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Mesh analysis is defined as the method of calculating the current flowing through a planar electric circuit.
- A planar circuit is described as a circuit drawn on a plane surface with no wires crossing one another.
- In mesh analysis, Kirchhoff's voltage law is used to determine the currents in each loop.
- In nodal analysis, Kirchhoff's current law is used to find the voltages at each node in an equation.
- According to Kirchhoff’s voltage law, also known as the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.
- It is also known as Kirchhoff’s second law.
Very Short Answers Questions [1 Mark Questions]
Ques. Mesh analysis is generally used to determine
- Current
- Resistance
- Voltage
- Power
Ans. The correct answer is a. Current
Explanation: Mesh analysis uses Kirchhoff's Voltage Law to determine all mesh currents. Therefore, it is a method for determining current.
Ques. Mesh analysis employs the method of
- KCL
- KVL
- Neither KVL nor KCL
- Both KVL and KCL
Ans. The correct answer is b. KVL
Explanation: Kirchhoff's voltage law (KVL) uses mesh analysis to determine the various mesh currents by determining the IR products in each mesh.
Ques. Mesh analysis can be used for
- Non-planar circuits
- Planar circuits
- Neither planar nor non-planar circuits
- Both planar and non-planar circuits
Ans. The correct answer is b. Planar circuits
Explanation: The meshes are not well defined if the circuit is not planar. Meshes are easily specified in planar circuits because they are easy to draw.
Ques. A mesh is a loop that contains ____ number of loops within it.
- 1
- 2
- 3
- 0
Ans. The correct answer is d. 0
Explanation: A loop is a closed path in a circuit, while a mesh is a loop that contains no other loops.
Ques. Mesh analysis is applicable to non-planar networks also.
- True
- False
Ans. The correct answer is b. False
Explanation: Mesh analysis is only useful for planar networks. If a circuit can be drawn on a plane surface without intersections, it is said to be planar.
Ques. What is the formula to find the number of mesh currents if there are M meshes, N nodes, and B branches, including reference nodes?
- 4B + (3N - 1)
- 2B + (2N + 1)
- B - (N - 1)
- 2B - (4N + 1)
Ans. The correct answer is c. B - (N - 1)
Explanation: The number of mesh equations in a graph is given by
Number of mesh equations = B - (N - 1)
Where
- B is the number of branches in the graph
- N is the number of nodes in the graph
Ques. If there are 5 branches and 4 nodes in a graph, then the number of mesh equations that can be formed are?
- 8
- 6
- 4
- 2
Ans. The correct answer is d. 2
Explanation: Number of mesh equations = B-(N-1)
Given that there are 5 branches and 4 nodes.
Hence, the number of mesh equations is 5-(4-1) = 2.
Ques. Name the method used when there is a current source between two loops.
- Super mesh
- Supernode
- Mesh-voltage analysis
- Node-current analysis
Ans. The correct answer is a. Super mesh
Explanation: When there is a current source n between two loops, the super mesh is considered, and both loops are treated as a single loop.
Ques. Which among the following methods is best for voltage sources?
- Integration method principle
- Nodal analysis
- Differentiation method
- Superposition principle
Ans. The correct answer is b. Nodal analysis
Explanation: The node analysis approach is useful for voltage sources since each voltage source connected to the reference node reduces the number of equations to be solved.
Ques. We can write a _____ number of independent equations when there are M branch currents.
- M
- M - 2
- 2M - 2
- M + 2
Ans. The correct answer is a. M
Explanation: M is the number of independent equations. Hence, if there are M branch currents, we can construct M numbers of independent equations.
Short Answers Questions [2 Marks Questions]
Ques. What is Mesh Analysis?
Ans. Mesh analysis is a method for solving planar circuits for currents at any point in an electrical circuit. Mesh analysis can also be known as loop analysis or mesh-current method.
Ques. What are planar circuits?
Ans. A planar circuit is one that can be drawn on a flat surface without any wires intersecting. This two-dimensional representation makes the layout and connections of the circuit easier to visualize and understand.
Ques. What is a Branch?
Ans. A branch is defined as a path that links two nodes and includes a circuit element. If the branch corresponds to only one mesh, then the branch current and mesh current are equal.
Ques. What is Super Mesh Analysis?
Ans. Super mesh analysis is used to solve large and complicated circuits in which two meshes share a similar current source.
Ques. What is a dependent source?
Ans. In an electrical network, a dependent source is either a voltage source or a current source whose value is determined by the voltage or current in the network. The dependent sources are classified as a voltage-controlled voltage source, voltage-controlled current source, current-controlled current source, and current-controlled voltage source.
Ques. What is Kirchhoff’s current law?
Ans. Kirchhoff's Current Law (KCL) says that the algebraic sum of all currents entering and exiting a node must equal zero. This law describes how a charge enters and exits a wire junction point.
Ques. What is Kirchhoff’s voltage law?
Ans. Kirchhoff's Voltage Law states that for every closed network, the voltage across a loop is the sum of all voltage drops in the same loop and equals zero.
Ques. What is a Wheatstone bridge?
Ans. A Wheatstone bridge is a type of electrical circuit that is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one of which contains the unknown component.
Ques. What is a meter bridge?
Ans. A meter bridge is a device used to measure the unknown resistance of a coil or any other conductor-like material. A meter bridge works in the same method as a Wheatstone bridge, which is used to measure the unknown resistance in a circuit.
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Long Answers Questions [3 Marks Questions]
Ques. What is the difference between a loop and a mesh?
Ans. The differences between a loop and a mesh are
| Loop | Mesh |
|---|---|
| A loop is any closed path across a circuit where no node meets more than once. | A mesh is a closed path within a circuit that contains no other pathways. |
| The loop is found during a loop with unique nodes that are not duplicated on more than one occasion. | A mesh is a loop that has no additional circuit paths. |
| A loop is a closed path in a circuit in which two nodes are not crossed twice except the initial point, which is also the last one. However, alternative pathways are frequently included within a loop. | Mesh is a closed path that cannot be broken down further into another closed path, whereas a loop can be a closed path that can or cannot be divided further into another closed path. A mesh can be a loop, but it is not required for a loop to be a mesh; it will only be a mesh if further division is not conceivable. |
Ques. What are the limitations of using mesh analysis?
Ans. The limitations of using mesh analysis are
- Mesh analysis is only applicable when the circuit is planar.
- As the number of meshes increases, so does the number of equations, making it difficult to solve.
- Mesh analysis is generally used to analyze circuits that contain linear elements like resistors, capacitors, and inductors. Applying mesh analysis to circuits containing non-linear elements, such as diodes and transistors, could be more difficult.
- It is not efficient for circuits with more nodes than meshes.
Ques. What are the applications of nodal analysis?
Ans. The following are the applications of nodal analysis
- The main purpose of nodal analysis is to find the voltages at each node in a circuit. This analysis is essential to understanding the overall voltage distribution as well as the behavior of circuit components.
- Nodal analysis is best for analyzing circuits containing voltage sources due to its direct focus on voltages. It efficiently handles circuits with multiple voltage sources, enabling the determination of voltage values at each node.
- By evaluating the voltage distribution, nodal analysis can be used to identify and troubleshoot circuit problems.
Very Long Answers Questions [5 Marks Questions]
Ques. What are the advantages of using mesh analysis?
Ans. The following are the advantages of using mesh analysis
- Mesh analysis is a method for solving complicated circuits that include a high number of branches and nodes in a systematic and organized manner. It divides the circuit into easy loops, making it simpler to study and understand.
- Mesh analysis is ideal for analyzing large and complicated circuits that have multiple loops.
- In general, mesh analysis requires fewer equations to solve than other approaches such as nodal analysis. This is because mesh analysis focuses on currents, which are often smaller than voltages.
- Mesh analysis is directly associated with Kirchhoff's loop equations, which regulate voltage drops in circuits. This makes the loop equations easier to understand and use.
- Mesh analysis is an effective method for circuit design since it allows for an analysis of different circuit designs as well as the measurement of current and voltage distributions.
Ques. What is the difference between mesh and nodal analysis?
Ans. The following are the differences between mesh and nodal analysis
| Mesh Analysis | Nodal Analysis |
|---|---|
| Mesh analysis focuses on the current. | The nodal analysis focuses on voltage. |
| Kirchhoff’s voltage law is used to solve the circuit. | Kirchhoff’s current law is used to solve the circuit. |
| It is suitable for large and complex circuits with multiple loops. | It is suitable for circuits with more nodes than meshes |
| It has a direct relation to resistors, capacitors, and inductors | It has a direct relation to voltage and current sources |
| It is more complex for simple circuits, less complex for complex circuits | It is less complex for simple circuits, and more complex for complex circuits. |
Ques. What are the procedures for solving a circuit using mesh analysis?
Ans. When using mesh analysis to solve the given electrical network, the following procedures must be used:
- Step 1: To identify the meshes and mark the mesh currents clockwise or counterclockwise.
- Step 2: In terms of mesh current, measure the amount of current that travels through each element.
- Step 3: Using Kirchhoff's voltage law and subsequently, Ohm's law, write the mesh equations for all meshes.
- Step 4: The mesh currents are obtained by repeating Step 3 and solving the mesh equations.
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