KCL
Kirchhoff's Law Circuit Solver
Solve branch currents and node voltage for two voltage sources sharing a common resistor
Circuit: V1 (through R1) and V2 (through R2) both feed into common node A; R3 connects node A back to the shared
ground/return. Kirchhoff's Current Law (KCL) at node A: current in from V1's branch + current in from V2's branch =
current out through R3. Combined with Ohm's law on each branch (I=(Vsource−VA)/R), this gives one
equation in one unknown (VA), solvable directly — this is the same result Millman's theorem gives as a shortcut:
VA = (V1/R1 + V2/R2) ÷ (1/R1 + 1/R2 + 1/R3). A negative current means the actual current flows opposite
to the assumed "into node A" reference direction shown in the diagram — that's a normal, correct outcome, not an error.