This says that, in a closed electrical circuit, current cannot accumulate at a junction. For an equation, take a look at this diagram:
          a ->       <- b      
                    |   ^
                    |   c

where a, b, and c represent the magnitude of current (Amps) flowing into the junction along the three wires. Kirchoff's Current Law dictates that a + b + c = 0.
Kirchhoff's Current Law, or KCL, is a fundamental law of circuit theory. It states that the total of all currents flowing into a node (or supernode) of a circuit must equal the total of all current flowing out of the node (or supernode). In other words, the algebraic sum of all the currents entering a node must be 0.

This law is caused by twin facts: (1)charge must be conserved and (2)charge cannot accumulate at a node. Thus, since whatever charge enters a node cannot be destroyed, and it cannot accumulate, it must leave. Since current is merely charge/time, KCL follows.

Typically, one uses KCL to determine some unknown current flowing into or out of a node, having other currents known. By simultaneously solving many KCL equations, one can perform node voltage analysis.

See also circuit, Kirchhoff's Voltage Law, current density, Kirchhoff, Gustav Robert.

Also very commonly misspelt Kirchoff's Current Law--about 40% of the time according to some quick searches I did on Google. (It caught me.)

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