Mesh analysis can be used for __________

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Planar circuits

Explanation: Mesh analysis relies on the application of Kirchhoff's Voltage Law (KVL) to independent closed loops known as meshes. This technique is exclusively applicable to planar circuits, which are circuits that can be drawn on a two-dimensional surface without any branches crossing each other.

Working Principle: In a planar circuit, every mesh is defined by a window (a loop containing no other loops). By assigning a mesh current to each window and applying KVL (sum of voltages around the loop equals zero), one obtains a set of linear equations. Non-planar circuits, defined by bridges that cannot be drawn without crossing lines, lack these defined meshes, rendering standard mesh analysis inapplicable without topological modifications.

Key Formulas: $\sum_{k=1}^{n} V_k = 0$ — Kirchhoff's Voltage Law (KVL) applied to a mesh; $I_{mesh} = \frac{\Sigma V}{R_{total}}$ — Relationship for current in a single mesh

Key Points: A planar circuit can be drawn on a plane without branch crossings.; Mesh analysis results in a system of linear equations represented by $[R][I] = [V]$.; If a circuit is non-planar (like a bridge with a crossing), Nodal Analysis must be used instead.; The number of independent mesh equations equals $b - n + 1$, where $b$ is branches and $n$ is nodes.

Advantages: Reduces the number of equations compared to Nodal Analysis when there are many loops.; Highly efficient for circuits with independent voltage sources.

Disadvantages: Cannot be directly applied to non-planar circuits.; Requires careful identification of meshes in complex diagrams.

Applications: DC resistive network analysis.; Steady-state AC network analysis using phasors.

Additional Info: Planar circuits are those representable on a plane without crossings, analogous to Kuratowski's theorem in graph theory.. Option B is incorrect because non-planar circuits (graphs with $K_5$ or $K_{3,3}$ minors) do not allow for the standard definition of mesh currents required by KVL.

Answer: A is correct — Mesh analysis is fundamentally based on identifying non-overlapping loops in a 2D planar diagram, a condition not met by non-planar circuits.

Exam Tip: If a circuit has crossing wires that cannot be rearranged, always default to Nodal Analysis as it is universal for all lumped-parameter circuits.

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