1. Slide 3 - 1 Copyright © 2009 Pearson Education, Inc. 3.7 Switching Circuits

2. Slide 3 - 2 Copyright © 2009 Pearson Education, Inc. Electrical Circuits Electrical circuits can be expressed as logical statements. T represents a closed switch (or current flow). F 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. Slide 3 - 3 Copyright © 2009 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. 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.

4. Slide 3 - 4 Copyright © 2009 Pearson Education, Inc. Series Circuit Switches in series will always be represented with a conjunction ^. In summary,

5. Slide 3 - 5 Copyright © 2009 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. 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.

6. Slide 3 - 6 Copyright © 2009 Pearson Education, Inc. Parallel Circuit Switches in parallel will always be represented with a disjunction V. In summary,

7. Slide 3 - 7 Copyright © 2009 Pearson Education, Inc. Example: Representing a Switching Circuit with Symbolic Statements a.Write a symbolic statement that represents the circuit. b.Construct a truth table to determine when the light will be on.

8. Slide 3 - 8 Copyright © 2009 Pearson Education, Inc. Example: Representing a Switching Circuit with Symbolic Statements a.Write a symbolic statement that represents the circuit. p and q are in series: p ^ q r and p are in parallel: r V p together we get: (p ^ q) V (r V p)

9. Slide 3 - 9 Copyright © 2009 Pearson Education, Inc. Example: Representing a Switching Circuit with Symbolic Statements b.Construct a truth table to determine when the light will be on.

10. Slide 3 - 10 Copyright © 2009 Pearson Education, Inc. Example: Representing a Symbolic Statement as a Switching Circuit Draw a switching circuit that represents [(p ^ ~q) V (r V q)] ^ s.

11. Slide 3 - 11 Copyright © 2009 Pearson Education, Inc. Equivalent Circuits Equivalent circuits are two circuits that have equivalent corresponding symbolic statements. 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.

12. Slide 3 - 12 Copyright © 2009 Pearson Education, Inc. Example: Are the Circuits Equivalent? Determine whether the two circuits are equivalent.

13. Slide 3 - 13 Copyright © 2009 Pearson Education, Inc. Example: Are the Circuits Equivalent? First circuit: p V (q ^ r) Second circuit: (p V q) ^ (p V r)

14. Slide 3 - 14 Copyright © 2009 Pearson Education, Inc. Example: Are the Circuits Equivalent? Answer columns are identical so p V (q ^ r) is equivalent to (p V q) ^ (p V r) and the two circuits are equivalent. 1st circuit: p O (q B r) 2nd circuit: (p O q) B (p O r)

15. Slide 3 - 15 Copyright © 2009 Pearson Education, Inc. Homework P. 161 # 6 – 26 all