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Mesh Analysis Procedure
Step-1: Assign reference current directions and reference polarities for voltages of 
all elements as per passive sign convention. If there are current sources that appear 
directly across resistors convert them into equivalent voltage sources in series with 
resistors. This is called ‘mesh reduction’. The resulting circuit is referred to as the 
reduced circuit.

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4.44
Nodal Analysis and Mesh Analysis of Memoryless Circuits
Step-2: Assign mesh current variables in the reduced circuit starting with leftmost 
mesh. Assign mesh current variables to a mesh only if its mesh current is not constrained 
directly by a current source (independent or dependent) and its mesh current is not 
decided by other mesh current variables already assigned along with current source 
functions.
Step-3: Prepare the mesh equations by applying KVL in meshes, starting at left bottom 
corner and traversing the mesh in clockwise direction. Ignore the meshes that are 
directly constrained by current sources (independent or dependent). Further, if two 
meshes share a current source, then, add the mesh equations for those two meshes to 
generate a new equation that will be used in solution process. The number of equations 
at the end of this step will be equal to number of meshes minus number of irreducible 
independent
current sources.
Step-4: Identify the controlling variable of dependent sources in terms of mesh current 
variables and express dependent source functions in terms of mesh current variables.
Step-5: Solve the mesh equations by elimination technique. The equations may also 
be expressed as a matrix equation and solved by using Cramer’s rule or matrix 
inversion.
Step-6: Use the mesh current values and apply KCL at various nodes in the original 
circuit to obtain element currents and voltages for all resistive elements (use Ohm’s 
law) and current through voltage sources.
Step-7: Use the element voltages calculated in the above step and apply KVL in various 
meshes in the original circuit to obtain element voltages for all current sources.
• An n-node circuit containing only linear resistors and independent current sources will have 
a Nodal representation given by