1. 1 Electronics Parallel Resistive Circuits Part 1 Copyright © Texas Education Agency, 2014. All rights reserved.

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 2 Copyright © Texas Education Agency, 2014. All rights reserved.

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 Copyright © Texas Education Agency, 2014. All rights reserved.

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 4 Copyright © Texas Education Agency, 2014. All rights reserved.

5. The Simplest Parallel Circuit The two resistors are different loads Load one is labeled R 1 and load two is labeled R 2 5 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

6. Paths for Current Flow Path One 6 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

7. Paths for Current Flow Path Two 7 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

8. Paths for Current Flow Path Two Now let’s apply Kirchhoff’s Voltage Law to each path 8 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

9. Voltage in Parallel Circuits Path One- place polarities for the two components 9 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

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 10 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

11. Kirchhoff’s Law in Parallel Circuits Path One- start from the top of the battery, and read polarities going into each component + V S – V R1 = 0 or V S = V R1 11 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

12. Kirchhoff’s Law in Parallel Circuits Path Two + V S – V R2 = 0 or V S = V R2 12 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved.

13. Voltage in Parallel Circuits This is the first equation for a parallel circuit This equation says that the voltage in each parallel path is the same 13 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. V S = V R1 = V R2 VSVS

14. Current in a Parallel Circuit Both paths exist at the same time The current that flows through R 1 does not flow through R 2 The current that flows through R 2 does not flow through R 1 14 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

15. Current in a Parallel Circuit 15 R1R1 R2R2 VSVS Copyright © Texas Education Agency, 2014. All rights reserved. Each current is separate and independent To calculate each current flow, use Ohm’s Law

16. Current in a Parallel Circuit 16 Copyright © Texas Education Agency, 2014. All rights reserved. R1R1 R2R2 VSVS

17. Current in a Parallel Circuit A node is where current splits or combines It is a junction or branching point for current 17 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

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 18 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

19. Current in a Parallel Circuit Current combines or comes back together here Current splits apart here 19 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

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 20 Copyright © Texas Education Agency, 2014. All rights reserved.

21. Water Flow Equivalent Here is a picture showing the same effect using water flow in a pipe Flow splits into two parts here 21 Copyright © Texas Education Agency, 2014. All rights reserved.

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 22 Copyright © Texas Education Agency, 2014. All rights reserved.

23. Current in a Parallel Circuit There are actually three different currents 23 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

24. Current in a Parallel Circuit There are actually three different currents Here is I 1 24 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

25. Current in a Parallel Circuit There are actually three different currents Here is I 1 Here is I 2 25 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

26. Current in a Parallel Circuit Here is I T (total current) I T is the current leaving and entering the battery 26 R1R1 R2R2 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

27. Water Flow Equivalent Here is the picture using current flow symbols 27 ITIT ITIT I2I2 Copyright © Texas Education Agency, 2014. All rights reserved.

28. Current in a Parallel Circuit From Kirchhoff’s Current Law I T = I 1 + I 2 28 R1R1 R2R2 ITIT Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

29. Current in a Parallel Circuit From Kirchhoff’s Current Law This is the second parallel circuit equation 29 R1R1 R2R2 ITIT Copyright © Texas Education Agency, 2014. All rights reserved. I T = I 1 + I 2 VSVS

30. Resistance in a Parallel Circuit 30 I T = I 1 + I 2 V S = V R1 = V R2 Copyright © Texas Education Agency, 2014. All rights reserved.

31. Resistance in a Parallel Circuit After substitution V S 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 31 Copyright © Texas Education Agency, 2014. All rights reserved.

32. Parallel Circuit Equations 32 I T = I 1 + I 2 V S = V R1 = V R2 Copyright © Texas Education Agency, 2014. All rights reserved. For two resistors

33. Parallel Circuit Equations 33 (current adds) (voltage is the same) (resistance is more complex, but it basically divides) Copyright © Texas Education Agency, 2014. All rights reserved. I T = I 1 + I 2 V S = V R1 = V R2

34. Parallel Circuit Equations 34 (current adds) (voltage is the same) (resistance is more complex, but it basically divides) Copyright © Texas Education Agency, 2014. All rights reserved. These three formulas (plus Ohm’s Law) form a “tool kit” to analyze parallel circuits. I T = I 1 + I 2 V S = V R1 = V R2

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 35 S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

36. Understanding Resistance in a Parallel Circuit Close S 1 and L 1 comes on We get current I 1 from the battery Each light is identical Total current = I 1, total resistance = R 1 36 VSVS S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, 2014. All rights reserved.

37. Understanding Resistance in a Parallel Circuit Next close S 2 and L 2 comes on We get additional current I 2 from the battery Total current = I 1 + I 2, double the current This means total resistance must be cut in half compared to the previous circuit 37 S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, 2014. All rights reserved. VSVS

38. Do the Math 38 Copyright © Texas Education Agency, 2014. All rights reserved. Use the following formula Assume R 1 = R 2 = 30 Ω

39. Example Problem 1 For the following circuit, calculate R T and I T Begin by writing down the equations we need Start with the formula for R T. Once we calculate that, we can solve for I T 39 Copyright © Texas Education Agency, 2014. All rights reserved. R 1 = 300 Ω R 2 = 200 Ω V S = 15 V

40. Example Problem 1 For the following circuit, calculate R T and I T Begin by writing down the equations we need 40 Copyright © Texas Education Agency, 2014. All rights reserved. R 1 = 300 Ω R 2 = 200 Ω V S = 15 V and

41. Example Problem 1 41 Copyright © Texas Education Agency, 2014. All rights reserved.

42. Example Problem 1 42 Copyright © Texas Education Agency, 2014. All rights reserved.

43. Example Problem 1 43 Copyright © Texas Education Agency, 2014. All rights reserved. R T = 120 Ω

44. Example Problem 1 44 Copyright © Texas Education Agency, 2014. All rights reserved. R T = 120 Ω

45. Example Problem 1 45 Copyright © Texas Education Agency, 2014. All rights reserved. R T = 120 Ω