Mesh analysis employs the method of _____________

Question

Examoogle · Accepted Answer

KVL

Explanation: Mesh analysis is a circuit analysis technique that determines the currents in a planar circuit by applying Kirchhoff's Voltage Law (KVL) to each mesh (or loop) of the circuit. It results in a system of linear equations where the unknown variables are the mesh currents.

Working Principle: In mesh analysis, we assign an unknown circulating current to each independent mesh of the circuit. By applying KVL, the sum of voltage drops around each closed loop is set to zero, typically represented as $\sum V_{sources} = \sum I_{mesh} 	imes R_{resistors}$. This system is then solved using matrix methods such as Cramer's Rule or Gaussian elimination.

Key Formulas: $\sum_{k=1}^{n} V_k = 0$ — Kirchhoff's Voltage Law statement for a closed mesh; $[R][I] = [V]$ — Matrix representation of a system of meshes

Key Points: Mesh analysis is applicable only to planar circuits.; The number of mesh equations equals the number of windows (meshes) in the planar circuit.; If current sources exist between two meshes, a 'supermesh' is created to avoid involving the unknown voltage across the source.

Advantages: Reduces the number of equations required compared to node voltage analysis in circuits with many meshes but few nodes.; Systematic method using matrix algebra.

Disadvantages: Requires the circuit to be planar (can be drawn without crossing wires).; Becomes cumbersome if many current sources are present.

Applications: Used extensively in power systems and electronic circuit design.; Simplifying complex resistive networks into solvable matrix form.

Additional Info: KCL is the fundamental law for Nodal Analysis, which is the dual of Mesh Analysis.. Option B is incorrect because KCL is used in nodal analysis, not mesh analysis.

Answer: A is correct — Mesh analysis is based on the application of Kirchhoff's Voltage Law (KVL) around each independent loop in a circuit.

Exam Tip: Always identify the number of meshes first; if a current source is shared between two meshes, remember to use a supermesh to simplify your calculation.

Related Questions

Discussion (0)