In this video we talk about physically what's going on when a capacitor is charged
we introduce the idea of capacitance for a parallel plate capacitor we talk about
the units of capacitance and we finish with a couple basic examples of capacitance calculations
so a parallel plate capacitor is just two conductive plates separated by a gap
so you should know that real capacitors are usually made by using two thin strips of foil
separated by a piece of paper but this parallel plate capacitor idea is a useful starting point
so in the circuit we're looking at here we have a battery on the left and that
battery maintains a potential difference of v across its terminals that's what a battery does
we have a parallel plate capacitor on the right and it's currently uncharged and we have a switch
that allows us to complete the circuit and begin the charging process it's important to realize
here that batteries don't create charge but they do cause charge to move around such that
the potential difference across the terminals is equal to v so when we close the switch charge
begins to flow in this circuit and positive charge is going to build up on the upper plates
until the potential there is equal to the potential at the high side of the battery
and then the charge flow is going to stop but there's a really important question where did the
plus charge come from and since batteries don't create or destroy charge this positive charge
must have come from removing a charge of q from the bottom plate so when we talk about the q in
a capacitor q is just the magnitude of the charge on one of the plates so there are two different
ways to look at how this charge separation arises and the first way is to say that positive charge
was moving clockwise in the circuit in other words we were taking plus charges from the
low side of that capacitor we were pumping them up to this high potential through the battery
and they were landing on the high plate of the capacitor and this process terminated once the
potential difference across the capacitor was equal to the potential difference of the battery
now this is good for most practical purposes but we know the real story is that atomic nuclei are
fixed in place and it's the electrons that are the charge carriers and the electrons are negative so
in this view of things we have electrons moving counterclockwise through the circuit so what's
happening here electrons from the high side of this capacitor they're attracted to that plus
terminal of the battery they end up popping out the negative side building up on the low plate of
the capacitor so how do i get the plus q on the high side of the capacitor that's a deficit of
electrons the minus q on the other plate is an excess of electrons so this is what's actually
happening physically all right so how do we measure how good a capacitor is at storing charge
that's called the capacitance and the capacitance is the charge per unit potential difference
if we look at the units of capacitance it might clarify what i mean a little bit
the units of capacitance and be careful i'm using c in two different ways here on the left that's
the capacitance on the right it's the units of charge coulombs coulombs per volts these units
get a special name they're called ferrads and maybe to aid your intuition here this definition
of capacitance it means that if a capacitor was twice as big it would store twice as much charge
for every volt of potential difference all right let's look at a couple simple examples in the
first example we have a 100 microfarad capacitor charged to a potential difference of 5.5 volts
and i want to compute the magnitude of the charge on each plate that's the q from the
formula so if i want the q from the formula let's just turn the formula around and write q equals cv
and i have a 100 microfarad capacitor i'm just going to go ahead and leave the prefix of
micro in there and i have 5.5 volts of potential difference across the plates and this gives me 550
micro coulombs of charge so that's one way to answer the question correctly
if you want to write it in scientific notation that's 5.5 times 10 to the
negative 4. coulomb's just replacing that micro prefix with 10 to the negative six
that's how i arrive at my scientific notation answer in our second example
we're told that by observing the current over a period of time as a capacitor charges to 6.3 volts
we're able to measure a total charge transfer of 3.2 coulombs so i actually did this in the lab a
couple days ago and i'll just go ahead and link to that video right now so in this problem we
know the potential difference and we know the amount of charge separation on the plates so
we should be able to get the capacitance from our basic definition charge per volt and so i
put in my 3.2 coulombs of charge by 6.3 volts of potential difference and i end up with zero points
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