Node Voltage (KCL)

Kirchhoff's Current Law

Kirchhoff's Current Law (KCL): the sum of all currents entering a node equals the sum leaving. Equivalently, the net current at any node is zero:

Σ I = 0

Solving for an Unknown Node Voltage

Consider a floating node connected to n known voltage sources through resistors:

V1 --[R1]--+
V2 --[R2]--+--- V_node  (unknown)
V3 --[R3]--+

Current from source k into the node: Iₖ = (Vₖ − V_node) / Rₖ

By KCL, all these currents sum to zero:

Σ (Vₖ − V_node) / Rₖ = 0

Solving for V_node (the weighted average of the source voltages):

V_node = Σ(Vₖ / Rₖ) / Σ(1 / Rₖ)

Each source is weighted by its conductance (1/R). A lower resistance pulls the node voltage closer to its source.

Examples

Your Task

Implement double node_voltage(double *v, double *r, int n) that returns the unknown node voltage using the KCL formula above.