1. Combination Circuits

2. Simplifying Resistors in Combination Circuits 3Ω3Ω 11Ω

3. 4 Ω 18 Ω

4. 4 Ω 18 Ω

5. Combo Circuits Quiz

6. Now we can analyze other aspects of a circuit…in order to do this we must first simplify. R 1 = 1 Ω R 2 = 8 Ω R 3 = 8 Ω 1 = 1 + 1 R 2,3 R 2 R 3 1 = 1 + 1 = 2 = 4 Ω R 2,3 8 Ω 8 Ω 8 Ω R 1 = 1 ΩR 2,3 = 4 Ω 100 V 0 V 100 V0 V

7. Next simplified the circuit down to one resistor. R 1 = 1 ΩR 2,3 = 4 Ω 100 V0 V Series = R T = R 1 + R 2,3 R T = 1 Ω + 4 Ω R T = 5 Ω 100 V0 V

8. We went from R 1 = 1 Ω R 2 = 8 Ω R 3 = 8 Ω 100 V 0 V to R 1 = 1 ΩR 2,3 = 4 Ω 100 V0 V to R T = 5 Ω 100 V0 V

9. Next find the total current flowing through the simplified circuit. R T = 5 Ω 100 V0 V I T = V T R T I T = 100 V 5 Ω I T = 20 A Now we can go back and un-simplify the circuit and find the current and voltage through specific resistors…

10. Find the current and voltage through R 1. Hint: Always find current first, then voltage. R 1 = 1 ΩR 2,3 = 4 Ω 100 V0 V R T = 5 Ω 100 V0 V We already found the current through R T and since this is a series circuit I T = I 1 = I 2,3 so I 1 = 20 A. Next find voltage…

11. R 1 = 1 ΩR 2,3 = 4 Ω 100 V0 V I 1 = 20 AI 2,3 = 20 A V 1 = I 1 R 1 In a series circuit V T = V 1 + V 2,3 so the voltages across both of these resistors will add up to 100 V. V 1 = (20A)( 1 Ω) V 1 = 20 V V 2,3 = I 2,3 R 2,3 V 2,3 = (20A)( 4 Ω) V 2,3 = 80 V Let’s check to see if the voltages make sense: V T = V 1 + V 2,3 100 V = 20 V + 80 V

12. Now we can find the separate currents and voltages through R 2 and R 3. R 1 = 1 ΩR 2,3 = 4 Ω 100 V0 V I 1 = 20 AI 2,3 = 20 A R 1 = 1 Ω R 2 = 8 Ω R 3 = 8 Ω 100 V 0 V I 1 = 20 A I 2,3 = 20 A

13. R 1 = 1 Ω R 2 = 8 Ω R 3 = 8 Ω 100 V 0 V I 1 = 20 A I 2,3 = 20 A R 2 and R 3 are in parallel so we know that V 2,3 = V 2 = V 3 therefore V 2 and V 3 are 80 V. Now we can find I 2 and I 3. I 2 = V 2,3 R 2 I 2 = 80 V 8 Ω I 2 = 10 A I 3 = V 2,3 R 3 I 3 = 80 V 8 Ω I 3 = 10 A V 1 = 20 V V 2,3 = 80 V

14. Let’s try another one… R 3 = 6 Ω R 1 = 4 ΩR 2 = 2 Ω Resistors R 1 and R 2 are in series so R 1,2 = R 1 + R 2 R 1,2 = R 1 + R 2 R 1,2 = 4 Ω + 2 Ω = 6 Ω R 3 = 6 Ω R 1,2 = 6 Ω 100 V0 V 100 V0 V

15. R 3 = 6 Ω R 1,2 = 6 Ω 100 V0 V 1 = 1 + 1 R T R 1,2 R 3 1 = 1 + 1 = 2 = 3 Ω R T 6 Ω 6 Ω 6 Ω R T = 3 Ω 100 V0 V

16. R 3 = 6 Ω R 1 = 4 ΩR 2 = 2 Ω 100 V0 V R 3 = 6 Ω R 1,2 = 6 Ω 100 V0 V R T = 3 Ω 100 V0 V

17. What do we do next? R T = 3 Ω 100 V0 V I T = V T R T I T = 100 V 3 Ω I T = 33.33 A Next we un-simplify the circuit and find the rest…

18. R 3 = 6 Ω R 1,2 = 6 Ω 100 V0 V I T = 33.33 A Since R 1,2 and R 3 are in parallel they have voltage in common: V T = V 1,2 = V 3 therefore V 1,2 and V 3 are both 100 V. We can now find each resistors individual current flow, I T = I 1,2 + I 3. I 1,2 = V 1,2 R 1,2 I 1,2 = 100 V 6 Ω I 1,2 = 16.67 A I 3 = V 3 R 3 I 3 = 100 V 6 Ω I 3 = 16.67 A

19. Now let’s separate R 1 and R 2 … R 3 = 6 Ω R 1,2 = 6 Ω 100 V0 V R 3 = 6 Ω R 1 = 4 ΩR 2 = 2 Ω 100 V0 V I 3 = 16.67 A I 1,2 = 16.67 A

20. R 3 = 6 Ω R 1 = 4 ΩR 2 = 2 Ω 100 V0 V I 3 = 16.67 A I 1,2 = 16.67 A R 1 and R 2 are in series with each other so they have the same amount of current flowing through them: I 1,2 = I 1 = I 2 therefore the current flowing through both of them is 16.67 A which will help us find the voltage drop across each resistor. V 1 = I 1,2 R 1 V 1 = (16.67A)( 4 Ω) V 1 = 66.68 V V 2 = I 1,2 R 2 V 2 = (16.67A)( 2 Ω) V 2 = 33.34 V

21. Let’s try another… R 1 = 2 Ω R 2 = 4 Ω R 3 = 4 Ω 21 V 0 V R 4 = 3 Ω Remember the steps: 1. Simplify the circuit so that there is only 1 resistor. 2. Find the total current of the simplified resistor. 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. 4. Be sure to do this using the correct equations that go with that section of the circuit.

22. 1. Simplify the circuit so that there is only 1 resistor. R 1 = 2 Ω R 2 = 4 Ω R 3 = 4 Ω 21 V 0 V R 4 = 3 Ω R T = 7 Ω 21 V0 V R 1 = 2 Ω 21 V0 V R 2,3 = 2 ΩR 4 = 3 Ω

23. 2. Find the total current of the simplified resistor. R T = 7 Ω 21 V0 V I T = V T R T I T = 21 V 7 Ω I T = 3 A

24. 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. R T = 7 Ω 21 V0 V R 1 = 2 Ω 21 V0 V R 2,3 = 2 ΩR 4 = 3 Ω I 1 = 3 A I 2,3 = 3 A I 4 = 3 A V 1 = I 1 R 1 V 1 = (3 A)( 2 Ω) V 1 = 6 V V 2,3 = I 2,3 R 2,3 V 2,3 = (3 A)( 2 Ω) V 2,3 = 6 V V 4 = I 4 R 4 V 4 = (3 A)( 3 Ω) V 4 = 9 V

25. R 1 = 2 Ω 21 V0 V R 2,3 = 2 ΩR 4 = 3 Ω I 1 = 3 A I 2,3 = 3 A I 4 = 3 A V 1 = 6 VV 2,3 = 6 VV 4 = 9 V R 1 = 2 Ω R 2 = 4 Ω R 3 = 4 Ω 21 V 0 V R 4 = 3 Ω V 2 = 6 V V 3 = 6 V I 2 = V 2 R 2 I 2 = 6 V 4 Ω I 2 = 1.5 A I 3 = V 3 R 3 I 3 = 6 V 4 Ω I 3 = 1.5 A I 2,3 = 3 A

26. Let’s try another… R 1 = 1 Ω R 2 = 3 Ω R 4 = 6 Ω 30 V 0 V R 5 = 1 Ω Remember the steps: 1. Simplify the circuit so that there is only 1 resistor. 2. Find the total current of the simplified resistor. 3. Work backward, un-simplifying the circuit, finding the current and voltage of each resistor along the way. 4. Be sure to do this using the correct equations that go with that section of the circuit. R 3 = 3 Ω

27. R 1 = 1 Ω R 2 = 3 Ω R 4 = 6 Ω 30 V 0 V R 5 = 1 Ω R 3 = 3 Ω R 1 = 1 Ω R 2,3 = 6 Ω R 4 = 6 Ω 30 V 0 V R 5 = 1 Ω R T = 5 Ω 30 V0 V R 1 = 1 Ω 30 V0 V R 2,3,4 = 3 ΩR 5 = 3 Ω

28. More practice… a)Which letter shows the graph of voltage vs. current for the smallest resistance? b) Which letter shows the graph of voltage vs. current for the largest resistance?

29. a)What is the total resistance of this circuit? b) What is the total current of this circuit? c) What is the amount of current running through each resistor?

30. a) What is the total resistance of this circuit? b) What is the total current of this circuit?

31. a) Find the equivalent resistance. b) Find the current (I T ) going through this circuit. c) Find potential drop across R 1 & R 2

32. a) Find combined resistance (R T ). b) Find the current in R 1. c) Find I 3. d) Find R 2. e) Find value of the second resistor.

33. a)If the voltage drop across the 3 ohm resistor is 4 volts, then what would the voltage drop be across the 6 ohm resistor? b) Find the total voltage in this series circuit. c) Find combined resistance in this circuit. d) Find the total current in this circuit.

34. a) Current in this circuit? b) Potential difference in 20 ohm resistor? c) Equivalent resistance in the circuit?

35. Find R 2.