1996 William J. Beaty
Date: Sat, 8 Jun 1996 14:17:53 -0700 (PDT) From: "Bill Beaty"
I have beefs with textbook explanations of capacitors too. "Capacitors
store charge." No! Flat out wrong! Wait and hear me out, I'm not
When we "charge" a conventional metal-plate capacitor, the power supply
pushes electrons into one plate, and the fields from these extra electrons
reach across the gap between the plates, forcing an equal number of
electrons to simultaneously flow out of the other plate and into
the power supply. This creates opposite areas
of imbalanced charge: one plate has less electrons and excess protons, and
the other plate has more electrons than protons. Each individual plate
does store charge.
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 capacitor
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 pump electric charge THROUGH the battery and none of it builds up
inside. Fuel-chemicals build up inside. Charge doesn't.
It's all terribly confusing. What are students to think if we
tell them that "charging a battery" does not 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, less misleading situation is similar: 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. But 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 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 in the other direction, and the
spring becomes "discharged." But no quantity of "belt" is stored inside
this motor. The belt flows THROUGH it, and we wouldn't want to label
this motor as a "machine which accumulates rubber." Yet this is exactly
what we say whenever we state that a capacitor "stores 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!!!! Not. A
capacitor is not a bucket for electrons. Instead it greatly resembles a
length of wire. But it's wire which, when you run a current along it, the
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 iron 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
sphere, where they act as connecting wires. The rubber plate is an
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", or "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, putting more iron into its spring? Lol.
Imagine that I now connect a single length of pre-filled hose between
the two halves
of the capacitor. As soon as the last connection is complete, the forces
created by the bent rubber plate will drive a
sudden immense 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
None! A momentary current has flowed through the sphere device, and the
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. I then 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 classroom learning. Maybe the experts are
experts only because they have fought free of the wrong parts of classroom
learning, while the rest of us are still living under the yoke of the many
electricity misconceptions we were taught in early grades.
[Hey, M. Steinberg's C.A.S.T.L.E. electricity curriculum uses the same analogy! In section 3.9, students construct a 2-chambered air capacitor with a balloon membrane stretched between the chambers. To "charge" it we take air from one side and pump it into the other. ]
Extra notes:Capacitors store just as much charge as coils do! Both capacitors and inductors are devices 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 set a coil atop an insulating platform, then use a VandeGraaff generator to give it a large net-charge! You can do the same with a capacitor. :)
Bill Beaty here again. Two points: First, this topic about currents between capacitor plates seems to be about VACUUM CAPACITORS. Modern capacitors are quite different, and there exists a large electron current in their dielectric. Relative Permittivity can be seen as a ratio between Maxwell's displacement current in the dielectric, versus dielectric polarization current (electron flow.) Modern ceramic capacitors' dielectric constant is above 2,000, so the vast majority of the current is carried by electrons in the ferroelectric ceramic. The displacement current is insignificant: well below 1%. Second: it might help to ask whether, down within any conductor, is there a current BETWEEN the flowing charge carriers? If there is, then there's certainly a current between the carrier-filled plates of any capacitor. Or said differently: if we have a current-sensor, and a charged particle approaches and passes it, does our sensor indicate an extremely brief pulse, where the pulse-width is associated with the diameter of the charged particle? Or, does our sensor see each moving particle as being "fuzzy," where the measured current extends forwards and back from the particle location? A clamp-on inductive sensor (Rogowski coil) doesn't detect charges or their motions, instead it detects changing flux- linkage. A clamp-on sensor would report that the current exists between the flowing charges, and not just on the particles' surfaces where the charge actually resides. A clamp-on sensor would 'see' currents in the capacitor's dielectric. Third (I lied!), suppose we construct a capacitor where the dielectric is much wider than the diameter of the capacitor plates. Use a long narrow lead-zirconate-titanate PZT rod with plates attached to its circular ends. Now apply some 27MHz amperes. Is the current within the rod zero? Really? Suppose we obtain a coil-shaped spiral rod of PZT. A "ferroelectric coil." If we apply some amperes, we'll certainly detect a strong radio-frequency b-field surrounding the rod. If the current is supposedly zero within the capacitor dielectrics, how can we explain this?