mr.p: Good morning. Today we're going to
review the electricity topics
covered on the AP Physics 1 exam.
Bo: Hey guys.
Billy: Hey Bo.
Bobby: Hi Bo.
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mr.p: Unlike electrostatics where charges were stationary,
electricity deals with moving charges.
The AP Physics 1 curriculum deals mostly
with charges moving on a wire,
so that's what we're going to concentrate on.
Current, the symbol for which is a capital I,
is the rate at which charges move.
If we could see the charges on the wire,
we could count them as they could by.
We could multiple by the charge of each particle
and then we could divide by the time
and that would give us the current.
The dimensions for current are coulombs per second
which are called amperes, or amps,
the symbol for which is a capital A.
Bo: Oh man. A stands for amplitude too.
Bobby: I hate it when they use duplicate symbols.
mr.p: (laughter) Yeah, me too.
It is important to understand
that current flows best through conductors
and conductors are materials that have electrons
that are free to move around rather easily,
called free electrons.
And, generally, conductors are metals.
Also, we're talking about conventional current
which is the direction that positive charges would flow
even though we know what is usually happening
is that negative charges are flowing
in the negative direction.
I forgot to mention that amperes are a base SI dimension
and coulombs are actually not a base SI unit,
so please be aware of that.
Next let's define resistance.
Resistance equals rho, the resistivity of the material,
multiplied by L, the length of the wire,
divided by A, the cross-sectional area of the wire.
Billy: I thought rho stood for density.
Bo: It does. Bobby: It does.
mr.p: Bo, what is the difference
between resistance and resistivity?
Bo: Resistivity is a material property
so it only depends on the substance
of which the material is made.
Resistance also depends on the geometric shape of the wire.
A longer wire means more resistance,
a bigger cross-sectional area means less resistance.
mr.p: True, but Bobby, what is resistance?
Bobby: Resistance is how much the resistor restricts
the flow of charges in the wire.
Increasing the resistance, decreases the rate
at which charges flow.
Billy: So, the current is decreased.
Bobby: That's what I said.
Bo: Assuming everything else stays the same.
Bobby: Right.
mr.p: Which brings us to electric potential difference,
or delta V.
Electric potential difference is the change
in the electric potential energy per charge.
The dimensions for electric potential difference
are Joules per coulomb, which we call volts, upper case V,
which means that the dimensions for resistance
are volts per amp, which we call ohms.
And the symbol for that is an upper case Greek letter Omega.
Billy: Which looks like an upside-down horseshoe,
remember Bobby?
Bobby: Yeah, I remember.
mr.p: Okay, let's draw a basic circuit.
Okay, so you can see we have all these wires
which, unless otherwise stated, have a resistance of zero.
This is the symbol for a resistor.
This is the symbol for a battery
where the longer line is the positive terminal
of the battery and the shorter line is the negative terminal
of the battery.
And delta V sub t stands
for the terminal voltage of the battery.
Which is the electrical potential difference
actually measured between the two terminals
of the battery.
This is a switch which is currently open
which means there is no current flowing in this circuit.
Billy, when I close this switch,
which direction will the current flow?
Billy: When you close the switch, because like charges repel,
the positive charges will be repelled
from the positive plate of the battery,
and because unlike charges attract,
the positive charges will be attracted to the negative plate
and, therefore, current will be in the clockwise direction.
mr.p: Let's take a look at a circuit with a battery
and two resistors in series.
Again, the current is going to be in a clockwise direction.
And because the charges have nowhere else to go,
every charge is going to go
through resistor one, resistor two, and the battery,
all the currents will be the same.
And because a charge moving all the way around a loop
in a circuit must end with the same
electric potential energy it started with,
the electric potential difference
all the way around a loop is equal to zero.
This is called Kirchhoff's Loop rule.
Which means the sum of the electric potential difference
across the battery and the electric potential difference
across the resistors adds up to zero.
And notice the electric potential difference
across each resistor is negative
because charges lose electric potential
as they go across a resistor
in the direction of the current.
Therefore, the electric potential difference
across the battery is equal to the sum
of the electric potential differences across the resistors.
And we can substitute in current times resistance
for all three electric potential differences.
To get the current across the terminals of the battery
times the equivalent resistance of the circuit
is equal to the current through resistor one
times the resistance of resistor one
plus the current through resistor two
times the resistance of resistor two.
Billy: Oh, and all three currents are the same
so they cancel out.
mr.p: Which gives us the equation
for the equivalent resistance
for resistors in series.
Now, it is important to remember
when resistors are in series, Bo?
Bo: When the charges have no other route to go through
other than both resistors.
Billy: Right, after a charge leaves resistor one
it must go through resistor two
so the two resistors are in series.
mr.p: Which means, these two resistors are in series
even though they are drawn parallel to one another,
and these two resistors are in series
even they are also drawn parallel to one another.
Speaking of parallel ...
These two resistors are in parallel
and using Kirchhoff's Loop rule,
we could show that they all have the same
electric potential difference.
Also we know that because of conservation of charge,
which states that the total charge
on a closed circuit will stay constant,
that the net current going into this junction
will equal the net current coming out of this junction
which is called Kirchhoff's Junction rule.
Which means, the current delivered by the battery
which goes into this junction
will equal the sum of the current
going through resistor one and resistor two
because they both go out of that junction.
And we can substitute in
electric potential difference divided by resistance
for each one of these currents.
And we get the electric potential difference
across the terminals of the battery, the terminal voltage,
divided by the equivalent resistance of the circuit
is equal to the electric potential difference
across resistor one divided by the resistance
of resistor one plus the electric potential difference
across resistor two divided by the resistance of resistor two.
Billy: Oh, and all three electric potential differences
are the same so they cancel out.
mr.p: Which gives us the equation
for the equivalent resistance
for resistors in parallel.
And, Bobby, please remind us,
when do we know resistors are in parallel?
Bobby: Two resistors are in parallel
when their electric potential differences are the same.
Bobby: Which means these two resistors
which you might initially think are in series
are actually in parallel.
mr.p: Okay, remember when you add a resistor in series,
you increase the equivalent resistance of the circuit.
And when you add a resistor in parallel,
you decrease the equivalent resistance of the circuit.
Okay, now let's talk about electric power.
Electric power equals current
times electric potential difference.
And just like mechanical power, it is in Joules per second
or watts and it is the rate
at which electric potential energy is being converted to,
primarily, heat and light.
And we can also get electric power
in terms of current and resistance.
Substituting in current times resistance
for electric potential difference,
gives us electric power equals current squared
times resistance.
And substituting in electric potential difference
divided by resistance for current,
gives us electric power is equal
to electric potential difference squared
divided by resistance.
Each of these three equations
for electric power is useful to know.
Okay, let's do an example problem.
In this circuit, the battery has a terminal voltage
of 6.0 volts and each resistor has a resistance
equal to its name.
Let's find the rate at which energy is being
dissipated in resistor two.
Bo, please get us started.
Bo: Well, resistors two and three are in parallel
because the electric potential difference
across each of them is the same.
Billy: Are you sure?
One and three look like they are in series to me.
Bobby: One and three are not in series
because a charge that goes through resistor one
could then go through either resistor two or three.
For two resistors to be in series,
every charge has to pass through both resistors.
mr.p: You are correct Bo that the electric potential difference
across resistors two and three are the same.
Let's take a look at that.
Now, remember the resistance of wires is equal to zero.
Therefore, the change in electric potential
across a wire is going to be zero.
Therefore, this wire right here is going
to have the same electric potential at every point.
Therefore, these points on these three resistors
will have the same electric potential.
It also means that this point
on each of these two resistors will be
at the same electrical potential, again,
because there's zero change in the electric potential
along this wire.
Which means the electric potential difference
across resistor two and the electric potential difference
across resistor three will be the same.
[mr.p] And Billy, resistors one and three are not
in series because the charge that goes through resistor one
could then either go through resistor two
or resistor three.
Bo, please keep going.
Bo: Therefore the equivalent resistor two-three
equals the inverse of the sum
of one over resistance two plus
one over resistance three.
So the inverse of one over two plus one over three
which is 1.2 ohms.
Then we know resistor one and equivalent resistor two-three
are in series which means
the equivalent resistance for all three resistors
equals the resistance of one
plus the resistance of equivalent resistor two-three
which is one plus 1.2 or 2.2 ohms.
Then we can figure out the current delivered
by the battery because we know the terminal voltage
equals the current delivered by the battery
times the equivalent resistance.
We can rearrange that to solve
for the current delivered by the battery
equals the terminal voltage divided
by the equivalent resistance
or six divided by 2.2
which is 2.72 amps
with the 72 repeating.
We know that is the same current
that passes through resistor one,
so we can determine the electric potential difference
across resistor one because it equals
the current through resistor one times its resistance
or 2.72 times one which is 2.72 volts.
Then we know the terminal voltage equals
the electric potential difference across resistor one
plus the electric potential difference
across resistor two-three
which means electric potential difference
across equivalent resistor two-three
equals the terminal voltage minus
the electric potential difference across resistor one
or six minus 2.72
which equals 3.27 volts
with the 27 repeating.
And we know that is the same as
the electric potential difference across resistor two.
Then we can use the electric power
across resistor two equals the electric potential difference
across resistor two squared
divided by the resistance of two
which is 3.27 squared divided by two, that is
5.35537
or with two sig figs,
5.4 Joules per second which is watts.
mr.p: Thank you Bo. That was really well done.
We have reached the end of my review of electricity
for AP Physics 1.
My next video has to do with what equations
I would suggest that you memorize
for the AP Physics 1 exam.
You are welcome to enjoy that video.
You can also visit my website
flippingphysics.com where you will find
all of my AP Physics 1 review lessons
organized with lecture notes.
Thank you very much for learning with me today.
I enjoyed learning with you.