Hello everyone.
I'm Jesse Mason.
In this episode of the Teach Me series, we'll learn the basics of Kirchhoff's Rules and
see how they're applied to circuits.
Kirchhoff's Rules, sometimes referred to as Kirchhoff's Circuit Laws, are a pair of rules
used typically to analyze DC circuits.
The first rule that we'll examine is Kirchhoff's Junction Rule.
The Junction Rule states that "The sum of the currents flowing" -- and yes, I know that
"current flow" is a bit redundantly redundant -- but anyway, "The sum of the currents flowing
into a junction is equal to the sum of the currents flowing out of said junction."
Mathematically speaking, Current-In equals Current-Out.
Sounds simple enough, right?
Let's take a look at a circuit diagram for a junction to elucidate this rule.
We'll take a simple three-way junction and label it j-1.
We'll draw current flowing into j-1 from the left, call it I-1, and current flowing out
the right leg and down the vertical leg, I-2 and I-3 respectively.
How exactly did we decide the directions and labels for these currents?
We'll address this very good question momentarily.
So applying the Junction Rule to j-1 we have: Current-In, that's just I-1, equals Current-Out,
which is I-2 plus I-3.
And that's it - that's how the Junction Rule is applied to a junction.
Before we move on I'm impelled to point out that Kirchhoff's Junction Rule is just a consequence
of a more physically significant principle, namely the Principle of Conservation of Charge.
So we can sort of think of j-1 as a fork in the road where the cars, I mean the charges,
either continue traveling to the right, or turn and move downward.
Got it?
Good.
Now let's examine Kirchhoff's other rule: The Loop Rule.
The Loop Rule states that "For any closed loop, the sum of the voltage "lifts" is equal
to the sum of the voltage "drops".
We'll define a closed loop as any continuous path in the circuit which ends where it started.
The Loop Rule, stated mathematically, is: The net voltage for a closed loop equals zero.
Okay, now let's examine a simple circuit to see how we apply the Voltage Rule.
Here we'll have a voltage across the source, V-sub-s, and a voltage across the resistor,
V-sub-r.
Since it's a simple circuit, we'll have a singular current and its direction of positive
charge flow is clockwise, due to the orientation of our voltage source.
Next we'll label our circuit loop "Loop A." Note that for most circuits, currents and
loops won't coincide and need to be explicitly labeled separately.
Okay.
To apply the Loop Rule to Loop A we'll travel clockwise around the loop summing voltages.
Starting on the bottom-left we have positive V-sub-s (a voltage"lift) and then we'll have
a negative V-sub-R (a voltage "drop"), equals zero.
And that's how we apply the Loop Rule.
By the way, Kirchhoff's Loop Rule, like the Junction Rule, has its physical roots in a
conservation law, namely the Principle of Conservation of Energy.
Okay, let's now discuss the conventions associated with Kirchhoff's Rules.
The first two conventions relate to the Loop Rule and identifying voltage "lifts" and "drops".
If we're moving around a loop and we travel through a battery (while summing voltages)
and we go from low to high (which is to say, going from the negative terminal to the positive
terminal) then the voltage of the battery is treated as a positive voltage (which we'll
call a voltage "lift" because of the increase in electrical potential).
If instead we travel through a battery high to low (that is, positive to negative) the
voltage is treated as negative (which we'll call a voltage "drop" because of the decrease
in electrical potential.)
So for voltage sources: low to high -- we have a positive voltage; high to low -- a
negative voltage.
It turns out that the sign of the voltage across a resistor also depends on the direction
of our labeled current.
So if we follow a current (while summing voltages) through a resistor, then the voltage across
the resistor, is negative V or, invoking Ohm's Law, negative I times R -- this is a voltage
drop.
If instead we oppose the direction of the labeled current as we pass through the resistor,
then the voltage across the resistor is treated as positive I times R -- a voltage lift.
So for resistors, follow the current -- negative IR; oppose the current -- positive IR.
Now a lot has been said about the directions of currents and loops.
How are these directions initially decided?
This is the best part.
The directions of loops and currents are assigned and labeled arbitrarily with absolutely no
preference in direction.
So long as the circuit is correctly analyzed using Kirchhoff's Rules, the actual direction
of positive charge flow will be revealed in our results.
Which is to say that if I-1 ends up having a negative amperage, we'll know that positive
charge flow is opposite the way we labeled it.
It's kind of like a Choose-Your-Own-Adventure in Physicsland.
Physicsland!
One final convention relating to labeling our circuit diagram: Typically, we'll use
one more loop than the number of junctions in the circuit, so be sure to have enough
of them labeled before applying Kirchhoff's Rules.
I'm Jesse Mason and I hope you found this video helpful.
If you have any suggestions for future Teach Me videos or just wanna say hello from your
part of the world, please do so in the comments below.
And as always, happy learning!