Mesh-Current Method
In Nodal Analysis we are analyzing the circuit using node voltages as the circuit variables. We choose node voltages instead of element voltages as circuit variables. In Mesh Analysis we will use mesh currents as circuit variables. We must recall that a loop is a closed path with no need passed more than once. Now, a mesh loop is a loop that does not contain any other loop within it.
Mesh Analysis applies KVL to find unknown currents. Mesh Analysis is only applicable to a circuit that is planar. A planar circuit is one that can be drawn in a plane with no branches crossing one another, otherwise it is nonplanar. A circuit may be have crossing branches and still be planar if it can be redrawn such that it has no crossing branches.
mesh - is a loop which does not contain any other loops within it.
Mesh Analysis without Current Sources
Steps to Determine Mesh Currents:
1. Assign mesh currents i1, i2, i3, ..., i n to the n meshes.
2. Apply KVL to each of the n meshes. USe Ohm's Law to express the voltages in terms of the mesh currents.
3. Solve the resulting n simultaneous equations to get the mesh currents.
note: the direction of the mesh current is arbitrary -(clockwise or counter-clockwise) and does not affect the validity of the solution.