2.3:
Mesh Analysis
Mesh analysis is a convenient method that employs mesh currents as circuit variables, effectively reducing the number of simultaneous equations involved in circuit analysis.
Unlike nodal analysis, mesh analysis applies only to planar circuits without crossing branches.
Determining the mesh currents in any planar circuit involves the following steps.
First, the total number of independent meshes in the circuit are identified, and mesh currents are assigned to each mesh.
Second, element voltages are expressed as functions of the mesh currents, and Kirchhoff's voltage law is applied to each mesh to obtain a set of linear equations.
Finally, the mesh currents are obtained by solving the set of equations.
For a circuit with "i" independent meshes, mesh analysis requires "i" independent equations to obtain the mesh currents.
Suppose the values of resistances and source voltages for the presented two-mesh circuit are known.
These values are substituted into the linear equations and solved to obtain the mesh currents.
Finally, the calculated values of the mesh currents can be used to determine the branch currents i1, i2, and i3.
2.3:
Mesh Analysis
Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed loop within a circuit that does not contain any other loops within it. Each mesh is assigned a mesh current, typically assumed to flow in a clockwise direction within its respective loop.
For mesh analysis to be applicable, the circuit must be planar, meaning it can be drawn on a flat surface without branches crossing one another. Planar circuits are ideal for mesh analysis, as it simplifies the process. The steps involved in mesh analysis are as follows:
- • Assign mesh currents to each of the "n" independent meshes in the circuit.
- • Apply KVL to each of the "n" meshes, expressing element voltages in terms of mesh currents using Ohm's law.
- • Solve the resulting "n" simultaneous equations to obtain the values of the mesh currents.
These mesh currents can then determine various branch currents within the circuit. It is important to note that mesh currents are distinct from branch currents unless a mesh is isolated.