KVL & KCL Circuit Analysis Examples

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