In class I asked my professor whether mesh current loops could enclose resistors in a linear circuit (That is, extend over multiple mesh current loops). He said that this is allowable and the mesh current equations can be solved be appropriately picking the loops. However, a few different textbooks require that the current loops do not enclose any resistive elements. Is my professor corrrect? If not, can anyone offer an example where extending current loops over resistors does not work?

 

I guess one has to firstly satisfy the general requirement that for a circuit with b branches and n nodes one requires m= b-n+1 independent mesh equations to solve the for the necessary circuit conditions. Provided the m selected mesh current paths are independent one can conceivably have a number of options for the particular independent paths.

I'm unsure of the meaning of enclosed resistor branches and their relevance to the matter.

One can easily test this by drawing a circuit and solving it with a few different loop configurations and possibly with loops which "enclose a resistor branch".

 

Should you perhaps be considering the limitations of the mesh method with respect to non-planar networks?

http://www.bing.com/search?q="mesh+analysis"+"planar+network"&go=&qs=n&sk=&first=11&FORM=PERE

 

I'm unsure of the meaning of enclosed resistor branches and their relevance to the matter.

For example,
http://www.allaboutcircuits.com/vol_1/chpt_7/1.html

In the example with parallel resistors, one possible current loop could be drawn in 1-3-6-8. In this case, resistor R1 is enclosed within the loop. My question is whether using this current loop is permissible in mesh current analysis and if not, why.

 

A simple parallel circuit like that wouldn't necessitate a mesh analysis approach - but yes you could select that loop as one independent case.

That circuit really only has two nodes and two branches. Any branch current can be 'solved' with a single independent equation.

Take the circuit in my attachment as a more realistic example. I have shown just two loop selection options - there are others.

 

A simple parallel circuit like that wouldn't necessitate a mesh analysis approach - but yes you could select that loop as one independent case.

That circuit really only has two nodes and two branches. Any branch current can be 'solved' with a single independent equation.

Take the circuit in my attachment as a more realistic example. I have shown just two loop selection options - there are others.

Oops! I should be more careful - that should be four 4 branches and two nodes.

 

For example,
http://www.allaboutcircuits.com/vol_1/chpt_7/1.html

In the example with parallel resistors, one possible current loop could be drawn in 1-3-6-8. In this case, resistor R1 is enclosed within the loop. My question is whether using this current loop is permissible in mesh current analysis and if not, why.

Well, if you do that "resistor-enclosing thing", it's more like you used KVL method rather than a mesh analysis.

If your professor told you that it is permissible, then you may just use it, since mesh analysis actually use KVL method anyway...

The difference is just that mesh analysis requires you to find currents in each loop first before looking for currents in each resistive elements, whereas KVL method allows you to find currents in each resistive elements without a need to find current in each loops.