4 ECE toolbox

Think about the electrical laws we have learned so far. They give us a toolbox of ways to find voltages and currents in circuits. We can use them together, sequentially, as well. Think of starting with what you know on the left and moving to what you want to know (your unknowns) on the right. Find a path through the equations that lets you move from what you know (the input to one method) to an output that can be input to another method and so on, until you get to what you want. Most likely, you are already doing this naturally, except that once in a while you might get stuck. Thinking about the inputs (what is known) and outputs (what is not) for each method may help you think through the solution method in a way that can get you unstuck. Give it a try.

To give you just a little
more review on that.

These are the equations that we have
you learn to used so far in this class.

We know how to use Kirchhoff's Laws.

They are two of them,
they can use separately or together.

In each of this cases, the arrows on the
left are telling us the input information,

and the arrows on the right
are telling us the output information.

The boxes in between are equations that
I'm assuming that you already know from

the class.

For example, in Kirchhoff's Voltage Law,

we know the summation of voltage
differences, that's what the delta means.

Voltage difference around
a loop is equal to 0.

Kirchhoff's Current Law, we know
that the sum of incoming currents is

equal to the sum of the outgoing currents,
and these are the branch currents.

So, if we knew for example our
voltage source, our current, and

our resistance, we could calculate
voltage differences around the loops.

If we knew the incoming and
the outgoing, incoming current,

we could find the outgoing current.

If we knew the outgoing current,
we could find the ingoing current.

If we combine these, if we do a series
of loops plus at least one node,

we can take in our sources,
our current or voltage sources, and

our resistance,
we can find the branch currents.

Resistors in Series and

Parallel are simply used to combine
many resistors into a simpler one.

Voltage Dividers are used to start with
our source voltage and resistance, and

find voltage difference.

Current Dividers are used to start with
our current source, our resistance which

we convert R to G,
remember that G is equal to one over R.

And that gives us the output
branch current, but

Ohm's Law equation, we use current.

So suppose, for

example, that we know a voltage difference
and a current, we can get resistance.

If we know a voltage difference and
resistance, we can get current.

If we know current and resistance,
we can get voltage difference.

Tell this thing to go away.

Okay, the Power equation,
if we know voltage difference and

current, we can get Power.

If we know voltage difference and
resistance, we can get Power, and

current, and resistance,
we can also get power.

This equation is telling
us about node voltages.

This is the only card that we have
that talks about node voltages, so

this is the only way we can find them.

If we know one node voltage and

voltage difference,
we can find all the other nodes.

If we know two node voltages,
we can find the voltage difference, or

if we know one node voltage, and I and
R, we can find all the other nodes.

So, let's just see a little bit
about a couple of these cards.

I would particularly like to
talk about how to use this card

right here if we have voltage differences.

What you do is you line up this current
with the current in your circuit, and then

you can see the two nodes on either side,
and you use this equation right here.

Voltage difference or the Va- Vb.

So this is our electrical engineering
toolbox, we have Kirchhoff's Laws.

We have No Voltage equations,
we have Ohm's law which tells us about

different voltages, the power which
uses voltage and current to get power.

This method of combining resistors and
series in parallel to simplify them,

voltage dividers that use
the volt source voltage and

resistance to get voltage difference.

Current divider that uses
the source difference and

conductance in work to get
current through each branch.

We can combine these by looking
at what comes in on the left and

what goes out on the right.

What I do usually,
is I take all of the things I know, and

I put them on the left, and
I put the things that I want on the right.

And then I make myself a track, so that
I can follow through from left to right,

until I'm able to solve the problem.

For example,

the problem that we just did, we had
Kirchhoff's, that it gave us current.

We then used our current and our
resistance to find our voltage difference,

and we used our voltage difference and

one node to be able to find all
of the other node voltages.

Other things we might have done, is we
might have first combined resistors in

series and parallel,
in order to make this simpler over here.

So we could have used this one first, and
sometimes we might use voltage dividers

in place of Kirchhoff's laws, or current
dividers in place of Kirchhoff's laws.

So we can use these particular sets
of equations to be able to solve for

the voltages and currents in our circuit.

In the next section of the class, what
we're going to do is add a few more tools.

Particularly, we're going to add node
voltage equations that often replace our

Kirchhoff's Laws.