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What is Mesh analysis?

A method that assigns a fictitious mesh current to each mesh (a loop containing no other branch inside it) of a circuit drawn on a plane, applies Kirchhoff's voltage law to each mesh and solves the resulting simultaneous equations. An element shared by two meshes carries the difference of the two mesh currents. It needs few equations for circuits with many voltage sources or series elements.

Japanese name: 網目解析

Mesh analysis appears in 1 practice question across 1 topic, including Circuit Analysis: AC, Linear Circuits and Transients.

DC circuit with two meshes + E1 R1 R2 + E2 R3 I1 I2
DC circuit with two meshes · View in diagrams

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Mesh analysis

In the circuit in the figure, E1 = 14 V, E2 = 7 V, R1 = 2 Ω, R2 = 1 Ω and R3 = 4 Ω. When the circuit is solved by mesh analysis with the mesh currents I1 and I2 in the directions shown in the figure, which of the following is the magnitude of the current in R3?

  1. A1 A
  2. B2 A
  3. C3 A
Show answer and explanation

Answer: B. 2 A

For the left mesh, E1 = (R1 + R3)I1 − R3 I2 gives 6I1 − 4I2 = 14; for the right mesh, E2 opposes I2, so −E2 = (R2 + R3)I2 − R3 I1 gives −4I1 + 5I2 = −7. Solving these simultaneous equations gives I1 = 3 A and I2 = 1 A. The two mesh currents flow through R3 in opposite directions, so its current is I1 − I2 = 2 A (downward). The voltage of the node above R3, 4 × 2 = 8 V, also confirms the current in R1, (14 − 8)/2 = 3 A, and in R2, (8 − 7)/1 = 1 A.

Mesh analysis in the explanations

Questions that mention Mesh analysis (1)

  1. In the circuit in the figure, E1 = 14 V, E2 = 7 V, R1 = 2 Ω, R2 = 1 Ω and R3 = 4 Ω. When the circuit is solved by mesh analysis with the mesh currents I1 and I2 in the directions shown in the figure, which of the following is the magnitude of the current in R3?

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