Mesh (Loop Current) Method: tightening-up my recipe

[Farina]

I'm an intro calc-based physics instructor, and recently uncovered some vagueness, or maybe errors (?), with my recipe. Can you please comment on the following?

Question 1: Loop Currents - MY RECIPE:
"Determine # of loop currents by connecting each circuit junction once, and only once, to a single path. The number of loop currents you need to draw equals the number of branches that are not part of this single path."

I'm guessing the above is valid, since I don't think it's ever failed me. However, I've heard an even simpler method is to simply draw the minimum number of current loops to include each and every branch. It this valid? Seems like it's failed me on some occasions, not sure though...

Question 2: "branch" - MY RECIPE:
"A branch is any path in the circuit that has a node at each end and contains at least one voltage source or resistor, but contains no other nodes.
I'm asking about this since the Loop Current recipe I use seems to successfully accommodate "device-less" branches, i.e., a straight wire segment between 2 nodes with no included resistors or voltage sources. This makes me nervous since I'm in the habit of saying only "branches" can be removed as part of my initial recipe directions (Question 1: Loop Currents above).

Thank you for any light you can shed.

 

[MrSparkle]

"Determine # of loop currents by connecting each circuit junction once, and only once, to a single path.

I'm not sure I understand this. What are you connecting? The number of meshes is very simple. Quoting 'Fundamentals of Electric Circuits', a mesh is a loop that does not contain any other loops. All you have to do is count the empty spaces.

"A branch is any path in the circuit that has a node at each end and contains at least one voltage source or resistor, but contains no other nodes.

again quoting Fundamentals, a branch is a single element. It can be more things than just voltage sources or resistors. It is any 2-terminal element. A straight wire segment is not an element or branch, it is part of an extended node.