Mesh Current Analysis is a method used in circuit analysis to find the currents circulating around loops (meshes) in a circuit. It simplifies solving circuits with multiple loops by reducing the number of equations required.

Mesh Current Analysis, also known as Loop Analysis or Maxwell’s Circulating Currents method, is a technique used to simplify the analysis of electrical circuits, especially when dealing with complex networks.

Instead of labeling each branch with a current (Kirchhoff’s Current Law), Mesh Current Analysis labels each “closed loop” in the circuit with a circulating current. This method reduces the amount of math needed and makes solving large circuits more manageable.

Here’s a step-by-step guide to make it easier:

## Mesh Current Analysis Steps

**Identify the Meshes:**A mesh is a loop that does not enclose any other loops within it. Identify all the meshes in the circuit. In above diagram abcdea is mesh.**Assign Mesh Currents:**Assign a current variable to each mesh. The currents are usually assumed to circulate in a clockwise direction, but you can choose any consistent direction.**Apply Kirchhoff’s Voltage Law (KVL):**Write KVL equations for each mesh. KVL states that the sum of all voltages around a closed loop is zero. Include voltage sources and the voltage drops across resistors (Ohm’s Law:*V*=*IR*) in the equations.**Solve the Equations:**Solve the simultaneous equations by cramer’s rule or other to find the values of the mesh currents.**Determine the Desired Quantities:**Use the mesh currents to find the voltages and currents in individual circuit elements, and calculate the power as needed.

## Mesh Current Analysis Example 1

Determine the mesh currents i_{1}, i_{2}, i_{3} in below circuit diagram.

**Step 1:** We identified all meshes of circuit as shown in above picture.

**Step 2: **We assigned all meshes of current which are i_{1}, i_{2}, i_{3} .

**Step 3: Applying Kirchhoff’s Voltage Law (KVL):**

so considering the circuit loop abcdea.

1(i_{1} − i_{2}) + 2(i_{1} − i_{3}) + 6 − 7 = 0

3i_{1} − i_{2} − 2i_{3} = 1 Equation-1

Now take the 2nd loop cfgdc.

2i_{2} + 3(i_{2} − i_{3}) + 1(i_{2} − i_{1}) = 0

−i_{1} + 6i_{2} − 3i_{3} = 0 Equation-2

Now take 3rd loop dghed.

3(i_{3} − i_{2}) + 2(i_{3} − i_{1}) + i_{3} − 6 = 0

−2i_{1} − 3i_{2} + 6i_{3} = 6 Equation-3

Now take a look on 3 mesh equations 1, 2 and 3.

3i_{1} − i_{2} − 2i_{3} = 1 −i_{1} + 6i_{2} − 3i_{3} = 0 −2i_{1} − 3i_{2} + 6i_{3} = 6

**Step 4: Solve the Equations:** Here we are using Cramer’s rule to solve the equations.

Mesh Current Analysis involves labeling loops, creating matrices for voltages and resistances, and solving a matrix equation to find the currents. This method simplifies circuit analysis, reducing the amount of math required.