Mesh Analysis Solver (Python)

A general-purpose mesh analysis solver for planar electrical circuits. It computes mesh currents by automatically constructing and solving Kirchhoff's Voltage Law (KVL) equations using symbolic algebra.

Originally developed during B.Tech 1st Year as a foundational circuits project, then refactored and improved in 3rd Year with clean architecture, proper naming conventions, docstrings, and modular function design.

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Table of Contents

1. Features
2. How Mesh Analysis Works
3. Algorithm Overview
4. Requirements
5. Installation
6. How to Run
7. Input Instructions
8. Examples
   • Example 1 -- Single Mesh
   • Example 2 -- Two Meshes with Shared Resistor
   • Example 3 -- Three Meshes
   • Example 4 -- Two Meshes with Multiple Voltage Sources
   • Example 5 -- Two Meshes with a Current Source
9. Project Structure
10. Future Improvements
11. Author
12. License

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Features

Capability	Description
Unlimited meshes	Supports any number of meshes (practical limit: 9 for common-resistor labelling)
Shared resistors	Handles common resistors between any pair of meshes
Voltage sources	Supports multiple voltage sources per mesh with sign convention
Current sources	Supports current source constraints on individual meshes
Automatic KVL equations	Equation terms are generated programmatically from user input
Symbolic solving	Uses SymPy's symbolic engine -- exact rational/algebraic solutions
Direction detection	Reports whether each mesh current flows Clockwise (CW) or Anti-Clockwise (A.CW)
Common resistor currents	Calculates and displays current through every shared branch with flow direction

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How Mesh Analysis Works

Mesh analysis is a systematic method for solving planar circuits. It is based on two principles:

1. Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltages around any closed loop (mesh) is zero.
2. Mesh currents: A fictitious current variable is assigned to each mesh, assumed to flow in the clockwise direction by convention.

Procedure

1. Assign a mesh current ($i_1, i_2, \ldots, i_n$) to each independent loop.
2. For each mesh, write a KVL equation:
   • Resistors exclusive to the mesh contribute $R \cdot i_k$.
   • Shared (common) resistors contribute a coupling term $R_c \cdot (i_k - i_j)$ between adjacent meshes $k$ and $j$.
   • Voltage sources add or subtract their value depending on polarity relative to the assumed current direction.
3. If a mesh contains a current source, the mesh current on that loop is directly constrained by the source value instead of a KVL equation.
4. Solve the resulting system of $n$ linear equations for $n$ unknowns.

A negative solution for a mesh current indicates the actual current flows anti-clockwise (opposite to the assumed direction).

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Algorithm Overview

START
  |
  v
[1] Read number of meshes (n) and number of current sources
  |
  v
[2] For each mesh:
      - Collect resistor values --> store in mesh_elements
      - If current source exists, record constraint
  |
  v
[3] For each mesh:
      - Collect voltage source values --> store in mesh_elements
  |
  v
[4] If n > 1:
      - Collect common (shared) resistor values between mesh pairs
      - Store negative coupling coefficients in mesh_elements
  |
  v
[5] Build KVL equation terms for each mesh:
      - Self-resistance terms:    R * i_k
      - Voltage terms:            V  (constant)
      - Coupling terms:          -R_common * i_adjacent
  |
  v
[6] Convert string terms to SymPy symbolic expressions
  |
  v
[7] Construct equation system:
      - Standard mesh:   sum_of_terms = 0   (KVL)
      - Current source:  i_k = I_source     (constraint)
  |
  v
[8] Solve using sympy.solve()
  |
  v
[9] Compute current through each common resistor:
      I_branch = i_k - i_j
  |
  v
[10] Remove duplicate branch pairs (R12 == R21)
  |
  v
[11] Display results with direction indicators
  |
END

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Requirements

Dependency	Version	Purpose
Python	3.8+	Runtime
SymPy	>= 1.12	Symbolic equation construction and linear system solving

Optional

Package	Purpose
colorama	Enables ANSI color support on older Windows terminals (CMD on Windows 8/7). Not needed on Windows 10+, Windows Terminal, PowerShell 7, or Linux/macOS.

The solver uses raw ANSI escape codes for colored terminal output. These work natively on all modern terminals. Install colorama only if you see garbled output on a legacy Windows console.

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Installation

1. Clone the repository

git clone https://github.com/<your-username>/mesh_analysis.git
cd mesh_analysis

2. (Recommended) Create a virtual environment

python -m venv venv

Activate it:

OS	Command
Windows (PowerShell)	.\venv\Scripts\Activate.ps1
Windows (CMD)	.\venv\Scripts\activate.bat
Linux / macOS	source venv/bin/activate

3. Install dependencies

Using the requirements file:

pip install -r requirements.txt

Or install manually:

pip install sympy

To verify installation:

python -c "import sympy; print(sympy.__version__)"

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How to Run

python Mesh_solver.py

The program launches an interactive terminal session. Follow the on-screen prompts to enter your circuit data. Results are displayed immediately after solving.

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Input Instructions

Parameter	Format	Notes
Number of meshes	Integer (e.g., 2)	Total independent loops in the circuit
Current sources	Integer count, then value per mesh	Enter 0 if mesh has no current source. Positive = CW, Negative = A.CW
Resistor values	Comma-separated (e.g., 2,5,10)	Enter all resistors in the mesh, including any shared resistor
Voltage sources	Comma-separated with sign (e.g., -5,10)	Positive = voltage rise in CW direction, Negative = voltage drop
Common resistors	One value per mesh pair	The shared resistance between Mesh i and Mesh j

Sign Convention

All values follow the clockwise (CW) positive convention:

• A voltage source whose positive terminal is encountered first when traversing the mesh clockwise is positive.
• A voltage source whose negative terminal is encountered first is negative.
• A current source flowing in the CW direction of the mesh is positive; A.CW is negative.

Important Notes

• Common resistors must also be included in each mesh's individual resistor list.
• Enter 0 for current source value if the mesh does not contain one.
• Units: Resistance in Ohms, Voltage in Volts, Current in Amperes.

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Examples

Example 1 -- Single Mesh (1 Mesh)

Circuit: A single loop with a 10V voltage source and two resistors (2 Ohm, 3 Ohm) in series.

        +---[ 2 Ohm ]---[ 3 Ohm ]---+
        |                            |
      (+)                            |
       10V                           |
      (-)                            |
        |                            |
        +----------------------------+
                  Mesh 1 (i1 -->)

Input:

Enter no of Meshes : 1
Enter the total no of Current sources in the circuit (if no current source enter 0(zero)) : 0
Mesh 1
Enter the values of all resistors(Ex: 2,5,10) : 2,3
Mesh1-R1 = 2 Ohm
Mesh1-R2 = 3 Ohm

Mesh 1
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 10
Mesh1-V1 = 10 V

Output:

 Mesh Currents :
Mesh 1  -->  i1 = 2.0 A in (CW)

Verification: $i_1 = \frac{10}{2 + 3} = 2.0\ \text{A}$

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Example 2 -- Two Meshes with Shared Resistor

Circuit: Two meshes sharing a 3 Ohm resistor. Mesh 1 has a 10V source and resistors 2 Ohm, 3 Ohm. Mesh 2 has a 5V source and resistors 3 Ohm, 4 Ohm.

        +--[ 2 Ohm ]--+--[ 4 Ohm ]--+
        |              |              |
      (+)          [ 3 Ohm ]        (+)
       10V         (shared)          5V
      (-)              |            (-)
        |              |              |
        +--------------+--------------+
          Mesh 1 (i1)    Mesh 2 (i2)

Input:

Enter no of Meshes : 2
Enter the total no of Current sources in the circuit (if no current source enter 0(zero)) : 0
Mesh 1
Enter the values of all resistors(Ex: 2,5,10) : 2,3
Mesh 2
Enter the values of all resistors(Ex: 2,5,10) : 3,4
Mesh 1
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 10
Mesh 2
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 5
Enter the no.of Common resistors B/W Meshes : 1

Enter Common resistance values B/W meshes :
Mesh 1 and Mesh 2 = 3

Output:

 Mesh Currents :
Mesh 1  -->  i1 = 2.83 A in (CW)
Mesh 2  -->  i2 = 1.93 A in (CW)

Current through common resistors :
I-R12(3 Ohm) = 0.9 A (in the direction of i1)

Verification (KVL):

Mesh 1: $5 i_1 - 3 i_2 = 10$

Mesh 2: $-3 i_1 + 7 i_2 = 5$

Solving: $i_1 \approx 2.83\ \text{A},\quad i_2 \approx 1.93\ \text{A}$

Current through shared resistor: $i_1 - i_2 = 0.90\ \text{A}$ (direction of $i_1$).

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Example 3 -- Three Meshes with Two Shared Resistors

Circuit: Three meshes. Mesh 1 and Mesh 2 share a 4 Ohm resistor. Mesh 2 and Mesh 3 share a 6 Ohm resistor. Each mesh has its own voltage source.

    +--[3 Ohm]--+--[5 Ohm]--+--[2 Ohm]--+
    |            |            |            |
  (+)        [4 Ohm]      [6 Ohm]       (+)
   20V       shared       shared         10V
  (-)            |            |          (-)
    |            |            |            |
    +------------+--[8 Ohm]--+------------+
      Mesh 1        Mesh 2       Mesh 3

Input:

Enter no of Meshes : 3
Enter the total no of Current sources in the circuit (if no current source enter 0(zero)) : 0
Mesh 1
Enter the values of all resistors(Ex: 2,5,10) : 3,4
Mesh 2
Enter the values of all resistors(Ex: 2,5,10) : 4,5,6,8
Mesh 3
Enter the values of all resistors(Ex: 2,5,10) : 6,2
Mesh 1
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 20
Mesh 2
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : -15
Mesh 3
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 10
Enter the no.of Common resistors B/W Meshes : 2

Enter Common resistance values B/W meshes :
Mesh 1 and Mesh 2 = 4
Mesh 1 and Mesh 3 = 0
Mesh 2 and Mesh 3 = 6

Output:

 Mesh Currents :
Mesh 1  -->  i1 = 2.82 A in (CW)
Mesh 2  -->  i2 = 0.07 A in (A.CW)
Mesh 3  -->  i3 = 1.30 A in (CW)

Current through common resistors :
I-R12(4 Ohm) = 2.89 A (in the direction of i1)
I-R23(6 Ohm) = 1.37 A (in the direction of i3)

Note: Enter 0 for the common resistance between Mesh 1 and Mesh 3 since they do not share a resistor.

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Example 4 -- Two Meshes with Multiple Voltage Sources

Circuit: Two meshes with multiple voltage sources per mesh. Mesh 1 has two voltage sources (20V and -5V). Mesh 2 has one voltage source (10V). The meshes share a 5 Ohm resistor.

    +--[3 Ohm]---(+20V-)---+---(-5V+)--[7 Ohm]--+
    |                       |                      |
    |                   [5 Ohm]                  (+)
    |                   shared                    10V
    |                       |                    (-)
    |                       |                      |
    +---[2 Ohm]------------+----------------------+
         Mesh 1                   Mesh 2

Input:

Enter no of Meshes : 2
Enter the total no of Current sources in the circuit (if no current source enter 0(zero)) : 0
Mesh 1
Enter the values of all resistors(Ex: 2,5,10) : 3,5,2
Mesh 2
Enter the values of all resistors(Ex: 2,5,10) : 5,7
Mesh 1
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 20,-5
Mesh 2
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 10
Enter the no.of Common resistors B/W Meshes : 1

Enter Common resistance values B/W meshes :
Mesh 1 and Mesh 2 = 5

Output:

 Mesh Currents :
Mesh 1  -->  i1 = 1.97 A in (CW)
Mesh 2  -->  i2 = 1.65 A in (CW)

Current through common resistors :
I-R12(5 Ohm) = 0.32 A (in the direction of i1)

Verification (KVL):

Mesh 1: $10 i_1 - 5 i_2 = 15$ (net voltage: $20 + (-5) = 15$)

Mesh 2: $-5 i_1 + 12 i_2 = 10$

Solving: $i_1 \approx 1.97\ \text{A},\quad i_2 \approx 1.65\ \text{A}$

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Example 5 -- Two Meshes with a Current Source

Circuit: Two meshes sharing a 4 Ohm resistor. Mesh 1 has a 20V voltage source and resistors 2 Ohm, 4 Ohm. Mesh 2 contains a 5A current source (flowing clockwise) and a 6 Ohm resistor along with the shared 4 Ohm resistor.

When a mesh contains a current source, the mesh current for that loop is directly constrained by the source value. No KVL equation is written for that mesh; instead $i_2 = -I_s$ is used.

    +---[ 2 Ohm ]---+---[ 6 Ohm ]---+
    |                |                |
  (+)            [ 4 Ohm ]        (5A source)
   20V           (shared)           CW
  (-)                |                |
    |                |                |
    +----------------+----------------+
       Mesh 1 (i1)     Mesh 2 (i2)

Input:

Enter no of Meshes : 2
Enter the total no of Current sources in the circuit (if no current source enter 0(zero)) : 1
Mesh 1
Enter the value of current source in Mesh 1 (in C.W) : 0
Enter the values of all resistors(Ex: 2,5,10) : 2,4
Mesh 2
Enter the value of current source in Mesh 2 (in C.W) : 5
Enter the values of all resistors(Ex: 2,5,10) : 4,6
Mesh 1
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 20
Mesh 2
Enter the values of all voltage sources(in C.W)[Ex: -5,10,20] : 0
Enter the no.of Common resistors B/W Meshes : 1

Enter Common resistance values B/W meshes :
Mesh 1 and Mesh 2 = 4

Output:

 Mesh Currents :
Mesh 1  -->  i1 = 6.67 A in (CW)
Mesh 2  -->  i2 = 5.0 A in (CW)

Current through common resistors :
I-R12(4 Ohm) = 1.67 A (in the direction of i1)

Verification:

Mesh 2 is constrained: $i_2 = 5\ \text{A}$.

Mesh 1 KVL: $6 i_1 - 4 i_2 = 20 \implies 6 i_1 = 40 \implies i_1 \approx 6.67\ \text{A}$

Current through shared resistor: $i_1 - i_2 = 1.67\ \text{A}$ (direction of $i_1$).

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Project Structure

mesh_analysis/
|-- Mesh_solver.py        # Main solver script (single-file application)
|-- requirements.txt      # Python dependency list
|-- README.md             # Project documentation
|-- .gitignore            # Git ignore rules

Module Layout (inside Mesh_solver.py)

Section	Description
Constants	ANSI color codes, unit symbols
Global Data Stores	Resistor/voltage/current tracking lists and dictionaries
collect_resistors()	Prompts and stores resistor values per mesh
collect_voltages()	Prompts and stores voltage source values per mesh
collect_common_resistors()	Prompts and stores shared resistor values between mesh pairs
build_kvl_equation_terms()	Constructs KVL string terms from mesh_elements
solve_mesh_equations()	Converts terms to SymPy equations and solves the linear system
compute_common_resistor_currents()	Calculates branch currents through shared resistors
remove_duplicate_pairs()	Filters duplicate common-resistor entries (e.g., R12 vs R21)
display_instructions()	Prints formatted usage instructions
display_mesh_currents()	Prints solved mesh currents with CW/A.CW direction
display_common_resistor_currents()	Prints current through shared branches with flow direction
Main Program	Orchestrates input, solving, and output in four sequential steps

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Future Improvements

• Web interface -- Flask/Streamlit front-end for browser-based circuit input and visualization.
• Graphical circuit diagrams -- Auto-generate circuit schematics from input data using matplotlib or schemdraw.
• Matrix display -- Show the assembled resistance matrix and voltage vector before solving.
• Export results -- Output solutions to CSV, JSON, or PDF report format.
• Input validation -- Robust error handling for malformed or inconsistent circuit data.
• Supermesh support -- Automatic supermesh detection when a current source is shared between two meshes.
• Unit tests -- Automated test suite with known circuit solutions for regression testing.

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Author

M. Abhiram

B.Tech Engineering Student

Originally Developed	1st Year B.Tech
Refactored & Improved	3rd Year B.Tech

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License

MIT License

Copyright (c) 2026 Abhiram M

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.