How to use the Mesh Analysis Solver
- 1. Write the KVL equationsOne per mesh, brackets allowed: 2(I1 − I2) + 4I1 = 10.
- 2. Or type the matrixRows like 3 −1 −2 | 1 for [R][I] = [V].
- 3. SolveSee Δ, Δ1…Δn, the elimination steps and the shared-branch currents.
Mesh analysis method
Mesh analysis applies KVL around each window of a planar circuit. Give every mesh a clockwise current I1, I2, … . A resistor shared by two meshes carries the difference of the two currents. Collect the terms to get [R][I] = [V]: the diagonal holds the total resistance of each mesh and the off-diagonal terms are minus the shared resistance.
Worked example (Hayt): 1(I1 − I2) + 2(I1 − I3) = 7 − 6, 1(I2 − I1) + 2I2 + 3(I2 − I3) = 0 and 2(I3 − I1) + 3(I3 − I2) + 1·I3 = 6. In matrix form [3 −1 −2; −1 6 −3; −2 −3 6][I] = [1; 0; 6]. Δ = 39, Δ1 = 117, Δ2 = 78, Δ3 = 117, so I1 = 3 A, I2 = 2 A and I3 = 3 A.
Exam tips for mesh analysis
- Use the same direction (clockwise) for every mesh current, so the [R] matrix comes out symmetric.
- A current source on the outer edge fixes that mesh current directly. A current source between two meshes needs a supermesh.
- Check the answer by putting the currents back into each equation. The tool does this for you.
- A negative current only means the real direction is anticlockwise.
Use plain numbers inside equations. Ω with V gives amperes, and kΩ with V gives mA.
Frequently asked questions
How many meshes can it solve?
Up to 4 unknowns, entered as equations (I1 to I4) or as a matrix with the right-hand side after a | sign.
Can I type equations without simplifying them?
Yes. Brackets, terms on both sides and fractions are all accepted, for example 5(I1 − I2) + 3I1 = 10 − 2I2.
Why does it say the determinant is 0?
Two equations are dependent (one is a multiple or sum of the others), so there is no unique answer. Check for a repeated KVL loop or a sign error.
Is this tool free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. All the maths runs in your browser.