1. Lesson 5 Basic Laws of Electric Circuits Equivalent Resistance

2. Basic Laws of Circuits Equivalent Resistance: We know the following for series resistors: Figure 5.1: Resistors in series. R eq = R 1 + R 2 +... + R N 1

3. Basic Laws of Circuits Equivalent Resistance: We know the following for parallel resistors: Figure 5.2: Resistors in parallel. 2

4. Basic Laws of Circuits Equivalent Resistance: For the special case of two resistors in parallel: Figure 5.3: Two resistors in parallel. 3

5. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. By combination we mean we have a mix of series and Parallel. This is illustrated below. Figure 5.4: Resistors In Series – Parallel Combination To find the equivalent resistance we usually start at the output of the circuit and work back to the input. 4

6. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Figure 5.5: Resistance reduction. 5

7. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Figure 5.6: Resistance reduction, final steps. 6

8. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. It is easier to work the previous problem using numbers than to work out a general expression. This is illustrated below. Example 5.1: Given the circuit below. Find R eq. Figure 5.7: Circuit for Example 5.1. 7

9. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Example 5.1: Continued. We start at the right hand side of the circuit and work to the left. Figure 5.8: Reduction steps for Example 5.1. Ans: 8

10. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Example 5.2: Given the circuit shown below. Find R eq. Figure 5.9: Diagram for Example 5.2. 9

11. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Example 5.2: Continued. Fig 5.10: Reduction steps. 10

12. Fig 5.11: Reduction steps. R eq 10  resistor shorted out Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Example 5.2: Continued. 11

13. Basic Laws of Circuits Equivalent Resistance:Resistors in combination. Example 5.2: Continued. Fig 5.12: Reduction steps. R eq 12

14. Basic Electric Circuits Wye to Delta Transformation: You are given the following circuit. Determine R eq. Figure 5.1: Diagram to start wye to delta. 13

15. Basic Electric Circuits Wye to Delta Transformation: You are given the following circuit. Determine R eq. Figure 5.13: Diagram to start wye to delta. 14

16. Basic Electric Circuits Wye to Delta Transformation: We cannot use resistors in parallel. We cannot use resistors in series. If we knew V and I we could solve R eq = V I There is another way to solve the problem without solving for I (given, assume, V) and calculating R eq for V/I. 15

17. Basic Electric Circuits Wye to Delta Transformation: Consider the following: We equate the resistance of R ab, R ac and R ca of (a) to R ab, R ac and R ca of (b) respectively. Figure 5.14: Wye to delta circuits. 16

18. Basic Electric Circuits Wye to Delta Transformation: Consider the following: R ab = R a + R b = R ac = R a + R c = R ca = R b + R c = R 1 + R 2 + R 3 R 2 (R 1 + R 3 ) R 1 (R 2 + R 3 ) R 3 (R 1 + R 2 ) Eq 5.1 Eq 5.2 Eq 5.3 17

19. Basic Electric Circuits Wye to Delta Transformation: Consider the following: Eq 5.4 Eq 5.5 Eq 5.6 18

20. 19 Eq 5.4 Eq 5.5 Eq 5.6 Basic Electric Circuits Wye to Delta Transformation: Observe the following: We note that the denominator for R a, R b, R c is the same. We note that the numerator for R 1, R 2, R 3 is the same. We could say “Y” below: “D” Go to deltaGo to wye

21. 20 Basic Electric Circuits Wye to Delta Transformation: Example 5.3: Return to the circuit of Figure 5.13 and find R eq. a b c Convert the delta around a – b – c to a wye.

22. Basic Electric Circuits Wye to Delta Transformation: Example 5.3: continued 21 Figure 5.15: Example 5.3 diagram. It is easy to see that R eq = 15 

23. 22 Basic Electric Circuits Wye to Delta Transformation: Example 5.4: Using wye to delta. The circuit of 5.13 may be redrawn as shown in 5.16. a b c Figure 5.16: “Stretching” (rearranging) the circuit. Convert the wye of a – b – c to a delta.

24. Basic Electric Circuits Wye to Delta Transformation: Example 5.4: continued a b c Figure 5.17: Circuit reduction of Example 5.4. (a) (b) 23 a b c

25. Basic Electric Circuits Wye to Delta Transformation: Example 5.4: continued Figure 5.18: Reduction of Figure 5.17. R eq = 15  This answer checks with the delta to wye solution earlier. 24

26. circuits End of Lesson 5 Basic Laws of Circuits Equivalent Resistance