Oh this is ELC-131 circuit
analysis one. And they were
going to talk about
Kirchhoff's laws.
Now, Kirchhoff's first law is
Kirchhoff's current law, which
states that the current entering
a point or node must leave that
point. How we define a
node is a junction of
two or more components?
So.
In this simple circuit we have a
voltage source VS and a resistor
R. And, where the positive
terminal of VS connects to R
is a node and will refer to
that as node A.
And where the resistor R
connects to the negative
terminal of the voltage source
is another node.
And will refer to
that as node B.
Now.
Remember, with our voltage
source, the schematic symbol for
the voltage source, the longest
line represents the positive
terminal and the shorter line
represents the negative terminal.
And from our previous
discussion, we've seen that.
When we have a source of
potential difference and we
provide a path for current, the
current will flow.
From positive
to negative and here again we
describe current is flowing
current flow as conventional
current flow. In other words, it
flows from positive to negative.
Now some current will leave the
voltage source and we'll call
that current IS.
For the source current and that
current enters node A.
Now some current will leave node A and flow through. The
resistor we'll call that current.
IR.
Now that current flows through IR
an enters. Node B.
IR not IB.
And the current IR enters the
node B and some current leaves
node B and flows back into the
source. We'll call that. Of
course IS.
Now Kirchhoff's current law
states that.
The current entering a point or
a node must leave that point. So
for this circuit we can say
simply that IS.
equals IR.
Kirchhoff's current law is
really just the the law of the
conservation of charge in a
system, and hopefully this sort
of makes sense. Because whatever
electrons we have leaving the
source. Have nowhere else to go
but go through the resistor and
after they go through the
resistor they go back into the
voltage source at a point of.
A deficiency of Electrons.
Now, Kirchhoff's voltage law states
that around any closed loop.
The sum of the voltage
differences or the potential
differences must equal 0.
So when we look at this circuit.
We have a closed loop
existing right here.
Now when we draw these closed
loops, it doesn't matter where
we start. Doesn't matter the
direction we go, but we have to
go all the way around this loop.
Now we know that when we
apply or connect this voltage
source to this closed loop, that
current is going to flow.
Through the resistor. Now when
current flows through a
resistive element we see a
difference in potential energy.
A drop in energy across that
resistor is developed and we'll call
that. Voltage difference, that
potential difference, that
voltage drop VR.
And note that I have assigned a
polarity that that voltage drop
positive to negative and this.
Polarity is determined solely by
the direction of current.
Current flows down through the
resistor. The voltage drop
across the resistor VR will be
positive to negative.
Now what we're going to do is
just simply travel around this
closed loop and add up the
potential differences. And these
potential differences should or
must. Add up to 0.
So we start here and the first
thing we encounter is a rise in
potential energy or potential
energy, right? There's a rise in
voltage. The voltage is from
negative to positive, so I'm
going to record this as plus.
VS.
Now as I continue around this
closed loop, we come to a
positive to negative difference
across. Resistor R.
VR is a drop in voltage, so
I'm gonna record this as minus
VR. And if I rearrange
this equation.
I end up with VS.
Equaling VR.
And this hopefully makes sense.
This is really just.
The conservation of energy.
VS is potential energy.
VR is kinetic energy, and we
know whatever energy we apply to
a system has to be used up
somewhere in that system.
