Good morning! A mass, m, in a gravitational field can have gravitational potential energy,
Ug. Similarly, a charge, q, in an electric field can have electric potential energy,
Ue. We can determine the electric potential energy per unit charge, V, it is called electric
potential. Electric potential equals electric potential energy divided by Q, a small test
charge.
However, most often we are interested in the change in electric potential energy per unit
charge which is called the electric potential difference, ΔV. The electric potential difference
is the change in electric potential energy between two points per unit charge. In other
words, between any two points in an electric field, there can exist an electric potential
difference which represents the difference between the electric potential energies of
those two locations per unit charge.
This means you do not need a charge for that electric potential difference to be there.
That electric potential difference is always there, essentially waiting to provide a charge
with a change in electric potential energy. You can determine the change in electric potential
energy on a charge by multiplying the charge by the electric potential difference.
Just you know, it is not unusual for people to drop the electric from electric potential
difference and just call it potential difference. I will do my best not to do that and always
to clearly identify ΔV as electric potential difference.
Bobby, please determine the units on electric potential difference.
[Intro] - Well, ΔV or electric potential difference equals change in electric potential
energy divided by charge, so the units should be joules per Coulomb.
- That is correct Bobby. Joules per Coulomb are called volts, and the symbol is a V. Electric
potential difference is also commonly referred to as voltage. Electric potential energy is
a scalar, therefore electric potential difference is also a scalar.
- Mr. P?
- Yes Bo.
- The symbol for electric potential difference is Delta capital V (ΔV), the units for electric
potential difference are volts which use the symbol V. Do electric potential difference
and volts really use the same symbol?
- And that is irksome. Yes they do and yes that does work irk me and likely you as well...
Sorry. Okay, voltage and volts are named after the Italian physicist Alessandro Volta who
was a pioneer of electricity and power and is credited with the invention of the electric
battery. And speaking of an electric battery, the maximum possible voltage a battery can
provide between its terminals is called the electromotive force or emf. In a non-ideal
battery, the emf differs from the battery’s terminal voltage, ΔVt, because the terminal
voltage which is the electric potential difference measured between the terminals of the battery
will be less than the emf of the battery because the internal resistance of the battery decreases
the terminal voltage of the battery. Until further notice, however, all batteries are
“ideal” and therefore, the electromotive force or emf and the terminal voltage, ΔVt,
are identical.
- Mr. P?
- Yes Billy.
- I'm sorry, I missed most of that.
- That's fine Billy I'll review. So, a battery has both an electromotive force or emf and
a terminal voltage, ΔVt. The emf is the ideal maximum voltage across a battery. For example,
this 9-volt battery is advertised to have a nine volt maximum electric potential difference
across its terminals... Because it is a real battery and not an "ideal" battery, when I
measure the terminal voltage, ΔVt, across the terminals of the battery, we get 8.9 volts
which is less than the emf of 9 volts.
This is because internal resistance in the battery slightly reduces the electric potential
difference across the terminals of the battery making the terminal voltage less than the
emf.
- But you said all batteries we work with will be ideal batteries and therefore emf
and terminal voltage will be treated as the same, unless otherwise specified, right?
- Bo, that is correct. For right now, emf and terminal voltage are assumed to be the
same because all of our batteries are assumed to be ideal. Okay, be aware emf has its own
symbol which looks like a curly uppercase E. And lastly, I will point out electromotive
force is an historical term which unfortunately we still use even though it is a misnomer
because electromotive force is not a force, it is an electric potential difference.
- Electro-motive force is not a force? - That is unfortunate.
- Yeah.
- Bo, what does it mean that this is a 9-volt battery?
- It means if we measure the electric potential difference across the battery, we will get
9 volts.
- But what does an electric potential difference of 9 volts really mean?
- It's nine volts...
- I think he is asking what an electric potential difference of nine volts means.
- I think we need to go back to the equation electric potential difference equals change
in electric potential energy divided by charge.
- Okay... That means change in electric potential energy equals charge times an electric potential
difference. So, 9 volts of electric potential difference means if we put a charge there,
it would experience a change in electric potential energy equal to the charge times 9 volts.
- We could compare that to gravitational potential energy. It's like there's a cliff which we
could drop a mass off of. The mass would experience a change in gravitational potential energy,
but without the mass, the cliff is still there just waiting to give a mass a change in gravitational
potential energy.
- So, the battery is like the cliff; it's just waiting for a charge so it can give the
charge a change in electric potential energy. The electric potential difference is an electrical
cliff and is measured in volts or joules per Coulomb.
- Electric potential difference is like an electrical cliff waiting to give a charge
a change in electric potential energy... I like that Bo.
- Thanks Billy.
- Very nice, I like the cliff analogy. Okay, let’s take a look at a basic circuit with
a battery, 2 connecting wires, and a resistor.
In real life, the circuit looks like this, and the circuit diagram for this circuit looks
like this. The battery is represented by this symbol where the long line represents the
positive terminal of the battery and the short line represents the negative terminal of the
battery. And I placed the emf symbol next to the battery.
The resistor symbol is this one which looks like an accordion fold of a wire and I have
placed an "R" for resistance next to the resistor. Sometimes you will see a resistor represented
with a rectangle instead of this zigzag pattern. However, I will usually use the zigzag resistor
symbol. And the wires are represented with lines.
- Mr. P?
- Yes Bobby.
- The wires in your real circuit are not straight like the circuit diagram. Can you really draw
straight lines like that in your circuit diagram? I mean, the real wires are not straight, they
are all curly and in circles and stuff.
- That is a valid point Bobby. Remember, all our wires are considered to be ideal. So,
the resistance of our ideal wires is considered to be zero. So, the shapes of the wires does
not matter. We could draw the circuit diagram with wires which are curly and in circles
and stuff, however, that would be more difficult to understand. So, we draw wires in straight
lines and in simple patterns to make the circuit diagrams as simple and easy to understand
as possible.
- Yeah that makes - that make sense. So, wires have zero resistance so because of that, the
shapes of the wires do not really matter. Thanks.
- Now they need to determine which direction current will flow in the circuit. To do that,
we place a small positive test charge at a location in the circuit and discuss what direction
that small positive test charge will experience an electric force.
So class, you get to be the small positive test charge. If you the small positive test
charge are located on the wire, will you be pulled toward the positive terminal of the
battery or will you be pushed away from the positive terminal of the battery?
- We are the small positive test charge? I don't get.
- It's pretend.
- Oh I - I have to pretend to be the small positive test charge and see if I'm pulled
toward or pushed away from the positive terminal of the battery?? How would I know that?
- The law of charges...
- The law of charges?
- Like charges repel unlike charges attract.
- Right, so, I am a positive charge and the positive terminal of the battery is positive,
so I am repelled from the positive terminal of the battery because like charges repel.
- And actually I'm also pulled toward the negative terminal of the battery because unlike
charges attract.
- Actually, no matter where we, the small positive test charge are placed in the circuit,
we are always pulled toward the negative terminal of the battery and pushed away from the positive
terminal of the battery. So, the current is clockwise through the whole loop of the circuit
and therefore up through the battery and down through the resistor.
- Hold up... I thought negative charges, the electrons were what moved through a circuit
to create current. Why are we using a positive test charge and not a negative one?
- You did not remember the law of charges but you remember electrons are what move in
wires to cause current?
- Yes.
- Remember, we are using what is called conventional current. We define current as the direction
positive charges would flow even though we know negative electrons actually move in the
negative direction, opposite direction from the direction of conventional current.
- Sure. Conventional current is the direction positive charges would flow and electromotive
force is an electric potential difference and not a force... Very logical.
- Yeah.
- Okay. So, we have the conventional current direction correct, that's good. So, now we
have added a switch to the circuit and we have replaced the resistor with a light bulb
so we can see evidence of current flow.
As you can see with the switch open, there is no closed loop for current to flow through
so current does not flow, the light bulb does not glow, and this is called an open circuit.
With the switched closed, there's now a closed loop for the circuit to flow through... Current
does flow, the light bulb glows and this is called a closed circuit.
So again, we have an open circuit and a closed circuit. Open circuit, closed circuit, open
circuit, closed circuit, uuu hu hu! [Laughter].
- Okay.
- Just so you know, the light bulb or the resistor in the previous circuit is called
the "electrical load" of the circuit. The “electrical load” is the part of the circuit
which is converting eclectic potential energy to heat, sound, and in the case of the light
bulb, light. Because the switch and all the wires are “ideal” and considered to have
zero resistance, those items are not a part of the electrical load. The battery is not
a part of the electrical load because the battery is an electrical power source; the
battery is a source of electric potential energy.
If we were to add a wire to this circuit which bypasses the load, this would be a short circuit.
A short circuit is a circuit which has a very little resistance and therefore a very large
current. Short circuits are usually the result of some sort of accident and should be avoided
because, with a very small resistance and a constant electric potential difference,
the electric power, or the rate at which electric potential energy is converted to heat, light,
and sound, can be very large and dangerous.
- Because electric power equals electric potential different squared divided by resistance.
- So, if resistance is very small, electric power or the rate at which electric potential
energy is converted to heat, light and sound could be very large.
- That could melt things and start fires! That sounds dangerous.
- Yeah.
- Exactly... As I said, short circuits are usually an accident and should be avoided.
The danger of short circuits is one of the reasons circuit breakers exist; to prevent
electrical fires.
Actually, I'd like to go back to the electrical cliff analogy and clarify something; the proper
comparison here is that the battery is analogous to me lifting the mass and giving it gravitational
potential energy. This is because the battery gives the charge electric potential energy.
The mass falling off the cliff is like the charge going through the resistor. As the
mass falls, its gravitational potential energy is converted to kinetic energy. As the charge
goes through the resistor, it's electric potential energy is converted to heat, sound and light
if it's a light bulb.
- But Mr. P, what are the wires then?
- And what's with the triple battery?
- Oh right. Okay, Billy, the charge moving through the wires is comparable to the time
when the mass is not changing its height above the zero line. Because the wires are ideal
and have no resistance, the electric potential energy does not change while the charge moves
along the wire just like the gravitational potential energy of the mass does not change
as it rests on the ground or on the top of the cliff.
And Bo, the triple battery is exactly what you said; it's three batteries in a row represented
by one emf. I needed the battery to be taller on the screen to better illustrate the gravitational
to electrical comparison. Oh and please realize there are many, many more charges than just
the one we show moving on the wire. We're just modeling it with one charge for simplicity
sake for now.
And lastly, I've seen many symbols used for light bulbs in circuits; there's the one I
used today, there is also a circle with an X through it and a circle with a semicircle
in it which I assume represents the filament of the light bulb which glows.
I will probably just use the first one I used today. And there is no real consensus as to
whether a light bulb is two words or one word. And sometimes a light bulb is called a lamp
instead so, sometimes you will see the word lamp instead of light bulb.
So, thank you very much for learning with me today, I enjoyed learning with you.