Mesh Current Analysis

Mesh Current Analysis is one of several basic methods for the analysis of electrical circuits. This method relies heavily upon the superposition of mesh currents in order to determine all unknown currents and voltages in the circuit.

The method is:

1. Identify each mesh.
2. For each mesh having a current supply not shared with any other mesh (i.e. on an "outside branch"), the current of that mesh is equal to the current emitted by the power supply, and in the direction indicated by the power supply.
3. For every other mesh, asign a variable to represent the current in the mesh, say I₁, I₂, I₃, etc. Also indicate the direction that each current is defined to flow--the direction chosen is arbitrary, but choosing a single direction for all currents is recommended.
4. Write Kirchhoff's Voltage Law (KVL) around each mesh.
5. Use the characteristics of each device in a mesh to write an equation for the voltage drop across that device in terms of the mesh current variables.

   For example, if the device is a resistor having resistance R, and there are two mesh currents traveling through it, say I₁ and I₂, in opposite directions, the voltage drop V will be:

   V = (I₁ - I₂) * R

6. Substitute these calculated voltages into the KVL equations.
7. Simultaneously solve the resulting equations. You will then have the values for all of the mesh currents in the circuit.
8. Substitute the currents you just found back into the voltage equations you derived earlier. This is done to calculate the voltage drop across each of the devices in the circuit. You should now be able to determine all of the voltages in the circuit.

This is also known as Mesh Analysis or perhaps just plain "Mesh Current".

Contrast: Node Voltage Analysis.