What is Mesh Analysis?
The method that is used to calculate the current flowing through a planar circuit is known as mesh analysis. A planar circuit is a circuit in which there are no wires crossing each other, and it is drawn on a plane surface. Therefore, it is also known as loop analysis or mesh-current method. We will consider the currents flowing through each mesh in mesh analysis, and this is the reason why mesh analysis is also termed as the mesh-current method.
Since the basic method for analysing any complex electrical circuit is given by Kirchhoff’s laws, different methods were evolved to improve this method by using Nodal voltage analysis and mesh current analysis.
Procedure of Mesh Analysis
While solving an electrical network using mesh analysis, the following steps are to be followed:
Step 1: Label and recognise the meshes in a circuit and name the mesh currents in either clockwise or anti-clockwise directions.
Step 2: Observe the amount of current in terms of mesh current that flows through each element.
Step 3: Using Kirchhoff’s voltage law and then Ohm’s law, write the mesh equations to all meshes.
Step 4: By following step 3, in which the mesh equations are solved, the mesh currents are obtained.
What is a Branch?
The path that joins two nodes in such a way that it contains a circuit element is known as a branch. The branch current and the mesh current will be equal to each other if the branch belongs to only one mesh. The branch current will be equal to the sum or difference of two mesh currents if a branch is common to two meshes.
Important Questions on Mesh Analysis
1) The mesh analysis is applicable for non-planar networks also. Is it true or false?
a) True
b) False
Correct Option: (b)
Explanation: The mesh analysis is applicable only for planar networks. If a circuit without crossovers can be drawn on a plane surface, then it is said to be a planar network.
2) How many loops does a mesh contain?
a) 5
b) 3
c) 6
d) no loop
Correct Option: (d)
Explanation: A mesh is defined as a loop because a loop is a closed path; hence, it does not contain any other loops within it.
3) In a graph, if there are 4 nodes and 5 branches, then how many mesh equations can be formed?
a) 2
b) 6
c) 4
d) 10
Correct Option: (a)
Explanation: According to the formula, the number of mesh equations = B-(N-1). Total branches = 5 and nodes = 4. Hence, the number of mesh equations = 5-(4-1) = 5 – 3 = 2.
4) We can write a _____ number of independent equations when there are M branch currents.
a) 2M-2
b) M-2
c) M
d) M+2
Correct Option: (c)
Explanation: Number of independent equations = M. Therefore, we can write M number of independent equations if there are M branch currents.
5) What is the formula to find the number of mesh currents if there are M meshes, N nodes and B branches, including reference nodes?
a) 2B + (2N+1)
b) 4B + (3N-1)
c) 2B-(4N+1)
d) B-(N-1)
Correct Option: (d)
Explanation: Including reference nodes, if there are M meshes, N nodes and B branches, the number of mesh currents is given as M = B-(N-1).
6) Which among the following methods is best for voltage sources?
a) Differentiation method
b) Nodal analysis
c) Integration method principle
d) Superposition principle
Correct Option: (b)
Explanation: The node analysis method is best for voltage sources because every source of voltage connected to the reference node lessens the equations to be solved.
7) Name the method used when there is a current source between two loops.
a) Supernode
b) Node-current analysis
c) Super mesh
d) Mesh-voltage analysis
Correct Option: (c)
Explanation: When there is a current source n between two loops, then the super mesh is taken into consideration, and both the loops are considered as one single loop.
8) Which method is used in mesh analysis?
a) KVL
b) KLM
c) Both KVL and KCL
d) None of these
Correct Option: (a)
Explanation: To find the different mesh currents, KVL is used in mesh analysis and by this method, we can find the IR products in each mesh.
9) Mesh analysis is generally used to calculate _____.
a) Power
b) Current
c) Voltage
d) Energy
Correct Option: (b)
Explanation: Kirchhoff’s Voltage Law is used in mesh analysis to find all the mesh currents. Hence, a mesh analysis method is used to determine the current.
10) Mesh analysis can be used for _____.
a) Planar circuits
b) Both planar and non-planar circuits
c) non-planar circuits
d) None of these
Correct Option: (a)
Explanation: The meshes are not clearly defined if the circuit is not planar. It is easy to draw the meshes in planar circuits; hence the meshes are clearly defined for planar circuits.
Practice Questions
- What is a Wheatstone bridge?
- Explain the working of a Wheatstone bridge.
- What is a metre bridge?
- What do you mean by mesh analysis?
- What is the difference between a loop and mesh?
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