Verifying Mesh Analysis with Arduino | Generated by AI

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Verifying Mesh Analysis with an Arduino involves constructing a circuit with multiple loops, applying Mesh Analysis theoretically to predict currents, and then using the Arduino to measure voltages across resistors to calculate actual currents for comparison. Mesh Analysis is a method in circuit theory where you assign loop currents to each independent loop and use Kirchhoff’s Voltage Law (KVL) to set up equations. The Arduino will help you measure the real-world behavior to confirm your calculations.

Below, I’ll guide you through designing a simple two-mesh circuit, performing Mesh Analysis manually, and using an Arduino to verify the results by measuring voltages and inferring currents (since Arduino can’t measure current directly, we’ll use Ohm’s Law: ( I = V/R )).


Step 1: Design a Two-Mesh Circuit

Circuit Description

Schematic Concept

5V ---- Node A ---- R1 ---- Node B ---- R2 ---- Node C (GND)
       |                        |
       +--------- R3 -----------+

Step 2: Perform Mesh Analysis Theoretically

Define Mesh Currents

Apply KVL to Each Mesh

  1. Mesh 1 (5V → R1 → R2 → GND):
    • Voltage source: +5V (going from GND to 5V in the loop direction).
    • Voltage drop across R1: ( -R1 \cdot I_1 ).
    • Voltage drop across R2: ( -R2 \cdot (I_1 - I_2) ) (current through R2 is ( I_1 - I_2 )).
    • Equation: ( 5 - R1 \cdot I_1 - R2 \cdot (I_1 - I_2) = 0 ).
  2. Mesh 2 (5V → R3 → GND):
    • Voltage source: +5V.
    • Voltage drop across R3: ( -R3 \cdot I_2 ).
    • Voltage drop across R2 (opposite direction): ( +R2 \cdot (I_1 - I_2) ) (current through R2 is ( I_1 - I_2 )).
    • Equation: ( 5 - R3 \cdot I_2 + R2 \cdot (I_1 - I_2) = 0 ).

Substitute Values

Solve the Equations

Calculate Voltages


Step 3: Verify with Arduino

Arduino Code

void setup() {
  Serial.begin(9600); // Start serial communication
}

void loop() {
  // Read voltages (0-1023 maps to 0-5V)
  int sensorValueR1 = analogRead(A0); // Across R1
  int sensorValueR2 = analogRead(A1); // Across R2
  int sensorValueR3 = analogRead(A2); // Across R3

  // Convert to voltage
  float VR1 = sensorValueR1 * (5.0 / 1023.0);
  float VR2 = sensorValueR2 * (5.0 / 1023.0);
  float VR3 = sensorValueR3 * (5.0 / 1023.0);

  // Resistor values
  float R1 = 330.0;
  float R2 = 470.0;
  float R3 = 680.0;

  // Calculate currents (I = V/R)
  float I1 = VR1 / R1;              // Mesh 1 current through R1
  float I2 = VR3 / R3;              // Mesh 2 current through R3
  float IR2 = VR2 / R2;             // Current through R2 (I1 - I2)

  // Output results
  Serial.println("Measured Values:");
  Serial.print("VR1 (V): "); Serial.println(VR1);
  Serial.print("VR2 (V): "); Serial.println(VR2);
  Serial.print("VR3 (V): "); Serial.println(VR3);
  Serial.print("I1 (mA): "); Serial.println(I1 * 1000);
  Serial.print("I2 (mA): "); Serial.println(I2 * 1000);
  Serial.print("I1 - I2 (mA): "); Serial.println((I1 - I2) * 1000);
  Serial.println("---");

  delay(2000); // Wait 2 seconds
}

Wiring Notes


Step 4: Compare Results

Expected vs. Measured

Verification


Tips and Troubleshooting

This setup confirms Mesh Analysis by aligning theoretical currents with measured ones. Let me know if you need help refining the circuit, debugging, or adding more meshes!


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