Kirchhoff’s current law (KCL), also known as Kirchhoff’s first law or Kirchhoff’s junction rule, states that, for any node in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node. In other words, the algebraic sum of currents at any node is zero (where we usually consider that current is signed positive if its direction is away from the node and negative if its direction is towards the node). Equivalently: $$\begin{equation}\sum_{i=1}^{n} I_i = 0\end{equation}$$ where $n$ is the total number of branches with currents flowing towards or away from the node. Notice that, in the case of time-dependent circuits, Kirchhoff’s current law holds at any moment in time and can be written as $\sum_{i=1}^{n} I_i(t) = 0$.

For instance, consider the circuit shown in Fig. 1. KCL, applied to the node shown in black, can be written as $$\begin{equation}I_{R_1}+I_{R_2}+I_{R_3}-I_2+I_{R_4}+I_1=0\end{equation}$$ Quite often, KCL is written in combination with Ohm's law in which case the current flowing through each resistor is expressed as the voltage across the resistor divided by the resistance.

Notice that KCL can also be written by considering that current is signed negative if its direction is away from a node and positive if its direction is towards the node. In this case, KCL becomes $$\begin{equation}-I_{R_1}-I_{R_2}-I_{R_3}+I_2-I_{R_4}-I_1=0\end{equation}$$ which is nothing else but the previous equation with all signs changed.