Kirchoff's laws

Kirchoff's laws govern electrical networks. Given an electrical network $G = (V, E)$ , it must satisfy the following laws:

Kirchoff's first law: for any $v \in G$ , the current coming in is equal to the current coming out:

\sum_{i \overset{e}{\to} v} I_{e} = \sum_{v \overset{e^{'}}{\to} i} I_{e^{'}}

Kirchoff's second law: For all undirected cycles in $G$ , the signed sum of the voltages in this cycle is 0.

Ohm's law: for all $e \in E$ ,

V_{e} = I_{e} \cdot R_{e}

See also potential function for equivalent conditions