However, if we consider
the capacitor as a whole, no electrons have been put into the capacitor.
None have been removed. The same number of electrons are in a "charged"
capacitor as in a capacitor which has been totally "discharged." Yes, a
certain amount of charge has been forced to flow momentarily during "charging," and a rising potential difference
has appeared. But the current is directed through the capacitor, and the
incoming electrons force other electrons to leave at the same time. Every
bit of charge that's injected into one terminal *must* be forced out of
the other terminal at the same time. The amount of charge inside the
never changes. The net charge on each plate is cancelled by the opposite
charge on the other plate. Capacitors are never "charged" with electric
Think about this:
When "charging" a capacitor, a momentary current causes the voltage to rise. Volts times electron-flow equals energy-flow ( V x I = P). Therefore during a momentary current through a capacitor, there is a joules-per-second transfer of energy from the power supply into the capacitor.
Similar trouble is caused when we say that we "charge" a battery. We
charge a battery with some energy in the form of stored chemical fuel, but
we do this by pumping electric charge through the battery and
none of it builds up inside. Fuel-chemicals build up inside. Charge
It's all terribly confusing. What are students to think if we
tell them that "charging a battery" doesn't store any charge,
yet charge must flow through the battery if we want to charge it! Ugh.
The word "charge" has far too many meanings. In Science, this is always a
Very Bad Thing.
Another situation is a bit, less misleading: think of the word "charge" as
applied to gunpowder. A charge is placed in an old cannon, followed by a
cannonball. It would be silly to assume that, because we've "charged" the
cannon, the cannon now has an electrical charge. Yet whenever we state
that we've "charged" a capacitor, we do assume that an electrical
charge has been stored inside. This is just as silly as mistaking
gunpowder for electrostatic charges. Charging a capacitor (or a battery)
is like charging a cannon; in both situations we are inserting energy, not
Here's yet another way to visualize it. Whenever we "charge" a capacitor,
the path for current is through the capacitor and back out again. The
extra electrons on one plate force electrons to leave the other plate, and
vice versa. Visualize a capacitor as being like a belt-driven wind-up
motor. If we shove the rubber belt along, the spring-motor inside the
capacitor winds up. If next we let the rubber belt go free, the wound-up
spring inside the motor drives the belt backwards, and the
spring becomes "discharged." But no quantity of "belt" is stored inside
this motor. The belt flows through the device, and we wouldn't
want to label
this motor as a "machine which accumulates rubber." Yet this is exactly
what we're saying whenever we state that capacitors "store charge."
One more try. Capacitors store charge in the same way that resistors
store charge, and inductors store charge. Inductors are full of mobile
electrons, inductors are devices for storing charge!!!! Nope. An
inductor isn't a bucket for accumulating electrons, and neither is a
capacitor. Instead, both types of component behave like piece of wire
But capaictors are magical wires which, whenever we run a
current along it, the total charge inside the wire stays constant, but a
voltage (and a charge imbalance) appears at the two ends.
My favorite capacitor analogy is a heavy hollow sphere which is
completely full of water and is divided in half with a flexible rubber
plate through its middle. Hoses are connected to the two halves of the
thick irong sphere, and they act as connecting wires. The rubber plate
analogy for the dielectric. The two regions of water symbolize the
Imagine that the rubber plate is flat and undistorted at the start. If I
connect a pump to the two hoses and turn it on for a moment, the pump will
pull water from one half of the iron sphere and simultaneously force it
into the other. This will bend the rubber divider plate more and more.
The more the plate bends, the higher the back-pressure the plate exerts,
and finally the pressure-diff will grow strong enough that the pump will
stall. Next I seal off the hose connections and remove the pump. I now
have created a "charged" hydraulic capacitor.
Now think: in this analogy, water corresponds to electric charge. How
much water have I put into my iron sphere? None! The sphere started out
full, and for every bit of water that I took out of one side, I put an
equal amount into the other at the same time. Same as when running a
current through a conductor. When the pump pushed water into one side,
this extra water also forced some water out of the other side.
No water passed through the rubber, instead there was some rubber-current
in the divide. Even so, essentially I drove a water
current through my hydraulic capacitor, and this current pushed on the
rubber plate and bent it sideways. Where is the energy stored? Not
in the water, but in the potential energy of the stretched rubber plate.
The rubber plate is an analogy to the electrostatic field in the
dielectric of a real capacitor.
It would be misleading to say "this iron sphere is a device for
accumulating water." And neither say "this sphere can be charged with
water, and the
stored water can be retrieved during discharge." Both statements are
wrong. No water was injected into the sphere while it was being
"charged." (And when I wind up an old watch, am I "storing steel"
inside it, putting more iron into its spring? Lol.
Imagine that I now connect a single length of pre-filled hose between the
two halves of my "energized" water sphere. As soon as the last connection
the bent rubber plate will drive a sudden
spurt of water through this already-full hose. Water from one side will
be pushed into the other side, and the rubber plate will relax. I've
discharged my hydraulic capacitor. How much water has been removed from
the sphere? None! A momentary current has flowed through the sphere
device, and the rubber plate is back to the middle again, and the water
has become a bit warm through friction against the surfaces of the hose.
The stored energy has been "discharged," but no water has escaped. The
hydraulic capacitor has lost its energy, but still contains the same
amount of water.
I never really understood capacitors until I started trying to construct
proper water-analogies for them. Then I discovered that my electronics
and physics classes had sent me down a dead-end path with their garbage
about "capacitors store electric charge." Since my discovery, I've gained
significantly more expertise in circuit design, which leads me to a sad
thought. Maybe the more skilled of electrical engineers and scientists
gain their extreme expertise not through classroom learning.
Instead they gain expertise in spite of our K-12 classroom learning.
Maybe the experts are experts only because they have fought free of the
wrong parts of grade school science, while the rest of us are still living
under the yoke of the many physics misconceptions we were carefully taught
in early grades.
[Hey, M. Steinberg's
C.A.S.T.L.E. electricity curriculum uses the same analogy! In all my
search of textbooks, this is the only one I've found. In
section 3.9, students construct a
2-chambered air capacitor with a balloon membrane stretched between the
two chambers. To "charge" it we take air from one side and pump it into
the other. ]
[Hey^2!!! I just found that Oliver Lodge was building mechanical
analogies for Maxwell's descriptions of EM fields and circuits... and for
an 1880 lecture he
built a capacitor hydraulic analogy consisting of a water-filled sphere
with rubber! His was a glass sphere containing a smaller balloon,
both full of water with no bubbles.]
Extra notes:Capacitors store just as much charge as coils do! In both devices the total amount of charge stays constant. Both capacitors and inductors are components for storing electromagnetic energy. They're two sides of the same EM phenomenon: a coil stores energy in a volume containing a magnetic field, while a capacitor does something similar with electric fields. Coils are "discharged" by interrupting a large current and collapsing the b-field, while capactors are discharged by shorting-out a large voltage and collapsing the e-field. Neither stores any "electricity" (unless by the word 'electricity' you mean magnetic field?) Of course you can place a coil atop an insulating platform, then use a VandeGraaff generator to give your coil a large net-charge! You can do the same with a big electrolytic capacitor too. :)
Bill Beaty here again. Two points:
First, the heated topic about currents being impossible between capacitor plates ...seems to be about Vacuum Capacitors, not capacitors in general. Modern capacitors are quite different than vacuum capacitors, and inside a modern dielectric is a large electron-current. Relative Permittivity can be seen as a ratio between the small Maxwell's displacement current inside a vacuum, versus the larger polarization current (electron flow: the shifting of electrons) in the ferroelectric PZT material. The dielectric constant in modern ceramic capacitors is above 2,000, so the vast majority of the current is a charge-flow, a real current from shifting the electrons in the ferroelectric ceramic. The Maxwell displacement current of the vacuum is insignificant: well below 1%.
Capacitors: physicists vs. engineers
> For the charge to flow in a circuit, there has to be a closed path.
No, there must be a closed path ONLY if the charges must flow continously
in the circuit forever (pure DC). But if the charges flow briefly, or if
they flow back and forth (AC), then an open path is sometimes acceptable.
For example, with a metal rod 1 meter in length, it is possible to create
a standing wave of charges oscillating lengthwise in the rod with
frequency 150MHz. Inside the rod, the charges move back and forth (this
resembles the motions of the compressible air inside one pipe of a church
organ.) The charges within the rod are acting like a compressible fluid.
At far lower frequencies, the electric current can still be large if the
ends of an open circuit are joined to the plates of a capacitor. On the
metal surfaces between the plates of the capacitor, the quantities of
charge carriers behave as a "compressible fluid", while the charges within
a wire behave as an "incompressible fluid."
Two ideas are necessary:
1. Metals are always full of movable charges even when they are electrically neutral. They contain a "fluid" made of electrons, and a "solid" made of protons (made of the nuclei of metal atoms.)See the "water analogy" diagram above. The rubber barrier represents the dielectric. Yet electrical forces can reach across the dielectric, just as physical forces can be transmitted through a rubber barrier.
If you forcibly inject electrons into one plate of a capacitor, these
electrons will repel the electrons hidden within the other uncharged
plate, and these other electrons will be forced out of the capacitor's
other terminal. However, if the other capacitor terminal is connected to
nothing, then those electrons cannot leave the other plate. They will
continue to repel the electrons in the first plate, and for this reason
very few electrons can be forced into the first plate. The rule for most
capacitors is: the current in both capacitor terminals is always the
same. This means: if charge is injected into one capacitor plate, then
an equal amount of charge is pushed out of the other capacitor plate, and
if equal charge cannot leave the second plate, then we cannot force
into the first plate.
If we ignore the space between the plates, the capacitor SEEMS to be a
kind of conductor. However, it is a strange "conductor" where the two
terminals are connected by electrical forces which reach across a narrow
space. It is not a true conductor, but neither is it a simple insulator.
I think this concept is explained very badly in physics textbooks. In
physics, a single metal sphere is considered to be a "capacitor," and two
metal spheres with a large separation between them is also a "capacitor."
Yet conceptually these are very different from capacitors used in electric
With single spheres and with pairs of separate spheres, the flow of charge
into a sphere need not be equal to flows of charge out of the other
sphere or elsewhere. The entire universe serves as an extra unseen
capacitor plate. Yet in electronics, "capacitor" means only one thing:
"two closely-spaced plates." As far as electronic equipment is concerned,
capacitors only have two plates, and the current in one terminal must
always equal the current in the other terminal. This is not true for two
distant conductors, but the "general case" in textbooks is much
harder to understand. Physics textbooks examine the general case where
the currents in the capacitor terminals are not equal, a distant ground is
part of the system, and the electrostatic coupling between the plates is
not very strong. Conventional capacitors in electronic equipment are
different: the electrostatic coupling between their plates is extremely
strong, the electrostatic coupling to the earth is essentially zero, and
the current in the terminals connected to the two plates is always equal.
The charge on their plates must be equal and opposite, always. But
in physics textbooks, you can have three coulombs on one metal sphere, and
two coloumbs on another.
Here is an "electrical engineering" way to understand it. Suppose the
capacitance between two parallel plates is X microfarads. Suppose we
force some charge into one plate, but we do not connect the other plate to
anything. In this case, the lines of electric force extend outwards from
both plates to the earth. Important question: what is the capacitance of
the "capacitor" formed by one plate and the distant earth? It is small.
very small, possibly millions or even billions of times smaller
than the number of microfarads existing between the two plates.
Therefore, if we connect both capacitor terminals to a circuit and force
charges "through" this capacitor, the voltage across the plates will rise
slowly, but if we instead try to force the same current into only
one plate (and leave the second plate disconnected), then the
voltage between the capacitor and the earth will rise millions or billions
of times faster for the same current. In other words, a two-plate
capacitor has immensely more capacitance than a one-plate capacitor. In
electronics we usually ignore the "one-plate" phenomena entirely, and
imagine that capacitors are a strange kind of two-terminal conductor.
Here is a model which exposes the problem. Rather than imagining a
capacitor to be like two metal spheres, imagine it to be like one sphere
which is divided into two parts, where the gap between the two parts is
extremely small, and the capacitance value between the two parts is far
larger than the capacitance value measured between each part and the
____ ____ __/ || \__ / || \ / || \ "Engineer's Capacitor" | || | | || | A spilt metal sphere with | || | a very narrow gap between | || | the two halves | || | | || | | || | \ || / \__ || __/ \____||____/Above is a model of an "engineer's" capacitor, as opposed to the two spheres of the "physicist's" capacitor. Because of the narrow gap, it behaves very differenly than two separate spheres.
______ ______ / \ / \ The "Physicist's Capacitor" / \ / \ | | | | Two separate metal spheres | | | | | | | | | | | | \ / \ / \______/ \______/
If we dump some excess charge onto one half of the engineer's capacitor,
something strange occurs: half of the charge apparantly migrates to the
other half of the device! The twin hemispheres behave as a single
conductive sphere because any excess charge on one half of the gap will
induce equal and opposite excess charge on the other half of the gap, and
this leaves excess alike charges on the second half (which then
distributes itself uniformly across that surface.) In physics terms, the
capacitance between the two hemispheres is very large when compared
to the capacitance measured from either hemisphere to distant
The split-sphere device behaves almost as if it has a conductive
connection between its two halves. This connection is as real as the
connection between the ends of a resistor... yet it is made out of
electrostatic forces in space, rather than being made out of carbon.
In my experience, the the two spheres of the "physicist's
capacitor" cause distortion in physicists' concept of what the electronic
component called "capacitor" really is.
Analogy: if we were talking about coils, and coils were
just as badly, then how would physicists
visualize electric transformers? They'd be very familiar with induced
currents between pairs of distant air-core coils, yet they would be almost
entirely unaware of of the strange effects arising with closely-coupled
coils of an iron core transformer. Power transformers behave very
differently than two widely-spaced air-core inductors. And the above
split-sphere "engineer's capacitor" is analogous to an iron-core
transformer, while the "two-sphere capacitor" of the physics textbooks is
analogous to a pair of widely separated coils. Whether we're dealing with
coils or dealing with
capacitor plates, whenever the coupling between
the two halves approaches 100%, everything starts acting very differently.
On Wimshurst machines and capacitors:
Do you believe that the energy in a capacitor is trapped permanently in
the dielectric? Many people do. Their belief is caused by a
famously misleading experiment called "Dissectable Leyden Jar." It's an
experiment which involves high
voltage and corona discharge. The effect it purports to prove does not
occur in capacitors at lower voltages.
First charge up a Leyden jar using a Wimshurst Machine (or other source of
high voltage.) Now, carefully remove the inner metal from the jar. Now
remove the outer metal. Discharge everything, then hand the parts around
the classroom. Next, put the parts together again, connect the two metal
cylinders, and BANG!, there is a loud discharge.
Doesn't this prove that the energy in a capacitor is stored in the
Whenever you take apart a Leyden jar or other high voltage capacitor,
there is a corona effect which makes very strange things occur. When you
electrify a Leyden jar, and then you pull the inner metal cylinder out of
the jar, the capacitance value drops, and this makes the potential
difference skyrocket to enormous levels. The potential tries to become
huge but it cannot, because instead it creates corona along the metal
edges, and and it leaks the excess charge into the air. This corona
allows the opposite electrical charges to "paint" themselves onto both
sides of the dielectric "jar" surface. So, if you pull a leyden jar
apart, the sharp edges of the metal plates sweep along and transfer a
large percentage of the separated charges from the metal plates to the
glass surfaces. The energy is still there! It's still stored as a field
in the dielectric, but those separated charges are not on the mental
plates anymore. Instead they are now TRAPPED ON THE GLASS SURFACE!
Strange idea, huh? A capacitor with no plates, just a dielectric.
Now reassemble the Leyden jar: momentarily touch each metal plate to
ground, and put it back together again. You'll find that it's still
strongly electrified! The trapped
charges on the glass surface can still induce equal charges on the
adjacent metal plates. Touch the two terminals with your fingers and
BOOM!, the momentary current in your muscles will throw you across the
This strange effect leads many people to claim that the energy in a
capacitor is permanently trapped in the dielectric, and that it is not
stored in the electric field. This is wrong.
In order to properly perform the take-apart capacitor experiment, you must
execute the entire demonstration inside a big tank full of oil. This
prevents the corona discharges from spewing charges from the edges of the
plate onto the dielectric.
Or, perform the whole experiment at 1.0 volts, not at 10,000 volts. (Use
an electrometer to measure the voltage.) You'll find that the dielectric
doesn't store energy anymore. In order for the charges to spray onto the
dielectric, the voltage must be high.
Or, use high voltage but do this instead: before doing anything, take
apart the leyden jar. Now, lay the metal parts on a plastic sheet and use
a Wimshurst machine to charge them up. Next, use plastic tongs to
assemble the leyden jar. (The voltage across the plates will be very
low.) NOW perform the leyden jar dissection. It shouldn't work anymore,
since the initial voltage is low enough that it will prevent corona
discharges from painting any charges on the dielectric.