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Kirchhoff's current law (KCL)

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node. This results from the conservation of electric charge.

$$\sum_{k=1}^n I_k = 0$$

with the $n$ currents $I_k \in {\mathop{\mathbb R}}$ going into a node.

Kirchhoff's voltage law (KVL)

The directed sum of the electrical potential differences (voltage) around any closed network is zero.

$$\sum_{k=1}^n V_k = 0$$

with the $n$ voltages $V_k$ for each closed loop.

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