Now that we've discussed electricity and how to discuss quantitatively
electricity, as well as some of the variables there, we're ready to talk about circuits.
To contextualize this, remember that we've already discussed all of our mechanics
and we'll be discussing magnetism after we cover
how electricity flows through all the circuits we're going to get into.
We'll start this by first introducing the two main ingredients of a circuit
that we'll need to remember and know how to deal with.
Those are resistors. So we'll talk about Ohm's law and resistors now
and then we'll talk about the other ingredient
which is a capacitor and then finally going to more complicated circuits
and see how to work with resistors and even capacitors in bigger circuits as well.
So let's start with Ohm's law and what a resistor is.
In order to introduce this topic, we first need to have an idea about
how we discuss the different variables that can be applied on a circuit
and then we'll discuss Ohm's law which gives us a relationship
between the variables that we introduce
and then finally we'll talk about resistors themselves
and how to deal with them on a circuit and how to add them together.
So first let's introduce three variables: the voltage, current and then the resistance.
The current in a circuit which will be one of the most important quantities
that we're trying to find or measure is telling you how much charge per second
is flowing past a given point. So for example in this wire that we have here,
we have a wire with current flowing through it.
That's all these electrons that we've shown moving here
and then they're all flowing past this dotted line,
this particular point in our circuit and current is measuring how many electrons
are passing this point in a given amount of time in a given second.
We measure therefore the current exactly as you would expect.
It's the number of coulombs, the amount of charge passing a given point per second
and we call this coulombs per second in Amp.
So amps which is symbolized by the letter A is telling us how much current is flowing in a circuit
or how may coulombs per second.
Interestingly, something important to know is that by historical convention,
again something of a historical accident,
we actually measure current in the positive direction.
So even though electrons themselves the actual electricity of the electrons
flowing through the circuit is the flow of negative charges
which is what the electrons are, we define current to be the flow of positive charge
which is to say the actual protons positive charges are moving
is just to say that the flow of positive charge is defined in the opposite direction
as the flow of negative charge. And usually, this won't be problem,
not something you have to actually worry about
but if you do see electrons drawn on the circuit flowing
always keep in mind that the current by definition
is defined in the opposite direction of that electron flow.
The second quantity that we actually be familiar with is the voltage.
We've already discussed the voltage in the sense of just electricity
and electric fields and the electric potential
but we're going to talk about voltage in circuits
as the energy per coulomb again except this time
we'll probably more think about the voltage as a pressure
in terms of trying to push the electrons to the circuit.
We'll talk about batteries as well and how these batteries are acting as pumps,
sort of pushing the electricity through your circuit.
So if you see this battery on the bottom here,
the way we talk about this battery is that the positive side of the battery
is the side with the longer line. So we represent the battery in this sort of series of lines
which is in fact representative of the cells, the battery cells
that are in this cell or battery and we always, by convention,
discuss the positive side of the voltage where which pushing
the current in the positive direction as the part of this battery with small line,
big line, small line, big line that ends in the bigger line
and so again this battery is a sort of a pump for our circuit.
It's trying to push the electricity to flow through the circuit.
Now, when we have a particular voltage flowing and pushing
rather a current through a particular circuit,
we can ask ourselves the exact same kind of question that we asked with fluid flow.
When we had fluid flow, we talked about the pressure,
how much pressure we were applying to a system
and then ask for a given amount of pressure how much current,
how much flow rate as we call it there was going to flow through our circuit.
And we saw that that dependent on the resistance of the circuit
and so in that context, we call it the Circuit Law for the Flowing Systems.
In this case, we are actually introducing the circuit law
by writing down the resistance as the ratio of the voltage,
the amount of pressure we apply per amount of current that we get out.
The resistance, this quantity that we've just introduced,
has units of volts per amp since it is the voltage divided by the current.
So we call one volt per amp an Ohm
and is represented by a capital Greek letter omega as you see here.