PROFESSOR: Today I'd like to
talk to you about a new method
for solving circuits.
Last time, we reviewed using
KVL, KCL, and Ohm's Law in
order to solve circuits
in a general sense.
This produced a lot of
equations, in particular, a
lot of redundant equations or a
lot of dependent equations,
that we don't necessarily need
for solving our circuit.
Today I'm going to review the
Node Voltage Component Current
method, which is very similar
to node analysis.
So if you hear one versus the
other, know that you're
talking about approximately
the same thing.
And I'll review the difference
in a second.
Once we know how to use the
NVCC method for solving
circuits, we can express the
relationships between
components in our circuit
more concisely and more
effectively, and possibly solve
our equations faster,
which is relevant when we're
working on a mid-term or in
the general sense, just
trying to save time.
Let's take a look at NVCC.
As I said before NVCC,
stands for Node
Voltage Component Current.
And what that means is if you
have a very simple circuit--
let's say just a voltage source
and a couple of resistors.
Previously, with KVL, we were
interested in the voltage drop
around the loop being
equivalent to 0.
In this case, we're actually
going to look at the voltages
associated with particular
nodes.
To do that we're going to label
our nodes, which are
anywhere our components
connect.
We're also going to go after
the component current.
When we're doing KCL, we
typically look at the flow in
and out of a particular node.
At this point, we're going to
look at the flow through a
given component.
So we're also going to label all
of the currents associated
with our circuit.
But when we approach NVCC
method, we're going to think
about the currents flowing
through a particular component
as opposed to and out of
a particular node.
NVCC is sort of the opposite of
KVL and KCL in that sense,
even though you're still going
to end up using the same
relationships.
So at this point, I've labeled
the currents going through--
I labeled one individual current
for every component in
my circuit.
The next step would be to
identify what I'm going to
call ground, or in particular,
one of my nodes --
I'm going to assign to ground
or relative voltage 0.
At that point, I'm going to
write out the relationships
between the voltage drop across
particular components,
the current flowing through that
particular component, and
whatever relationship the
component requires the voltage
and the current to have
to one another.
That's a whirlwind review
of NVCC method.
Node analysis is very similar.
The main difference between node
analysis and NVCC method
is when your component
is a voltage source.
And there are multiple currents
flowing into that
voltage source.
You can treat this as
a single voltage.
You can treat this as a single
voltage node, where this
voltage it has value 0.
And actually write your KCL
equations as though this point
were collapsed.
So current flowing in and
current flowing out, or vice
versa, have to sum to 0.
That's the major difference.
Let's look at an example.
You can find this example
repeated in
6.4.3 of the reading.
And I'm going to walk through
these directions.
So the first thing I'm going
to do is label my
nodes and my currents.
People interchangeably
use e or n.
It doesn't really matter.
I guess n in particular could
refer to the node, while e in
particular could refer
to the voltage
associated with that node.
Now I'm going to specify the
voltage drop across a
particular component in terms
of the node voltages.
I'm also going to assign
n0 to 0 as my ground.
As a consequence, I know that
n1 is going to be 15 Volts.
My voltage drop is typically
specified in the same
direction as the current -
that I've also decided.
So this convention
is arbitrary.
But if you want to be consistent
in your work, and
make it easier to get partial
credit or get help in office
hours, et cetera, then assume
that the voltage drop occurs
in the same direction
as the current.
That's it for our relationship
associated with voltage drop.
Now I'm going to go over KCL
for the relevant nodes.
And in the last step I'm going
to combine the two into the
equation that you're certainly
allowed to use to express your
work on midterms.
Or if you can skip
to the third step
immediately, then that's OK.
Just check your signs.
Here's the second step.
Flowing into n1 is i0 and
flowing out is i1.
So i0 is going to
be equal to i1.
Flowing into n2 is i1 and i3.
And flowing out of n2 is i2.
Flowing into n0 is i2,
and flowing out of
n0 is i0 and i3.
we're almost certainly
not going to end
up using that equation.
Because it's the last of our KCL
equations and is dependent
upon the other equations
that we've already
written out for KCL.
I3 is equal to 10 Amperes.
So we can go ahead and make
that substitution.
I still have to work with
i1 and i2 though.
And I can go after expressions
for them in terms of my node
voltages and components by
using the equations for
voltage drop I made earlier.
This is the equation that you
can jump straight to, if you
understand where this expression
comes from, as a
consequence, of our KCL and also
our component voltages.
I'm going to substitute in
15 Volts for n1 here.
And now I have an expression
that only contains n2 and
known values.
So I can solve for n2.
and I'll do that real
quickly right now.
So first I'm just going
to copy this over.
I'm going to multiply
through by 6 Ohms.
And I solved for the voltage
associated with n2.
At this point, I can solve
for i2 and i1.
Sorry about that.
What do I have left?
i3 I know is 10 Amperes.
i0 is equal to i1, which
is negative 1 Amperes.
There's a voltage drop
associated with the 3 Ohm
resistor, which is 15 minus
18, negative 3 Volts.
And the voltage drop associated
with the 2 Ohm
resistor is 18 Volts,
since n0 is ground.
This concludes my introduction
to node voltage component
current method or node analysis
without the ability
to collapse voltage
sources for KCL.
