Mesh and Nodal Analysis by Inspection

It can seem cumbersome and demanding to write correct nodal and mesh equations using the methods outlined in Sections above. Although it is crutial that students have a clear understanding of underlying concepts, nonetheless there are methods devised to write nodal and mesh equations by inspection using ad hoc relationships. This provides a useful way to quickly analyse a given circuit to determine a specific voltage or current.

Mesh Analysis

To demonstrate writing mesh equations by the inspection, consider Figure (c) which consists of the 3 meshes with currents denoted as I1, I2 and I3. The mesh equations have been derived earlier in

Equations below and reproduced below for convenience

 

In matrix form, above equations can be stated as
 
The order of resistance matrix (R) is same as number of loops in circuit. Additionally it has a general structure as outlined below which is independent of number of equations or meshes.
   

Nodal Analysis

The circuit diagram in Figure (c) can be used to demonstrate technique to write nodal equations by inspection. The equations for the circuit have been derived previously and reproduced below for reader's convenience.
 
 
Noting that

I/R= G, the above equations can be rewritten as follows
 

In matrix form


 

The conductance matrix G has same order as number of nodes excluding reference node. It has a general structure as outline below which is independent of number of nodes in the network.

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