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E E 1205 Circuit Analysis

E E 1205 Circuit Analysis. Lecture 2 - Circuit Elements and Essential Laws. Five Fundamental Elements. Ideal Voltage Sources Independent Dependent Ideal Current Sources Independent Dependent Resistors Inductors (to be introduced later) Capacitors (to be introduced later).

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E E 1205 Circuit Analysis

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  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 + V1 + V2 + V3 + V4 = 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. • va and vb are known. • R1, R2 and R3 are known. • v1, v2 and v3 are unknowns. • ia, ib, i1, i2 and i3 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 V KVL: 48 V Ohm’s Law: 6 A

  29. Example 2 (3/4) KCL: 3 A Ohm’s Law: 12 V KVL: 60 V

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

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