“The algebraic sum of all the currents entering any node is equal to zero”
This law represents a mathematical statement of the fact that charge cannot accumulate at a node. A node is not a circuit element, and it certainly cannot store, destroy, or generate charge. Hence, the currents must sum to zero. A hydraulic analogy is sometimes useful here:
for example, consider three water pipes joined in the shape of a Y. We define three “currents” as flowing into each of the three pipes. If we insist that water is always flowing, then obviously we cannot have three positive water currents, or the pipes would burst. This is a result of our defining currents independent of the direction that water is actually flowing.
Therefore, the value of either one or two of the currents as defined must be negative.
A compact expression for Kirchhoff’s current law is