Configure meshes and enter component values to perform mesh analysis.
Note: Circuit diagram updates in real-time showing mesh currents and component values with calculated results.
Note: Circuit diagram updates in real-time showing mesh currents and component values with calculated results.
Note: Matrix solver uses Gaussian elimination method for accurate results.
Circuit: Two voltage sources (12V, 8V) with resistors (3Ω, 2Ω, 4Ω)
Complex bridge configuration with multiple sources
Mesh analysis assigns a circulating current to each independent loop, writes Kirchhoff’s voltage law round each one, and solves the resulting system. In matrix form it is [Z][I] = [V] — an impedance matrix multiplying unknown mesh currents.
The key idea that makes it efficient is that mesh currents are not branch currents. A component shared between two meshes carries the difference of the two mesh currents, so the shared-branch current falls out of the solution automatically rather than needing its own equation.
Both give the same answer, so the practical criterion is which produces fewer equations.
A ladder network with many rungs has many nodes but few loops, so mesh analysis is usually shorter. A circuit with several parallel branches between two rails has few nodes and is better suited to nodal analysis.
A current source shared between two meshes cannot have a defined voltage across it, so KVL cannot be written through it directly. The remedy is a supermesh: write KVL round the outer boundary of the two meshes, ignoring the shared branch, then add the constraint that the difference of the two mesh currents equals the source current. That restores the missing equation.
Mesh analysis applies only to planar circuits — those that can be drawn without crossing wires. Non-planar circuits have no well-defined set of meshes, and nodal analysis, which has no such restriction, must be used instead.
A method that assigns a circulating current to each independent loop, applies Kirchhoff's voltage law round each, and solves the resulting system as [Z][I] = [V].
No. A branch shared between two meshes carries the difference of the two mesh currents. That is what makes the method efficient, since shared-branch currents need no separate equations.
Whichever yields fewer equations. Mesh needs one per independent loop and handles voltage sources naturally; nodal needs one per node minus the reference and handles current sources naturally.
A technique for handling a current source shared between two meshes. KVL is written round the outer boundary of both meshes, and the constraint that the mesh-current difference equals the source current supplies the missing equation.
Because meshes are defined as the windows of a flat drawing. A circuit that cannot be drawn without crossing wires has no well-defined mesh set, so nodal analysis must be used instead.
It circulates opposite to the assumed direction. The magnitude is correct and there is no need to redo the work.
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