# Kirchoff’s Current Law

While analyzing a circuit may seem like a daunting task at first, circuit theory is simply a matter of breaking down larger circuits into smaller, more manageable sections and applying a few fundamental principles to these sections. One of these basics is known as Kirchoff’s Current Law.

### Kirchoff’s Current Law (KCL)

KCL states that the sum of the currents entering a node is equal to the sum of the currents leaving.

$\sum_{}^{} i_{entering} = \sum_{}^{} i_{leaving}$

In Figure 1, node 1 has three currents entering (a, c, and d) and two currents leaving (b and e).  Using KCL, all five currents are related to each other by the equation.

$\sum_{}^{} i_{entering} = \sum_{}^{} i_{leaving}$ $a + c + d = b + e$

It is important to understand the definition of a node.  A node is defined as a point where the voltage is the same.  While it is easy to identify the node in the example above as the point where all of the wires meet, that is not always the case.

Consider Figure 2.  When analyzing a schematic, do not assume a node is merely the intersection of wires.  For the sake of appearance, schematic diagrams cannot bring every wire to the same point as I have in Figure 1.  There are several intersecting wires in Figure 2, yet there are only three nodes in the circuit or, in other words, three different voltages.  Everywhere along the red wire, the voltage is 12 V.  Everywhere along the black wires, the voltage is 0 V.  After taking this class, you should be able to find the voltage at the blue node.

### Labeling Voltage on a Schematic

Before moving on to KVL, you should know how to read voltages on a schematic.  Voltage sources and other components often have plusses and minuses labeled on either side of them.  Keep in mind that voltage is the electric potential difference between two points.  This implies that voltage is a relative measure; one voltage is taken with respect to another.  The plusses and minuses are needed to signify the reference point for a measured voltage.  Finding the voltage across a component is a matter of finding the voltage at the ‘plus’ node and the ‘minus’ node and then subtracting the latter from the former.  For the supply on the left, Vs can be found from the following equation.

$V_{s} = V_{a} - V_{b}$