Kirchhoff’s Law Circuit Solver

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KCL

Kirchhoff's Law Circuit Solver

Solve branch currents and node voltage for two voltage sources sharing a common resistor

Circuit Values
Circuit
Result
Node Voltage VA
BranchCurrentDirection
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.
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