1. Lecture 4 Review: Circuit analysis examples
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