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Lecture 2: Circuit Elements and Series/Parallel Resistors Nilsson 2.1-2.5, 3.1-3.2

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. June 24, 2014. Overview. Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors.

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Lecture 2: Circuit Elements and Series/Parallel Resistors Nilsson 2.1-2.5, 3.1-3.2

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

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

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

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

  5. Dependent Sources Voltage Sources Current Sources

  6. Schematics

  7. Schematics (w/dependents)

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

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

  10. Ohm’s Law

  11. Conductance • Conductance, G • Units: siemens [S]

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

  13. Examples

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

  15. Designing a Circuit Model

  16. Additional Elements Short Circuit Open Circuit Switch

  17. Schematic 1.5V 9V

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

  19. The Setup

  20. Kirchhoff’s Current Law (KCL) 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) 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

  23. KCL Example

  24. KVL Example

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

  26. Finding vo

  27. Finding vo KVL: KCL: Ohm’s Law:

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

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

  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

  31. Example

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

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