# Problem with Network Topology based on circuits

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 :

BRANCHES

This circuit has 5 branches :

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

NODES

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.

MESHES

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

• 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. – Elliot Alderson Mar 21 '19 at 13:35
• Independent loop = mesh based on what you say I probably translated it poorly from Greek – NickDelta Mar 21 '19 at 13:38