1. Combination Electrical Circuits This workforce solution was funded by a grant awarded by the U.S. Department of Labor's Employment and Training Administration. The solution was created by the grantee and does not necessarily reflect the official position of the U.S. Department of Labor. The Department of Labor makes no guarantees, warranties, or assurances of any kind, express or implied, with respect to such information, including any information on linked sites, and including, but not limited to accuracy of the information or its completeness, timeliness, usefulness, adequacy, continued availability or ownership. This work is licensed under a Creative Commons CC BY 3.0 Unported License. http://creativecommons.org/licenses/by/3.0/

2. 100V 40Ω 30Ω15Ω When analyzing combination circuits we must first determine the Total Values in the circuit. We already know the total EMF, or E T, which is 100V 1 E T = 100VR1 R2R3 Next

3. 100V 40Ω 30Ω15Ω 2 Here are the parallel resistors in this combination circuit Rules for adding resistors in parallel circuits: 1/R T = 1/R 1 + 1/R 2 +…+ 1/R N Where N is the number of resistors in parallel E T = 100V Next

4. 100V 40Ω 30Ω15Ω 3 Here are the parallel resistors in this combination circuit Also, if the resistors are in parallel and are the same value, there is a shortcut rule: R/N, where R is the common resistor value and N is the number of resistors with that value E T = 100V Next

5. 100V 40Ω 30Ω15Ω 4 Here are the parallel resistors in this combination circuit There is another shortcut rule that can be used if there are only two resistors in parallel: R1 X R2 where R1 and R2 are the two resistors R1 + R2 u E T = 100V Next

6. 100V 40Ω 30Ω15Ω 5 Here are the parallel resistors in this combination circuit This last formula is the formula we are going to use for this circuit because we have only two resistors in parallel, and they are not the same. E T = 100V Next

7. 100V 40Ω 30Ω15Ω Because there are only two resistors in parallel, I can use the formula: R1 x R2 R1 + R2 15 x 30 15 + 30 = 450 45 = 10 Click Here First Click Here Next 6 E T = 100V Next

8. 100V 40Ω 30Ω15Ω10Ω This gives an equivalent resistance of 10Ω In order to continue, we redraw the diagram to show the “equivalent resistor” 7 E T = 100V Next

9. 100V 40Ω 8 10Ω These two resistors, the original 40Ω resistor and our calculated equivalent resistor of 10 Ω, are in series, so we are just going to add them together using our series formula R T = R 1 + R 2 + R 3 … R N E T = 100V Next

10. 100V 6 40Ω + 10Ω = 50Ω E T = 100V 40Ω And, as before we redraw the circuit to reflect the “equivalent resistance” of 50Ω 10Ω 50Ω Next

11. 100V 6 40Ω + 10Ω = 50Ω E T = 100V 40Ω And, as before we redraw the circuit to reflect the “equivalent resistance” of 50Ω 10Ω 50Ω Next

12. 100V 6 E T = 100V Since there is no more multiple resistors to combine, we have now reached the Total Resistance of the circuit 50Ω R T = 50Ω Next

13. 100V 6 E T = 100V Now we need to solve for I T, or Total Current. We use Ohms Law to figure this out. E = IR 50Ω R T = 50Ω Next

14. 100V 6 E T = 100V We will use an excellent tool to remember the formula! 50Ω R T = 50Ω Just cover over the letter that represents the value you are solving for … in this case I for Current. Therefore our formula is E divided by R E IR Ohms Triangle Next

15. 100V 6 E T = 100V 50Ω R T = 50Ω E T = 100V and R T = 50Ω E IR Ohms Triangle Therefore, E T /R T = 100V/50Ω = 2A I T = 2A Next

16. 100V 6 E T = 100V 50Ω R T = 50Ω BUT WAIT! WE ARE NOT DONE! E IR Ohms Triangle We have to go backward now and solve voltage and amperage for each of the original resistors I T = 2A Next

17. 100V 6 E T = 100V R T = 50Ω Lets put the values next to the equivalent resistor above E IR Ohms Triangle Great! Now lets start to work backward and expand to the original circuit. I T = 2A 50Ω 2A 100V Next

18. 100V 6 E T = 100V 40Ω We have now expanded backward to the previous circuit, and the two resistors are now split back out into two resistors in series. 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1 Next

19. 100V 6 E T = 100V 40Ω If you remember your lessons, when I have resistors in series, voltage changes across each resistor, but amperage remains the same. 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1 And we know what the amperage is from the last slide … 2A. Next

20. 100V 6 E T = 100V 40Ω So, lets put the amperage at each resistor. 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1 Now, using Ohms Triangle, we determine the formula to find E. 2A We see that to find E we must multiply I times R. Next

21. 100V 6 E T = 100V 40Ω For the resistor at the top, R 1, I = 2A, R 1 = 40Ω 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 2A X 40Ω = 80V 2A For the resistor on the right: 2A X 10Ω = 20V Note that when I add the voltages together they equal the total voltage. Next

22. 100V 6 E T = 100V 40Ω Now we put the voltages on each of the resistors 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 2A 80V 20V Next

23. 2A 100V 6 E T = 100V 40Ω All right. The next step is to expand the resistor on the right to its original position, which were two parallel resistors 10Ω E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 80V 20V We also need to remove the 10Ω equivalent value and replace it with the two values we had started with 30Ω15Ω Next

24. 2A 100V 6 E T = 100V 40Ω In a parallel circuit the voltage stays the same and the amperage changes, so we are going to use voltage now to determine the amperage at each resistor E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 80V 20V We place the voltage that we calculated in the previous calculation (20V) and place it with each of the parallel resistors and remove the amperage rating. 30Ω15Ω 20V Next

25. 2A 100V 6 E T = 100V 40Ω Again we use Ohms Triangle to determine the formula to find amperage (I). E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 80V As seen, the formula is E divided by R. For the rightmost resistor this is 20V / 30Ω or.67A and for the leftmost resistor it would be 20V / 15Ω or 1.33A. Note the two add up to 2A 30Ω15Ω 20V Next

26. 2A 100V 6 E T = 100V 40Ω Now place the two amperage values next to their corresponding resistors. E IR Ohms Triangle E T = 100V R T = 50Ω I T = 2A R1R1 80V Finally, a list can be made to show the different values on the left side to make identification easier. 30Ω15Ω 20V.67A1.33A R2R2 R3R3 E 1 = 80V E 2 = 20V E 3 = 20V I 1 = 2A I 2 = 1.33A I 3 =.67A Next

27. Congratulations!