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KVL & KCL Circuit Analysis Examples

This lecture reviews Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) and provides examples of circuit analysis using these principles. Includes tips, examples, and information on series and parallel circuit elements.

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KVL & KCL Circuit Analysis Examples

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  1. Lecture 4 Review: KVL, KCL Circuit analysis examples Series, parallel circuit elements Related educational modules: Section 1.4, 1.5

  2. Review: KVL & KCL • KVL: algebraic sum of all voltage differences around any closed loop is zero • KCL: algebraic sum of all currents entering a node is zero

  3. Review: Circuit analysis • General circuit analysis approach: • Assign element voltages, currents according to passive sign convention • Apply KVL, KCL, and voltage-current relations as necessary to solve for desired circuit parameters • The general idea is to write as many equations as you have unknowns, and solve for the desired unknowns

  4. Circuit analysis – example 1 • For the circuit below, determine: vAC, vX, vDE, RX, and the power absorbed by the 2 resistor

  5. Example 1 – continued

  6. Talk about open circuit, short circuit terminology

  7. Circuit analysis tips • There are (generally) multiple ways to do a problem • Some time spent examining the problem may be productive! • Subscript notation on voltages provides desired polarity • It may not be necessary to determine all voltages in a loop in order to apply KVL • The circuit does not need to be physically closed in order to apply KVL

  8. More circuit analysis tips • KVL through a current source is generally not directly helpful • Get another equation, but the voltage across a current source is not defined  additional unknown introduced • KCL next to a voltage source generally not directly helpful • Get another equation, but the voltage across a current source is not defined  introduce an additional unknown

  9. Circuit analysis – example 2 • Determine the voltages across both resistors.

  10. Example 2 – continued

  11. Circuit analysis – example 3 • We have a “dead” battery, which only provides 2V • Second battery used to “charge” the dead battery – what is the current to the dead battery?

  12. Non-ideal voltage source models • Add a “source resistance” in series with an ideal voltage source • We will define the term series formally later

  13. Non-ideal current source models • Add a “source resistance” in parallel with an ideal current source • We will define the term parallel formally later

  14. Example 3 – revisited • Our battery charging example can now make sense • Include internal (source resistances) in our model

  15. Ideal sources can provide infinite power • Connect a “load” to an ideal voltage source:

  16. Be sure to discuss previous results relative to open, short-circuit expectations

  17. Non-ideal sources limit power delivery • “Loaded” non-ideal voltage source

  18. Validate previous result with open, short-circuit discussion.

  19. Ideal sources can provide infinite power • Connect a “load” to an ideal current source:

  20. Be sure to discuss previous results relative to open, short-circuit expectations

  21. Non-ideal sources limit power delivery • “Loaded” non-ideal current source

  22. Validate previous results with open vs. short circuit discussion.

  23. When are ideal source models “good enough”? • Ideal and non-ideal voltage sources are the “same” if RLoad >> RS • Ideal and non-ideal current sources are the “same” if RLoad << RS

  24. Series and parallel circuit elements • Circuit elements are in series if all elements carry the same current • KCL at node “a” provides i1 = i2

  25. Series and parallel circuit elements • Circuit elements are in parallel if all elements have the same voltage difference • KVL provides v1 = v2

  26. Circuit reduction • In some cases, series and parallel combinations of circuit elements can be combined into a single “equivalent” element • This process reduces the overall number of unknowns in the circuit, thus simplifying the circuit analysis • Fewer elements  fewer related voltages, currents • The process is called circuit reduction

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