Kirchhoff's Current Law (KCL)
Let's take a closer look at that last parallel example circuit:
Solving for all values of voltage and current in this circuit:
At this point, we know the value of each branch current and of
the total current in the circuit. We know that the total current in
a parallel circuit must equal the sum of the branch currents, but
there's more going on in this circuit than just that. Taking a look
at the currents at each wire junction point (node) in the circuit,
we should be able to see something else:
At each node on the negative "rail" (wire 8-7-6-5) we have
current splitting off the main flow to each successive branch
resistor. At each node on the positive "rail" (wire 1-2-3-4) we have
current merging together to form the main flow from each successive
branch resistor. This fact should be fairly obvious if you think of
the water pipe circuit analogy with every branch node acting as a
"tee" fitting, the water flow splitting or merging with the main
piping as it travels from the output of the water pump toward the
return reservoir or sump.
If we were to take a closer look at one particular "tee" node,
such as node 3, we see that the current entering the node is equal
in magnitude to the current exiting the node:
From the right and from the bottom, we have two currents entering
the wire connection labeled as node 3. To the left, we have a single
current exiting the node equal in magnitude to the sum of the two
currents entering. To refer to the plumbing analogy: so long as
there are no leaks in the piping, what flow enters the fitting must
also exit the fitting. This holds true for any node ("fitting"), no
matter how many flows are entering or exiting. Mathematically, we
can express this general relationship as such:
Mr. Kirchhoff decided to express it in a slightly different form
(though mathematically equivalent), calling it Kirchhoff's
Current Law (KCL):
Summarized in a phrase, Kirchhoff's Current Law reads as such:
"The algebraic sum of all currents entering and exiting a
node must equal zero"
That is, if we assign a mathematical sign (polarity) to each
current, denoting whether they enter (+) or exit (-) a node, we can
add them together to arrive at a total of zero, guaranteed.
Taking our example node (number 3), we can determine the
magnitude of the current exiting from the left by setting up a KCL
equation with that current as the unknown value:
The negative (-) sign on the value of 5 milliamps tells us that
the current is exiting the node, as opposed to the 2 milliamp
and 3 milliamp currents, which must were both positive (and
therefore entering the node). Whether negative or positive
denotes current entering or exiting is entirely arbitrary, so long
as they are opposite signs for opposite directions and we stay
consistent in our notation, KCL will work.
Together, Kirchhoff's Voltage and Current Laws are a formidable
pair of tools useful in analyzing electric circuits. Their
usefulness will become all the more apparent in a later chapter
("Network Analysis"), but suffice it to say that these Laws deserve
to be memorized by the electronics student every bit as much as
Ohm's Law.
- REVIEW:
- Kirchhoff's Current Law (KCL): "The algebraic sum of all
currents entering and exiting a node must equal zero"
|
