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Electronics

Electronics. Parallel Resistive Circuits Part 1 . What is a Parallel Circuit?. A parallel circuit is a circuit with more than one path for current flow This type of circuit is very common This is the type of circuit that is used to deliver power to an outlet in your home

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Electronics

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  1. Electronics Parallel Resistive Circuits Part 1

  2. What is a Parallel Circuit? • A parallel circuit is a circuit with more than one path for current flow • This type of circuit is very common • This is the type of circuit that is used to deliver power to an outlet in your home • Circuit analysis in a parallel circuit starts the same way as a series circuit—with Kirchhoff’s Laws

  3. Review of Kirchhoff’s Law’s • Voltage law- the sum of all voltages in a closed loop is equal to zero • The sum of the voltage drops equals the sum of the voltage sources • All of the voltage is always used in a loop • Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node • The current into a conductor is the same as the current out of the conductor

  4. The Simplest Parallel Circuit • Here is an example of the simplest parallel circuit • This circuit has a power supply and two paths for current flow

  5. The Simplest Parallel Circuit • The two resistors are different loads • Load one is labeled R1 and load two is labeled R2 VS R1 R2

  6. Paths for Current Flow • Path One VS R1 R2

  7. Paths for Current Flow • Path Two VS R1 R2

  8. Paths for Current Flow • Path Two • Now let’s apply Kirchhoff’s Voltage Law to each path VS R1 R2

  9. Voltage in Parallel Circuits • Path One- place polarities for the two components VS R1 R2

  10. Kirchhoff’s Law in Parallel Circuits • Path One- place polarities for the two components • In a path for current flow from one side of the battery to the other, the sum of the voltage in a closed loop equals zero VS R1 R2

  11. Kirchhoff’s Law in Parallel Circuits • Path One- start from the top of the battery, and read polarities going into each component • + VS – VR1 = 0 or • VS = VR1 VS R1 R2

  12. Kirchhoff’s Law in Parallel Circuits • Path Two • + VS – VR2 = 0 or • VS = VR2 VS R1 R2

  13. Voltage in Parallel Circuits VS = VR1 = VR2 • This is the first equation for a parallel circuit • This equation says that the voltage in each parallel path is the same R1 R2 VS

  14. Current in a Parallel Circuit • Both paths exist at the same time • The current that flows through R1does not flow throughR2 • The current that flows through R2does not flow throughR1 R1 R2 VS

  15. Current in a Parallel Circuit • Each current is separate and independent • To calculate each current flow, use Ohm’s Law R1 R2 VS I1= I2=

  16. Current in a Parallel Circuit • I1 = ,I2 = • Apply Kirchhoff’s Current Law to this circuit • Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node R1 R2 VS

  17. Current in a Parallel Circuit • A node is where current splits or combines • It is a junction or branching point for current R1 R2 VS

  18. Current in a Parallel Circuit • A node is where current splits or combines • It is a junction or branching point for current • Here are the nodes R1 R2 VS

  19. Current in a Parallel Circuit • Current combines or comes back together here • Current splits apart here R1 R2 VS

  20. Water Flow Equivalent • Here is a picture showing the same effect using water flow in a pipe • Water flow here is the same as water flow here

  21. Water Flow Equivalent • Here is a picture showing the same effect using water flow in a pipe • Flow splits into two parts here

  22. Water Flow Equivalent • Here is a picture showing the same effect using water flow in a pipe • These two points are the equivalent of an electrical node or junction • Where flow splits and then comes back together

  23. Current in a Parallel Circuit • There are actually three different currents R1 R2 VS

  24. Current in a Parallel Circuit • There are actually three different currents • Here is I1 R1 R2 VS

  25. Current in a Parallel Circuit • There are actually three different currents • Here is I1 • Here is I2 R1 R2 VS

  26. Current in a Parallel Circuit • Here is IT(total current) • ITis the current leaving and entering the battery R1 R2 VS

  27. Water Flow Equivalent • Here is the picture using current flow symbols IT IT I2

  28. Current in a Parallel Circuit • From Kirchhoff’s Current Law IT = I1 + I2 IT R1 R2 VS

  29. Current in a Parallel Circuit • From Kirchhoff’s Current Law • This is the second parallel circuit equation IT = I1 + I2 IT R1 R2 VS

  30. Resistance in a Parallel Circuit • Start with the equation for parallel circuit current • Using Ohm’s Law, substitute for current I = so • Recall the voltage rule in a parallel circuit • Substitute this rule into the previous equation IT = I1 + I2 IT= , I1= , I2= = + VS = VR1 = VR2

  31. Resistance in a Parallel Circuit • After substitution • VS is the same in each term so it divides out, giving us the following formula for resistance in a parallel circuit • This is the third parallel circuit equation = +

  32. Parallel Circuit Equations For two resistors IT = I1 + I2 VS = VR1 = VR2

  33. Parallel Circuit Equations IT = I1 + I2 (current adds) VS = VR1 = VR2 (voltage is the same) (resistance is more complex, but it basically divides)

  34. Parallel Circuit Equations IT = I1 + I2 (current adds) VS = VR1 = VR2 (voltage is the same) (resistance is more complex, but it basically divides) These three formulas (plus Ohm’s Law) form a “tool kit” to analyze parallel circuits.

  35. Understanding Resistance in a Parallel Circuit • Resistance looks a little more complicated, so let’s examine it more closely • Consider the following circuit • Each switch is open; each light is off S1 S2 S3 VS L1 L2 L3

  36. Understanding Resistance in a Parallel Circuit • CloseS1andL1comes on • We get current I1from the battery • Each light is identical • Total current = I1 , total resistance =R1 S1 S2 S3 VS L1 L2 L3

  37. Understanding Resistance in a Parallel Circuit • Next close S2andL2comes on • We get additional current I2from the battery • Total current = I1 +I2, double the current • This means total resistance must be cut in half compared to the previous circuit S1 S2 S3 VS L1 L2 L3

  38. Do the Math • Use the following formula • Assume R1 = R2 = 30 Ω = = .0333 + .0333 = 15 Ω

  39. Example Problem 1 • For the following circuit, calculate RTandIT • Begin by writing down the equations we need • Start with the formula for RT.Once we calculate that, we can solve for IT R1 = 300 Ω R2 = 200 Ω VS = 15 V

  40. Example Problem 1 • For the following circuit, calculate RTandIT • Begin by writing down the equations we need R1 = 300 Ω R2 = 200 Ω VS = 15 V IT= and

  41. Example Problem 1 =

  42. Example Problem 1 = = 0.00333 + 0.005 = 0.00833 =

  43. Example Problem 1 = = 0.00333 + 0.005 = 0.00833 = RT = 120 Ω

  44. Example Problem 1 = = 0.00333 + 0.005 = 0.00833 = RT = 120 Ω IT = =

  45. Example Problem 1 = = 0.00333 + 0.005 = 0.00833 = RT = 120 Ω IT = = = .125 A

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