1. E E 1205 Circuit Analysis Lecture 2 - Circuit Elements and Essential Laws

2. Five Fundamental Elements Ideal Voltage Sources –Independent –Dependent Ideal Current Sources –Independent –Dependent Resistors Inductors (to be introduced later) Capacitors (to be introduced later)

3. Independent Voltage Source Voltage may be constant or time- dependent Delivers nominal terminal voltage under all conditions

4. Independent Current Source Current may be constant or time- dependent Delivers nominal terminal current under all conditions

5. Voltage-Controlled Dependent Voltage Source Terminal voltage is a function of the voltage drop of a different branch Delivers nominal terminal voltage under all conditions

6. Current-Controlled Dependent Voltage Source Terminal voltage is a function of the current flow in a different branch Delivers nominal terminal voltage under all conditions

7. Voltage-Controlled Dependent Current Source Current is a function of the voltage drop of a different branch Delivers nominal terminal current under all conditions

8. Current-Controlled Dependent Current Source Source current is a function of the current flow in a different branch Delivers nominal terminal current under all conditions

9. Electrical Resistance (Ohm’s Law) Electrical resistance is the ratio of voltage drop across a resistor to current flow through the resistor. Polarities are governed by the passive sign convention.

10. Power Consumed by Resistors Resistors consume power. v and i are both positive or both negative.

11. Conductance Defined Conductance is the reciprocal of resistance. The units of conductance are called siemens (S) The circuit symbol is G

12. Creating a Circuit Model A circuit model is usually two or more circuit elements that are connected. A circuit model may have active elements (sources) as well as passive elements (such as resistors). By the assumption that electric signal propagation is instantaneous in a circuit, our circuit model has lumped parameters.

13. Example of a Circuit Model

14. Kirchhoff’s Voltage Law The sum of the voltage drops around a closed path is zero. Example: -120 + V 1 + V 2 + V 3 + V 4 = 0

15. Kirchhoff’s Current Law A node is a point where two or more circuit elements are connected together. The sum of the currents leaving a node is zero.

16. Apply KCL to Example

17. Combine KVL, KCL & Ohm’s Law

18. Lamp Voltage & Battery Voltage

19. Battery Power and Lamp Power Loss: Efficiency:

20. Using Loops to Write Equations KVL @Loop a: KVL @ Loop b: KVL @ Loop c: Loop c equation same as a & b combined.

21. Using Nodes to Write Equations KCL @ Node x: KCL @ Node y: KCL @ Node z: KCL @ Node w: <== Redundant

22. Combining the Equations There are 5 circuit elements in the problem. v a and v b are known. R 1, R 2 and R 3 are known. v 1, v 2 and v 3 are unknowns. i a, i b, i 1, i 2 and i 3 are unknowns. There are 2 loop (KVL) equations. There are 3 node (KCL) equations. There are 3 Ohm’s Law equations. There are 8 unknowns and 8 equations.

23. Working with Dependent Sources KVL @ left loop: KCL @ top right node: Substitute and solve:

24. Example 1 (1/3) By KCL: By Ohm’s Law:

25. Example 1 (2/3) By KVL: Power:

26. Example 1 (3/3)

27. Example 2 (1/4) Find Source Current, I, and Resistance, R.

28. Example 2 (2/4) Ohm’s Law: 36 VKVL: 48 VOhm’s Law: 6 A

29. Example 2 (3/4) KCL: 3 AOhm’s Law: 12 VKVL: 60 V

30. Example 2 (4/4) Ohm’s Law: 3 AKCL: 6 A Ohm’s Law: R=3  KCL: I=9 A KVL: 24 V