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!
