- Mesh Definition: A mesh is the smallest loop in a circuit without any smaller loops inside it.
- Mesh Analysis: Mesh analysis, based on Kirchhoff’s Voltage Law, helps find voltage, current, or power in planar circuits.
- Single Mesh Circuits: In single mesh circuits, Ohm’s law is used directly to find current or voltage.
- Multi Mesh Circuits: Multi mesh circuits have multiple meshes, making the analysis more complex.
- Steps for Mesh Analysis: Identify if the circuit is planar, count the meshes, label currents, write KVL equations, and solve for the currents.
Like the other network analysis procedures, we can use Mesh Analysis to find out the voltage, current or power through a particular element or elements. Mesh analysis is based on Kirchhoff Voltage Law. We can use Mesh analysis only on planar circuits. The planar circuit is the one which is possible to draw on a plane surface in such a way that no branch passes over or under any other branch. This circuit does not contain any branch which passes over or under any other branch.
Single Mesh
If in a closed circuit the number of mesh is only one, then that types of circuits are known as single meshed circuits.
In these types of analysis, the current or voltage across any element can be found out directly by using Ohm’s law. However, if the circuit elements are in parallel then also we can convert them into a single mesh by using the law of parallel combinations of the circuit elements.
Multi Mesh
A multi mesh circuit is defined as a circuit with more than one mesh. Analyzing multi mesh circuits is more complex than analyzing single mesh circuits due to the additional meshes.
If you would prefer a video explanation, we go over an example in the video below:
Steps for Mesh Analysis
The steps followed in mesh analysis are very simple, they are as follows-
- Frst we have to determine whether the circuit is planar or non planar. If it is a non planar circuit, we have to perform other methods of analysis such as nodal analysis.
- Then we have to count the number of meshes. The number of equations to be solved is same as the number of meshes.
- Then we label each of the mesh currents according to the convenience.
- We write KVL equation for each of the meshes. If the element lies between two meshes then we calculate the total current flowing through the element by considering two meshes. If the direction of two mesh currents is same then summation of currents is taken as the total current flowing through the element and if the direction is opposite then the difference of mesh currents is taken. In second case the current in the mesh under consideration is taken as the greatest among all the meshes currents and the procedure is followed.
For mesh ABH, the KVL is
For mesh BCF, the KVL is
For mesh CDEF, the KVL is
For mesh BFG, the KVL is
For mesh BGH, the KVL is
- Organize the equation according to the mesh currents.
- Solve the mesh equations for i1, i2, i3, i4, and i5.
- If any dependent source is there in the circuit or any unknown other than mesh currents, express that source in the suitable mesh currents.
Disadvantages of Mesh Analysis
- Mesh analysis is only useful for planar circuits.
- If the network is large, the number of meshes and corresponding equations increases, making the method inconvenient for complex circuits.
Conclusion of Mesh Analysis
Though, it has some disadvantages, this method is a very powerful tool which may be used in circuit analysis. It is a widely used method in case of a small network, containing small number of meshes. It is so because the method is simple, easy to understand and gives quick results if the network is small.
