This video is about ammeters and voltmeters - measurement devices we use
in circuits. These are the symbols for ammeters and
voltmeters. Ammeters measure the current in a wire, so literally they're
like "amp-meters." They must always be placed in series with the location being
measured (I'll explain why in just a moment) and an ideal ammeter has a
resistance of zero ohms, because any resistance would change the current
being measured. So again, I'll do some examples of that in a moment. A voltmeter
measures the voltage in a wire, and voltmeters must always be placed in parallel
with the location being measured. Again I'll explain why in just a moment. An
ideal voltmeter has a resistance of infinity ohms. It has an infinite
resistance because it needs to stop any current from moving through it and
taking away from what it's measuring. So just as an example I can see here that,
using V = IR and the equivalent resistance of the circuit is 5, that
the total current moving through this circuit is 2 amps. So if I were to
place an object to measure the current, I need the current going through that
measurement device to be the same as the rest of the circuit, so I would place it
in series with the rest of the circuit because the rule is that in series the
current stays the same for all objects, so that 2 amps is also going through
that ammeter, and because this is zero ohms the total equivalent resistance of
the circuit is still 5 which means that the total current is still 2, so
if we keep this at 0 ohms it's not going to affect the current at all. So we
would say the ammeter reads two amps so we would know that 100% because we know
that 2 amps are flowing through the region where the ammeter is placed. We
call an ammeter with 0 ohms an ideal ammeter, so this is an example of an
ideal ammeter. We put it into the circuit without it affecting our measurements at
all. So because it perfectly measures the circuit itself without affecting the
results, we say that it's an ideal ammeter so zero ohms of resistance means
an ideal ammeter. Now let's imagine that we place an ammeter down that does not
have a resistance of 0. Let's say it has a resistance of 5 ohms as an
example. I can see now that the equivalent resistance of the circuit is
2 plus 3 plus 5 because the ammeter is in series with the other resistors, so
that's going to mean that the current is now 1 amp because V = IR. So 10
volts divided by 10 ohms of resistance is equal to 1 amp of current, so this
ammeter is now changing the current that it's supposed to measure, which is bad. We
do not want our measurement devices to change what we're trying to measure. So
this is an example of a non-ideal ammeter. This is something that's
changing the results and unfortunately in the real world all ammeters are
non-ideal to some extent. Most of them have very low resistances and we can get
very close results, but there's no true ideal ammeters. Now we can add a
voltmeter and measure the voltage with it. So I'm going to imagine that we're
measuring the voltage across this 3 ohm resistor, so to do that according to our
rule we need to put the voltmeter in parallel with the part of the circuit
that we want to measure the voltage of. So here I want to know how much the
voltage drops as the current crosses the 3 ohm resistor, so I put that voltmeter
in parallel with the 3 ohm resistor so I'm gonna take a moment to show you
why it is that we place that in parallel and why it is that we need that
voltmeter to have an infinite resistance. So I'm going to show you both right now.
So to build up your intuition on this we don't want any current moving through
that voltmeter. Ideally the voltmeter wouldn't be affecting how much current
is moving through the 3 ohm resistor. It wouldn't be taking any for itself, it's
just leaving the current to move through the 3 ohm resistor. So if that voltmeter
has an infinite resistance, and resistance is the voltage drop over the
current. That means that infinity is equal to the voltage over the current,
and that basically leaves two options: either the voltage is equal to infinity
or I is equal to zero, because as a denominator approaches zero the value
approaches infinity, and we know that the battery isn't giving infinite voltage to
this circuit. So the only other option is that the current in the voltmeter
specifically is zero. So if we make that resistance infinite, no current will pass
through the voltmeter, leaving the current in the circuit unaffected. I can
also show that the equivalent resistance for that parallel part of the circuit
(because one over infinity is the same as zero)
is just going to be three ohms. So because the resistance of the voltmeter
is infinite, the equivalent resistance of that parallel part of the circuit is
just the same as if the voltmeter weren't even there, If it were just the 3 ohm
resistor. So this is good we want ideal ammeters and voltmeters to basically
behave as if they're not there. They're just measuring what's already present
without affecting it at all, so this is the reason why we want an infinite
resistance in volt meters so because the total resistance in the whole circuit is
still 5 ohms, and the voltage is 10, the current is still 2 ,and because no
current is going through the voltmeter itself, all that current is going through
the 3 ohm resistor. So I can see that the voltage drop is 6 in the 3 ohm resistor
using V = IR. And because the voltage is the same for all paths in
parallel, that means that the voltmeter is also experiencing a 6 volt drop. So
because that's moving through the voltmeter as well, the voltmeter can
detect that and that's how we read the voltage drop on the 3 ohm resistor, by
putting the voltmeter with infinite resistance in parallel with it. So we
would say the voltmeter reads 6 volts and this is an ideal voltmeter because
it is not affecting the voltage drop of the circuit. We can measure any region
that we want with a voltmeter. For example, we could put it like this and in
this case we're measuring the voltage drop across both the 2 ohm and the 3 ohm
resistor, and again we're giving this infinite resistance, and so this is still
a 2 amp current, and so therefore the voltages are still 4 and 6. So altogether
the total voltage here is 10, and you can also prove that that's 10 by saying "oh
well those two resistors are in series, so they add up to 10" and the total
resistance on one side of a parallel circuit is the same as the other. So in
the voltmeter that total voltage in the voltmeter must equal the voltages in the
other side, so when you add those together you get 10. So again the
voltmeter is just measuring that total voltage drop across that region. So here
we would say the voltmeter reads 10 volts. If we put it over here there's no
voltage drop. All the voltage is happening here in the resistors, so
because there's no voltage out there, if we put the voltmeter there
that would just read 0 volts. Now let's look at a non-ideal voltmeter. I'm
going to give this voltmeter a very high resistance but not an infinite
resistance, so this is 1 kilo-ohm, or 1000 ohms. If I plug this into my equivalent
resistance equation, I can see that the equivalent resistance of that part of
the circuit is going to be 2.99 ohms. So very close to 3 ohms but not quite.
Because the voltmeter is not ideal it is ever so slightly decreasing the
resistance of that part of the circuit. So when I add this to the 2 ohm resistor
and then use the V = IR I find that the current moving through the circuit
is 2.004 amps, which is just a little bit too big. It's just a
little bit bigger than what we had before, so I can see that the voltage
drop in that first resistor is going to be 4.008 volts. So that means that
because the total voltage is 10 and it dropped 4.008 volts the second
voltage drop across that parallel arrangement is going to be 5.992
volts here and here. So the voltmeter ever so slightly
changed the voltage that it was trying to measure because it didn't have an
infinite resistance. So you would say that this is a non-ideal voltmeter. Any
voltmeter with a non-infinite resistance is not ideal. There are going to be
specific problems that ask you where you should place voltmeters and ammeters to
measure the voltage and current in different resistors, so just as an
example I'm just gonna throw a bunch on this circuit and tell you what each one
is measuring. So this one can measure the voltage drop across resistor 1, this
one measures the voltage in resistor 2, resistor 3, resistor 4, we can also
measure across both resistor 2 and resistor 3 or across the whole
parallel arrangement like that, or even across all the resistors in the circuit
together. For the ammeters, this ammeter can measure the current moving through
resistor 1, which you can see is also the total current in the circuit. If we
placed it right here it would measure the current in resistor 4 and if we
placed it right here it would measure the current in resistors 2 and 3.