The Physics
Hypertextbook
Opus in profectus

Dielectrics

search icon

Practice

practice problem 1

Since capacitance is directly proportional to plate area, a lot of metal is needed to make a big capacitor. Since capacitance is also inversely proportional to plate separation, this metal foil should be separated by a very thin dielectric film. A thinner film means less metal foil is needed, but dielectric films can only be made so thin. Thus, big capacitances require big capacitors (capacitors with a large volume).

That is, if one uses conventional materials and conventional designs. Enter the ultracapacitor (also known as the supercapacitor or electrochemical capacitor). Instead of two metal plates separated by a dielectric, an ultracapacitor uses a porous carbon electrode soaked in electrolytic paste. This effectively compresses a football field worth of surface area into a teaspoon of volume and shrinks plate separation down to the atomic scale.

According to one manufacturer…

An ultracapacitor gets its area from a porous carbon-based electrode material. The porous structure of this material allows its surface area to approach 2000 square meters per gram, much greater than can be accomplished using flat or textured films and plates. An ultracapacitor's charge separation distance is determined by the size of the ions in the electrolyte, which are attracted to the charged electrode. This charge separation (less than 10 angstroms) is much smaller than can be accomplished using conventional dielectric materials.

Maxwell Technologies, 2009

Determine the total…
  1. surface area,
  2. mass, and
  3. volume
of the electrodes in a one farad ultracapacitor. (One angstrom is 10−10 m and the density of activated carbon is 0.50 g/cm3.)

solution

  1. Answer it.
  2. Answer it.
  3. Answer it.

Ultracapacitors can be used…

  • in place of rechargeable batteries for long periods in low current devices (like computer back up memory) and for shorter periods in high current devices (like power tools).
  • to provide a bridge current when power is switched from one source to another (when subway cars switch tracks, for example, or while waiting for a backup generator to come online during a blackout).
  • for load levelling high voltage, low energy devices connected to low voltage, high energy sources (remote radio transmitters connected to solar arrays, for example).

practice problem 2

Write something.

solution

Answer it.

practice problem 3

Write something.

solution

Answer it.

practice problem 4

Write something completely different.

solution

Answer it.