Deriving Kirchhoff's two laws from charge and energy conservation

Step 1 of 4: Charge accumulation at a junction

\frac{dQ_{\text{nút}}}{dt} = \sum_k I_k^{(\text{vào})} - \sum_k I_k^{(\text{ra})}

Analysis

Let $Q_{\text{node}}$ be the total charge inside a small region around the junction (where the wires meet). Its rate of change equals the difference between the total current flowing in and the total current flowing out — this is the continuity equation (charge conservation) applied to the node.