1. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.7 Switching Circuits

2. Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Switching circuits 3.7-2

3. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Electrical Circuits Electrical circuits can be expressed as logical statements. T (true) represents a closed switch (or current flow). F (false) represents an open switch (or no current flow). In a series circuit the current can take only one path. In a parallel circuit there are two or more paths the current can take. 3.7-3

4. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Series Circuit Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T. Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is off, F. 3.7-4

5. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Series Circuit Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is off, F. Case 4: Both switches are open; that is, p is F and q is F. The light is off, F. 3.7-5

6. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Series Circuit Switches in series will always be represented with a conjunction ⋀. In summary, 3.7-6

7. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Parallel Circuit Case 1: Both switches are closed; that is, p is T and q is T. The light is on, T. Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is on, T. 3.7-7

8. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Parallel Circuit Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is on, T. Case 4: Both switches are open; that is, p is F and q is F. The light is off, F. 3.7-8

9. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Parallel Circuit Switches in parallel will always be represented with a disjunction ⋁. In summary, 3.7-9

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Representing a Switching Circuit with Symbolic Statements a.Write a symbolic statement that represents the circuit. 3.7-10

11. Copyright 2013, 2010, 2007, Pearson, Education, Inc. p and q are in parallel: p ⋁ q q and r are in series: q ⋀ r together we get: (p ⋀ q) ⋁ (q ⋀ r) Example 2: Representing a Switching Circuit with Symbolic Statements Solution 3.7-11

12. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Representing a Switching Circuit with Symbolic Statements b.Construct a truth table to determine when the light will be on. 3.7-12

13. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Representing a Switching Circuit with Symbolic Statements Solution 3.7-13

14. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Representing a Symbolic Statement as a Switching Circuit Draw a switching circuit that represents [(p ⋀ ~q) ⋁ (r ⋁ q)] ⋀ s. Solution 3.7-14

15. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Equivalent Circuits Equivalent circuits are two circuits that have equivalent corresponding symbolic statements. 3.7-15

16. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Equivalent Circuits Sometimes two circuits that look very different will actually have the exact same conditions under which the light will be on. The truth tables have identical answer columns. 3.7-16

17. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Are the Circuits Equivalent? Determine whether the two circuits are equivalent. 3.7-17

18. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Are the Circuits Equivalent? p ⋁ (q ⋀ r) (p ⋁ q) ⋀ (p ⋁ r) Solution 3.7-18

19. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Are the Circuits Equivalent? The answer columns are identical. Solution 3.7-19

20. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Are the Circuits Equivalent? Therefore, p ⋁ (q ⋀ r) is equivalent to (p ⋁ q) ⋀ (p ⋁ r) and the two circuits are equivalent. Solution 3.7-20