1. Lecture 2: Circuit Elements and Series/Parallel Resistors Nilsson 2.1-2.5, 3.1-3.2 ENG17 (Sec. 1): Circuits I Summer 1 2014 1 June 24, 2014

2. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 2

3. 5 Ideal Basic Circuit Elements Voltage Sources Current Sources Resistors Inductors Capacitors 3

4. Ideal Sources 4 Voltage Source (const. voltage) Current Source (const. current)

5. Dependent Sources 5 Voltage Sources Current Sources

6. Schematics 6

7. Schematics (w/dependents) 7

8. Schematics - GND Ground (GND) is a common connection Typically connect to Earth GND Always a zero [V] reference potential 8

9. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 9

10. Ohm’s Law 10

11. Conductance 11

12. Power & Ohm’s Law 12 Therefore… Ohm’s Law Power Relationship

13. Examples 13

14. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources 14

15. Designing a Circuit Model 15

16. Additional Elements 16 Short Circuit Open Circuit Switch

17. Schematic 17 1.5V9V

18. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 18

19. The Setup 19

20. Kirchhoff’s Current Law (KCL) 20 The algebraic sum of all the currents at any node in a circuit equals zero. Therefore: Assign signs to currents at each node Positive (+) for current leaving a node Negative (-) for current entering a node Or vice versa

21. Kirchhoff’s Voltage Law (KVL) 21 The algebraic sum of all the voltages around any closed path in a circuit equals zero. Therefore: Assign signs to voltages in a loop Positive (+) for voltage rise Negative (-) for voltage drop Or vice versa

22. Observations 7 equations  4 equations –Because I and V are related through R, we only need one With only 2 branches at a node (in series), we only need to know 1 current 22

23. KCL Example 23

24. KVL Example 24

25. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 25

26. Finding v o 26

27. Finding v o 27 KVL: KCL: Ohm’s Law:

28. Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 28

29. Series Connected Elements Resistors in series carry the same current –KCL proves this Resistors in series can be summed –KVL proves this 29

30. Parallel Connected Elements Resistors in parallel have same voltage across their terminals –KVL proves this Resistors in parallel can be summed inversely –KCL proves this –Conductances are summed 30

31. Example 31

32. Recap Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 32