Kirchhoff's Current Law (KCL)
Let's take a closer look at this 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:
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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"
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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 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, but suffice it to say that these Laws
deserve to be memorized by the electronics student every bit as
much as Ohm's Law.
Kirchhoff's Current Law (KCL): "The algebraic sum of all currents
entering and exiting a node must equal zero"
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