How it works
Mesh analysis steps: (1) identify and label meshes with assumed clockwise currents; (2) write KVL for each mesh: for mesh k, (sum of resistors in mesh k)×I_k − (shared resistors)×adjacent mesh currents = net voltage rise. In matrix form: [R][I] = [V]. For a current source shared by two meshes (supermesh): write KVL around the periphery of both meshes combined, then add the constraint that the current source value equals I₁ − I₂. Nodal analysis: (1) select reference node; (2) assign node voltages V₁, V₂...; (3) write KCL at each non-reference node expressing currents as (V_node − V_adjacent)/R.
Key points to remember
Nodal analysis uses N−1 equations for N nodes; mesh analysis uses B − N + 1 equations. Choose nodal analysis when the circuit has more loops than nodes; choose mesh when it has more nodes than loops. For a circuit with a voltage source between two non-reference nodes, form a supernode: combine KCL for both nodes and add the voltage source constraint equation V₁ − V₂ = V_s. The conductance matrix [G] in nodal analysis has diagonal entries equal to sum of conductances at each node and off-diagonals equal to negative of shared conductance — this mirrors the resistance matrix in mesh analysis. Dependent sources add a controlled term to the equations without changing the method.
Exam tip
The examiner always asks you to solve a two-mesh or two-node circuit by the matrix method and verify with power balance — calculate total power delivered by sources and total power absorbed by resistors separately, because they must be equal for the solution to be correct.