Dielectrics

Problems

practice

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 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.)
2. Write something.
3. Write something.
4. Write something completely different.

conceptual

1. problem