CIRCUIT ANALYSIS GUIDE
Two-node nodal analysis with a conductance matrix
Nodal analysis writes Kirchhoff current law equations at each unknown node. A DC resistor network becomes a coefficient matrix where conductances multiply node voltages.Explore engineering methods & units →FORMULA OR CORE IDEA
G · V = I, where G is the conductance matrix, V is the node-voltage vector, and I is the current-injection vectorWORKED EXAMPLE
For R1 from node 1 to ground, R2 from node 2 to ground, R12 between nodes, and current injections I1 and I2, write KCL at both nodes, convert each resistor to conductance G = 1/R, then solve the 2×2 matrix for V1 and V2.STEP BY STEP
Choose the reference node
Ground is the reference voltage. Every unknown node voltage is measured relative to ground, so the solver reports V1 and V2 as node voltages.
Convert resistors to conductances
Use G = 1/R. A resistor from a node to ground adds conductance to that node's diagonal matrix term.
Handle the resistor between nodes
A resistor between node 1 and node 2 adds conductance to both diagonal terms and adds negative conductance to the off-diagonal terms.
Place current injections on the right side
Positive I1 and I2 values mean current is injected into the corresponding node. Those values form the I vector in G·V = I.
Solve for voltage and branch current
After solving the matrix, calculate branch current with (V1 − V2) ÷ R12 and check whether the sign matches the assumed current direction.