I have started reading a book lately which covers an introduction to electric circuits. Currently, I'm trying to learn the basic network topology needed to solve exercises in a more efficient manner. To help me understand where I'm mistaken I'll describe you the circuit you see below in topology terms :


This circuit has 5 branches :

  • 3 resistors.
  • 1 Voltage Source.
  • 1 Current Source.


This circuit has 3 nodes :

  • Node a where R1 and V1 are connected.
  • Node b where R2, R3 and I1 are connected through cables.
  • Node c where the V1, R2, R3 and the I1 are connected through cables.


This circuit has 2 meshes :

  • abca.

  • mesh created between R3 and I1.

So if the above are correct then according to the basic network topology theorem:

$$b=l+n-1 <=> 5 = 2 + 3 - 1 <=> 5 = 4 $$

which obviously isn't correct. Where am I making a mistake ?


simulate this circuit – Schematic created using CircuitLab

  • \$\begingroup\$ How do you define an "independent loop"? We usually speak in terms of loops and meshes, where a mesh is a loop that does not enclose any other loops. \$\endgroup\$ – Elliot Alderson Mar 21 '19 at 13:35
  • \$\begingroup\$ Independent loop = mesh based on what you say I probably translated it poorly from Greek \$\endgroup\$ – NickDelta Mar 21 '19 at 13:38

There are three independent loops: one that includes V1, R1, and R2; one that includes R2 and R3; and one that contains R3 and I1. If you count R2 and R3 as separate branches then you need to count the mesh that they form.

  • \$\begingroup\$ My book says (translated from Greek) : The third loop could be the one that includes R2 and R3 but this is not an inpedendent system of loops. So what it tries to say is that this loop is independent too but it doesn't have any real usage in a mathematical system ? \$\endgroup\$ – NickDelta Mar 21 '19 at 13:48
  • \$\begingroup\$ If the R2-R3 loop is not "independent" then your definition of "independent" is not the same as our common definition of a "mesh". I don't know what you mean by a "mathematical system" but we must consider the R2-R3 mesh and write an equation for it in order to use the mesh-current method of circuit analysis. \$\endgroup\$ – Elliot Alderson Mar 21 '19 at 16:06

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