Now, how do we measure current
and voltage in a circuit?
Even in the digital age,
we use the same concepts.
But let me show you this
with an analog multimeter.
You'll notice this
one's been stripped down
just a little bit.
There used to be a needle here,
and there's a bar magnet right
here, and there's a coil--
it's called a moving
coil-- in here.
You can just see
maybe the copper
wires moving around the coil.
As I move from one range
to another run function,
all I'm doing on
the back is I am
moving to a different circuit
with different resistors.
So let's talk about
how this works.
First off, the analog voltmeter.
Here's my circuit down here.
I've got a DC battery
or a DC power supply,
and the load, which is hard to
read, but really does say load.
And I hook up the
voltmeter in parallel.
Here's my voltmeter right here.
So I put the leads
on in parallel.
And I've got the meter resistor.
And the meter resistor is huge.
The meter resistor
is way, way bigger
than the load resistance.
This might be 20
ohms or 100 ohms.
This is going to be like
2 and 1/2 million ohms.
So if you're an
electron and you're
heading through
this circuit, you
can either go up this
path or this way.
And this way has got
100 ohms, and this way
has got 2 and 1/2 million ohms.
So most of flow is
going to go this way.
But the nice thing
is the voltage
across the load is the
same as the voltage drop
across the resistor because
they're in parallel.
So the voltage across the
load is equal to the voltage
through the meter.
OK.
Now, here's the clever bit.
This is a permanent
magnet, just a bar magnet.
And this is a
spring-loaded needle,
and it's got numbers up
here, and it tells you
what kind of current, or in
this case, what kind of voltage
you have.
This wire comes up
and it wraps around.
This cylinder is
attached to the needle.
And the wire wraps around
the cylinder many, many,
many times.
If I looked at it from the side,
it would look more like this,
but much denser--
lots of copper wire.
And when you wrap the
copper wire around
and you run a current through
it, it's an electromagnet.
So I've got this.
As I run current through here,
I turn on the magnetic field.
And the bigger the current,
the stronger the magnet.
And as the magnetic
field increases,
it drives this to
rotate towards this pole
of the permanent magnet,
and it moves the needle.
So what you do is you
just set full scale.
You say, that's
going to be when I've
got maybe 20 microamps of
current flowing through.
That'll be a strong
enough magnetic field
to drive this full
scale, and then
I just set all the
other ranges that way.
With a knob, I can switch
to different resistances,
and so I can adjust the scale.
For example, let's say,
example, voltmeter.
Let's say-- there's my needle
moving in this direction--
that the maximum current
through the moving coil--
I'll call it MC, because
this is the coil.
It's a moving coil.
Maximum current through the
moving coil is 20 microamps.
And let's say the
resistance of the meter
that I've got hooked
up right there
is 2 and 1/2 million ohms.
Well, what would the
full-scale voltage be equal to?
What number should I put?
When it's pegged all the way
over here, what's that reading?
Well, the voltage
for full scale is
going to be the full-scale
current of the moving
coil times the resistance to the
meter that you've switched to.
And that's going
to be 20 microamps.
Well, instead of micro--
micro means times
10 to the minus 6.
So I'll write 20 times 10 to
the minus 6 amps times 2 and 1/2
times 10 to the sixth ohms.
And I wind up with 50--
10 to the minus 6 and 6 is 0--
50 volts.
So that would be
your 50-volt scale.
That's a pretty cinchy
way to do things.
How about the ammeter?
Oh, and by the
way, it's linear--
the magnetic field.
So if I was wondering
what half-scale would be,
I'd be running 10 microamps, and
straight-up would be 25 volts.
So it's a linear relation.
So you just put the needle on.
It's pretty nice.
Now, for the ammeter, I
want to measure current.
I run it a little
bit differently.
This right here is
the moving coil side.
And I run-- let's see.
I've got to hook it
up in series, too.
But I'm going to
run a shunt here,
and the shunt resistor
is usually a fuse.
There's the shunt resistance.
And I've got to hook
this up in parallel,
so I'll just run it like that.
Stick my resistor
here for the load.
Yeah.
So now I've got an ammeter.
Notice that now the shunt
resistor and the resistance
in the moving coil,
which is not much,
but it's more than the shunt--
they're in parallel.
So the voltage drop
across the moving coil
is the same as the voltage
drop across the shunt.
Now, with Ohm's law, voltage
is current times resistance.
So the current through
the shunt times
the resistance of the shunt
is equal to the current
through the moving coil times
the resistance for the moving
coil.
It's designed so that the
resistance of the shunt
is way, way less than the
resistance to the moving coil.
That means that
most of the flow is
going to go through the shunt.
So let's see.
I solve for the shunt
current, and the shunt current
is pretty much the total current
because it's so much bigger
than the moving coil current.
And if I solve for the shunt,
that's equal to the current
through the moving
coil, and we know
what full-scale is,
times of resistance
through the moving coil divided
by the resistance of the shunt.
So let's see.
The shunt would be much less.
So if the moving coil
current was 20 microamps
and the resistance of the
moving coil was maybe 2 ohms
and the resistance in
the shunt is 0.2 ohms,
then the current would read--
let's see.
It would be 20 microamps times
the resistance in the moving
coil, which is 2 ohms,
divided by 0.2 ohms,
which would be 2 times
10 to the minus--
let's see.
20 microns-- that's 40 microns.
2 times 10 the minus 5 is 2
times 10 to the minus 3 amps,
which would be 2 milliamps.
There are lots of
other transducers.
We've talked about
a few basic ones.
But even just the concepts
we've talked about,
they're applied to all kinds
of different situations.
Where you drive up
to traffic lights,
underneath the pavement,
there's a little loop
of wire attached to the post
with the traffic light is,
and it's running an AC current.
And when your car pulls up,
the conductors in your car,
they feel that magnetic
field sloshing.
And it sloshes them, and
that causes a back-slosh,
which depresses the current
and tells the traffic
light that there's a car
there and it should change it.
So many of these concepts are
applied so many different ways.
So if you look at a transducer
and it looks like it's magic,
it's probably something
that we can all understand.
