 = 150 Ohms V2 = VT RT = V3 = A V2, I2 V3, I3 V V V1, I1 R3 R1 R2 IT IT = I1 = I2 = I3 =

  31. R1 = VT = 120V Rwire = 0.067 Ohms R2 = V1 = R3 = V2 = VT RT = V3 = A V2, I2 V3, I3 V V V1, I1 R3 R1 R2 IT IT = I1 = 5A I2 = 5A Find the equivalent resistance Req of this parallel network I3 = 5A

  32. Parallel Circuit: • Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. A VT V2, I2 V3, I3 V1, I1 R3 R1 R2 IT

  33. Parallel Circuit: • Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. Vt= V1= V2= V3= It = I1= I2= I3= Rt= R1= R2= R3= Pt= P1= P2= P3= A VT V2, I2 V3, I3 V1, I1 R3 R1 R2 IT

  34. Parallel Circuit: • Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. Vt=9 V1= 9 V2=9 V3=9 It =9.5 I1= 3 I2=1.97 I3= 4.5 Rt=0.95 R1=3 R2=4.6 R3=2 Pt=85.5 P1= 27 P2=18 P3=40.5 A VT V2, I2 V3, I3 V1, I1 R3 R1 R2 IT

  35. Electrical Power & Ohm’s Law • Volt = Joules / Coulomb • Ampere = Coulomb / second • Watt = Joule / Second • Resistance = Kg m2/(Coulomb * sec2) • Ooops!

  36. Power • Power is the rate of doing work (Watts) • Power = Work / time • Power = Volt * q / t but q/t = I • Electrical Power = Voltage * Current = VI • Electrical Energy = Power * Time = VIt

  37. More Electric Energy Equations • P = W/t Watt • P = VI = V2/R =I2R • Electric Energy (W)= Pt = VIt = V2/Rt =I2Rt • Joules for all types of Energy

  38. Electrical Power • Electrical Power is priced in kWh • One kiloWatt = 1000 Watts • One kWh = One kW for one hour

  39. Calculate your electrical cost • List appliances you use • Estimate wattage • Estimate usage • Calculate cost

  40. Homework: • Chapter 23: • Problems:page 488 • 1-6

  41. Electrical Power & Ohm’s Law • Volt = Joules / Coulomb • Ampere = Coulomb / second • Watt = Joule / Second • Resistance = Ohms

  42. More Power • Problems • P. 466: 19, 20, 21-25 • Use the simplest form of the equation that matches the givens • Check it with another form if desired

  43. Practice Parallel • Homework: • Problems 8-14, ****16

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