EGR 119/Spring 2011/Lectures
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This page will be used to answer specific questions that come up from lectures in EGR 119. If you ask a question, be sure to use the Q Template to alert folks that a question has been asked.
Lecture 1 1/12/2011
How to count loops?
From e-mail: "I am confused by how to count independent loop because count in different way I get different answers. For example, Figure 2.11, if I count loop abc with 2 omega resistor, 3 omega resistor, and current source respectively, I get 3 independent loops. But if I count abc with 2 omega resistor and bc with 3 omega resistor and current source, I get only 2 loops, any other loop will have a branch included in the previous 2 loops, thus not independent. Am I counting wrong?"
Answer: The circuit in 2.11 has three meshes:
- 1: c - 10 V - a - 5 Ohm - b - 2 Ohm - c
- 2: c - 2 Ohm - b - 3 Ohm - c
- 3: c - 3 Ohm - b - 2 A - c
There are a total of *six* loops:
- loop 1
- loop 2
- loop 3
- superloop 12 (c - 10 V - a - 5 Ohm - b - 3 Ohm - c)
- superloop 23 (c - 2 Ohm - b - 2 A - c)
- superloop 123 (c - 10 V - a - 5 Ohm - b - 2 A - c)
and a variety of ways to pick three independent ones:
| 1 2 3 | 1 3 23 | 2 3 12 | 2 23 123 |
| 1 2 23 | 1 3 123 | 2 3 123 | 3 12 23 |
| 1 2 123 | 1 12 23 | 2 12 23 | 3 23 123 |
| 1 3 12 | 1 12 123 | 2 12 123 | 12 23 123 |
as well as several *dependent* and thus invalid sets of three; in each case, the sum of the equations stemming from the first two listed loops will equal the equation for the third listed loop:
| 1 2 12 | 2 3 23 | 1 23 123 | 4 12 123 |
Loops *can* share branches and still be independent (for example, loop 1 and loop 2 share the 2 Ohm resistor, but their equations are independent). DukeEgr93 14:43, 15 January 2011 (EST)
