EGR 224/Spring 2011/Lectures

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)