What is mesh current analysis?

The key concept in mesh current analysis is to assign loop currents to each individual loop (mesh) within the circuit. These loop currents are imaginary currents that circulate around each loop in a consistent direction. By doing this, we can create equations based on KVL for each mesh and then solve for the unknown mesh currents. Once we find the mesh currents, we can use them to determine other quantities such as branch currents, voltages, and power dissipation in the circuit.

The general steps for mesh current analysis are as follows:

Identify the number of independent meshes in the circuit: Independent meshes are loops that are not shared with other loops.

Assign a unique mesh current variable (e.g., I1, I2, etc.) to each independent mesh. Typically, the direction of the mesh current is chosen arbitrarily.

Apply KVL to each mesh, using the assigned mesh currents. This involves summing up the voltage drops across the resistors and voltage sources within each loop and setting it equal to zero. For a resistor with resistance R and a mesh current I, the voltage drop across it is R * I.

Solve the resulting system of equations simultaneously to find the values of the mesh currents.

Use the mesh currents to calculate other circuit quantities of interest, such as branch currents, voltage drops, and power dissipation.

Mesh current analysis is a powerful method for solving complex circuits with many loops, as it reduces the number of equations needed to solve the circuit compared to other techniques like nodal analysis. It is widely used in electrical engineering and circuit design to analyze and understand the behavior of various circuits.