Basic Concepts

There are just a few points about Kirchhoff's Current Law that need to be made.

• The complete expression of KCL is "The sum of all the currents entering a node is equal to the sum of all the currents leaving the node."
• Kirchhoff's Current Law holds at every node in a network.
• Kirchhoff's Current Law holds at every instant of time.

        We introduced this lesson with a simulation.  That simulation seems to say a lot, and it really shows what KCL means.  We'll let you look at it again.

        The simulation shows what KCL is trying to describe mathematically.  Current flows through elements.  At nodes it splits, or comes together, or both.  All of that charge moving around is described by KCL.

        In this section we'll look at circuits that are just a little more complex than the example circuit we used in the last section.  As you go along in this section keep in mind that circuits can be very complex, with many nodes and loops, and that you may need to write KCL many times just to analyze a single circuit if that circuit is complex.

        KCL can be applied to more complex circuits.  Here's a circuit with four nodes, A, B, C and ground (G).  (Each node where KCL can be written is shown with a red square.)  KCL can be applied to this circuit.  We'll examine this circuit and write KCL for all possible situations.

        The problem with this circuit is that you can write KCL for a number of different nodes, that is A, B, C and G. In a circuit like this one, KCL can be written at every node.  Writing KCL at each node will produce, in this particular case, four (4) equations - one equation for every node.  You can write KCL for every one of those nodes.  If you want to write those KCL equations - and you will want to write them if you ever analyze a circuit - you will need to have currents defined for every possible current entering or leaving a node.  We've taken care of that in the diagram.

        We'll work on node A first.  There are three currents for node A.  Two currents are leaving (I₁ and I₅), one is entering (I_V).  Remember, the complete expression of KCL is:

• The sum of all the currents entering a node is equal to the sum of all the currents leaving the node.

• Note the currents entering and leaving the node.  In this case, those currents are:
• Two currents are leaving (I₁ and I₅),
• One current is entering (I_V).
• Applying KCL in the form that says "The sum of the currents entering a node equals the sum of the currents leaving the node" gives us:
• I_V = I₁ + I₅
• And, that is the KCL equation we get for that node.

        After you have learned about KCL, it's worthwhile to reflect on exactly what KCL says.  Here are some things to think about.

• KCL does not depend upon the elements in the circuit.  When you write KCL equations for a circuit, you do the following.
• You define currents symbolically, including polarity.
• You write KCL at every node.
• In the process, you do not need to know anything about the elements in the circuit.
• Clearly, if you want to determine voltages and/or currents in the circuit you are going to need information about the elements.  You just don't need that information to write KCL.
• That means that KCL is determined entirely by the topology of the circuit.