Why Do You Need To Know About KCL?You are at: Basic Concepts - Kirchoff's Laws - KCLFacts About KCLUsing KCL To Write Equations For CircuitsProblems
Kirchhoff's Current Law - KCL - is one of two fundamental laws in electrical engineering, the other being Kirchhoff's Voltage Law (KVL).
What should you be able to do after this lesson? Here's the basic objective.
Given an electrical circuit:These goals are very important. If you can't write KCL equations and solve them, you may well be lost when you take a course in electronics in a few years. It will be much harder to learn that later, so be sure to learn it well now.Be able to write KCL at every node in the circuit.
Be able to solve the KCL equations, especially for simple circuits.
At this point, you have learned the fundamentals of charge and current. There is one important law, Kirchhoff's Current Law that you will need to learn. It is not as complex as it might seem. All you really need to know is that charge is conserved, so KCL is really based on one simple fact.
Let's examine a circuit simulation. It's shown below. Charge (current) is flowing through the circuit. The simulation shows some charge - the large red blob - flowing through a battery (where it picks up energy, but that's another story. Click here for that lesson.) That charge flows through Element #1 in the simulation. After the charge flows through Element #1 it splits. Some of the charge goes through Element #2, and some goes through Element #3. (Notice that it does not split equally! Sometimes it does. Sometimes it doesn't.) When, in the course of its flow through the circuit, there is no possibility of splitting, all of the charge entering a node will flow through the next element. (That element is said to be in series. Element #3 and Element #4 are in series because all of the current going through #3 goes through #4. Elements #1 and #2 are not in series.)
There is one node in the simulation where charge flowing through two elements comes together and "reunites" and flows back into the battery.
Note that this simulation emphasizes the
conservation of charge. When charge flows through Element #1 when
it gets to the end of Element #1 it splits into two. However, what
arrives at that node is what leaves that node, so the amount of charge
that enters the node - the big red blob - equals the amount of charge that
leave that node - the sum of the charge on the medium sized red blob and
the charge on the small red blob.
this circuit, charge flows from the battery, through Element #1 to the
node. Willy Nilly observes that 35 coulombs flows through Element
#1 in 20 seconds, and that, in that same time, 17 coulombs flows through
Element #2. How much charge flows through Element #3 in that time?
much charge flows through Element #4 in that time?
Charge usually flows through some sort of metallic wire, flowing through the atomic lattice. Although it is physically unlike water flowing in a pipe, that analogy is sometimes drawn. Like water confined to the interior of a pipe, charge is confined to flow within a wire, and it doesn't leave the surface of the wire. You may want to think in those terms as you interpret current flow in the sketches and diagrams that follow. We will be developing rules for current flow in circuits in this section. You will need to know about that in order to be able to analyze larger circuits with lots of elements.
In practice current flows in wires and often splits between two or more devices. We need to consider what happens in networks of conductors in which current can split. Single wires carrying current aren't the most important case we can look at, and you need to learn about Kirchhoff's Current Law which describes those situations where we have large networks of interconnected elements carrying current. Those kinds of circuits will have many connection points (called nodes) where current can split into smaller currents. Shown below is part of a circuit. Current (I) comes in from the left and splits into two parts, I1 and I2. There is one simple relationship between these two currents and the current, I, flowing in from the left below.
Here, a red dot has been placed over both of the nodes in the picture.
Focus attention on a very short time, DT. Assume all currents constant during DT.
When we have the expression:
3. In this circuit - which you saw above - determine the current I2, in terms of trhe other two currents. You will need to write KCL at the node marked with a red dot. Notice that we have defined current symbols and polarities for all the currents involved.
5. Here is another circuit.
You need to determine a value for the current, I4, given the following numerical values for some other currents. First, you'll need to get an algebraic expression for I4. Click on the corrrect expression.
Now, determine the numerical value for I4 when I3 is 0.45A.
6. Here's a problem for you. In 10 seconds, an observer - Willy Nilly - notices that 35 coulombs of charge leaves node "n" in this circuit, heading for node "x". (Vn is the voltage at node "n", etc.) In the same ten seconds, 22 coulombs of charge leaves node "n" heading for node "z". Determine the current, Iy.
There are just a few points about Kirchhoff's Current Law that need to be made.
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 (IV). Remember, the complete expression of KCL is:
What is the correct expression of KCL for Node G in the circuit?
7. Here's a KCL problem for you. The circuit for this problem is shown below.
In this circuit, four
(4) amperes enters node B through Element #1. 2.5 amperes flows through
Element #3 from Node B to Node C. How many amperes flows through
much charge flows through Element #4 in 3 seconds? Give your answer
Finally, here is a link to a
slightly more complex problem.
After you have learned about KCL, it's worthwhile to reflect on exactly what KCL says. Here are some things to think about.