[islandlabs] Electrostatics: What is a 1 Farad Capacitor?

Burns, William burns at cshl.edu
Mon Sep 21 22:29:38 EDT 2009


Hey:

Another question came up at the last meeting:
"What is a Farad?"

Also, there seemed to be a question about what a capacitor actually was,
so the second question could be:
"What is a capacitor?"

As per usual, I gave the best answers I could at the time, but without
the feeling of confidence/conviction that the subject deserves.
After spending some time w/ Google:


WHAT IS A CAPACITOR?
A capacitor is a tiny battery for storing electrical charges.
It will conduct electricity for only a brief period until it is filled
then (as a battery does) can apply it's small charge to other parts of a
circuit.
note 1: I say "tiny battery" because most of the capacitors we see are
very small. 
note 2: Originally, the term "battery" referred to collections of
capacitors, and was later applied to the electro-chemical devices that
we call batteries today.


HOW DO CAPACITORS WORK?
Capacitors work by storing opposing (positive and negative) charges.
Conductive elements (like wire, or tin-foil) have free electrons that
can move about "freely".
If a voltage is applied to a pair of parallel wires: (where the wires do
not touch each other, one wire gets a positive voltage applied to it,
and the other wire gets a negative voltage)
Some negative electrons will be drawn (borrowed/donated) out of the
"positive" wire, and an equal number of electrons should be pushed into
the "negative" wire.
The wires are now said to be the charged elements of a "charged"
capacitor. This is slightly misleading. Even though one wire has "too
many" electrons, and the other wire has "too few", the *net* charge on
the *pair* of wires remains the same.


CAPACITY
Capacitance measures how "easy" it is for a capacitor to store large
numbers of electrons in the negative element, and "donate" from the
positive element.
The electron "capacity" of these pairs of elements varies
proportionately w/ the "area" of the element, and inversely w/ the
distance between them.
So, widely spaced wires would have a much lower capacity for
storing/donating electrons than closely spaced sheets of conductive
foil.


HYDRAULIC ANALOGY (for how capacitors work)
I like the "balloon" analogy for capacitors.
Imagine that wiring is like plumbing, a battery is like a pump, and
voltage is like the pressure created by the pump.
A capacitor would be like a wide section of pipe that had a balloon
stretched across it's opening before being fitted together w/ another
section of pipe.
Water can be pumped through the wide pipe until the pump pressure is
matched by the balloon. The balloon stores that water until the pressure
is relieved, and then it pushes the water back the way it came.
If the wide capacitor_pipe were in parallel w/ the pump, the
capacitor_pipe could maintain water pressure in the event of a (very)
brief pump failure.


WHAT IS A FARAD?
When asked what a farad was, I answered that it's a measure of charge.
Really, it's the coulomb that measures charge.  (roughly 6.24*10^18th
electrons worth)
The Farad is the measure of capacitance.

To be more correct, I should have said that: 
The farad is a unit for measuring the charge required to raise the
potential-difference across a capacitor by 1 volt.
A 1 Farad capacitor would read 1 volt, when it was holding a 1 coulomb
charge.
A 1000 microfarad (MFD a.k.a uF) capacitor would read 1 volt when
holding a .001 coulomb charge, would hold .012 coulombs when connected
to a 12-volt battery, or read 1000 volts when holding a 1 coulomb
charge. (if it didn't explode first)


CHARGING RATES
The Amp is the unit for measuring of the rate of current flow. (1 Amp =
1 coulomb per second)
So...

If we could maintain a constant 1-amp current flowing through a 1 Farad
capacitor (which would be very difficult) the potential difference
across that capacitor would increase by 1 volt per second, until the
capacitor reached it's rated voltage. Charging a capacitor beyond it's
rated (breakdown) voltage is an invitation for catastrophic capacitor
failure.

If we apply a 1-volt potential-difference to a 1 Farad capacitor (which
is much easier) the charge on the capacitor will asymptotically approach
1 Coulomb.
Figuring out the charge rate of a capacitor in an R.C. timing circuit is
crucial to predicting the oscillation frequency of that circuit. (or you
could just try random guesses 'cause I don't know how to do that yet)


I hope that helps someone.
If anyone can figure out how to fit that onto a 3x5 card, please let me
know.

-Bill


Charging rate of a capacitor: 
www.algebralab.org/practice/practice.aspx?file=Reading_ChargingCapacitor
.xml

Leyden Jar: 
http://en.wikipedia.org/wiki/Leyden_jar

Electrostatic demonstrations: 
http://www.lhup.edu/~dsimanek/scenario/e-stat.htm



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