So we´ve introduced some key components to what makes up a circuit.
So now we´re going to get into a few of the more advanced topics of circuits.
So we´re going to get into something like this where we have a few more components.
So first, we´ll talk a little bit more about the circuit properties
as well as how to measure those properties.
Then we´ll talk about Kirchhoff?s law about how we measure voltage
as it drops throughout a circuit. Then we´ll talk about the conductivity
as oppose to the resistivity that we already introduced
and then we´ll end with a brief overview of AC or alternating current circuits
but first, let´s talk about some circuit properties and how we measure those properties.
So first of all, it´s important to know that voltage in a parallel circuit
will drop the same way across both parallel paths.
In other words, if we have a voltage coming into a circuit like we have here.
It can take one of two paths as we´re tracing our way through a circuit.
The amount that the voltage is dropped across either the top path or the bottom path has to be the same.
So, delta V1 or the change in the voltage across the top path
and delta V2 or the change in voltage across the bottom path have to be the same
and the reason for this is that if the voltage difference across maybe the top path
as opposed to the bottom path were different, maybe higher,
then we would have a lack of equilibrium in the system.
There would be too much pressure in one and not enough pressure in another,
and anytime this happens in a circuit, the circuit very, very quickly equilibrates as we say
and for this reason the voltage drop across either path always has to be the same.
On the other hand, exactly the opposite,
the current that is flowing into this junction when it crosses that junction will have to split.
In other words, some of the electrons that are flowing
will have to take one path and the other ones will have to take the other path.
So, the current will do the exact opposite of voltage
and not be the same over both paths but will instead split into two paths, I1 and I2.
Because the total current is conserved, I1 plus I2 will still be equal
to the amount of current that came into the system
and then when I1 and I2 recombine, we´ll have the same amount of current again on its way out.
In series, we have the opposite situation.
In series, the voltage drops are the thing that can be different.
For example, the current going through each of these resistors.
We´ve already seen that the voltage drop depends not only on the current going through the resistor
but how much resistance each resistor has
and so the voltage drop in series going through each resistor
can be different for each resistor. On the other hand the current,
again because current is conserved, will be the same through both resistors
because it doesn´t have anywhere else to go
and so whatever current is in this first resistor here has also to be in the second resistor.
Now we´re going to talk a little bit about how we practically measure quantities like the voltage.
First of all, the voltage is measured by a volt meter and again voltage is about a difference.
It´s about a difference in pressure between one point in your system and another.
So, we measure in fact differences in voltage.
To measure that difference, we could for example measure the voltage
across this battery and in this case, if we had a 12 volt battery,
our volt meter would measure for us 12 volts
because the difference in the voltage from one side of this battery to the other
is exactly that, it´s going to be 12 volts.
We could also do the opposite and measure the voltage drop across a resistor
and as we´ve discussed with Ohm?s law,
the amount of voltage difference that our volt meter would read in this case
is equal to the current going through that resistor times the resistance in that resistor.
Let´s look very quickly at what a volt meter is
if we actually got to peer inside and see how it works.
The way a volt meter works is that if I opened up the lid
if you will and see in black here exactly the components of a volt meter.
We have a resistor as well as the circle with a G which is called the galvanometer.
First of all, the resistor that we would put in parallel
with the normal circuit which has a normal resistance in it,
this resistor inside the volt meter is a very, very high resistance
and there´s a reason we do this.
This high resistance that we put in parallel with a normal resistor in the circuit
will have a total resistance that is approximately unchanged
and the reason we know that it will be unchanged is that if I wanted to add
the resistance of the normal resistor in the circuit to the very high resistance
that we have inside our volt meter,
because they´re in parallel we would use our parallel addition law for resistance
saying that the 1 over the total resistance will be
1 over each of the individual resistances. However, if R in this volt meter,
R sub v, is a very, very, very large number then this second term in our equation,
1 over R plus 1 over Rv. That 1 over Rv term would be zero or close to zero
because we have a very high resistance in our volt meter.
What this does is simplifies the equation for the total resistance experienced down to 1 over R again.
In other words, the total resistance is still very close to the actual resistance
in the circuit so we are not too worried about accidentally changing the circuit itself.
Once we have this parallel resistor which causes there to be a very high resistance in the volt meter,
very little current will flow through the volt meter
because there?s this great resistance to taking that path.
This very tiny current is measured by this galvanometer
and that´s the key thing to know about galvanometers,
you don´t need to memorize a lot of what we?re going to talk about,
about the inner workings of these mechanics
but it is good to know that a galvanometer can measure these very small currents.
When we measure this current, it will be easy for us to switch it
into a voltage or interpret what voltage must have gone through it
because we already know because we designed the volt meter
exactly what this high resistance is in a circuit with a galvanometer.
An ammeter which measures the amps or measures the current in a circuit
operates in the other way, rather than being put in parallel with the circuit,
it´s put directly into the circuit so that the wire has to go through the ammeter.
The inner workings of an ammeter are slightly different than that for a volt meter.
What we have instead is a small resistor in parallel
and a very large resistor in series
and we do this for the same type of reason that we did for the volt meter.
We will have a small total resistance, R sub p, for R parallel
and this parallel resistance when we add it in parallel
with the small resistance in series with the regular circuit,
will have the same sort of effect that we have with the volt meter
that the resistance in parallel is so great that this term in the addition of the resistances here
that is 1 over R parallel will approximately be zero because R parallel will be such a great value.
So when we put these two resistances together,
we get that the total resistance introduced into the circuit by our ammeter
is just going to be the resistance from the very small resistor.
In other words as we would hope,
we have a very small resistance added to our overall circuit
because we don´t want to change the dynamics of the circuit,
we just want to measure what´s happening in the circuit
and again once we´ve done this, and because we have a very small resistance in series,
we´ll have some current going through our galvanometer
and as we said the galvanometer measures current and so for an ammeter,
the galvanometer will be able to measure that current directly.