Challenge: To create a capacitor with the highest energy density possible.
Parameters: You will have to build a capacitor with found materials with a minimum mass of 25 grams, and a minimum voltage of 50 Volts. You will need to provide the measurements, materials, and mathematical analysis of your capacitor's theoretical capacitance and breakdown voltage.
Scoring: You will be evaluated based on the measured capacitance and energy density of your capacitor, as well as the agreement between theoretical capacitance and measured capacitance.
Score = (100-ln|%difference|)(CV^2/2m) -20% if capacitor shorts
Where V is the maximum capacitor voltage you achieved in Volts, measured by Mr. J's high voltage DC power supply circuit, C is capacitance in Farads, calculated by analyzing your capacitor in Mr. J's oscillator circuit tester, and m is mass in kilograms. Note, the capacitance will be measured before the voltage, just in case your capacitor shorts before your desired voltage. If it does, your score will be reduced by 20%. The units of your score will be Joules per kilogram.
Rank will be based on score, with highest score earning highest rank.
Physics: Oppositely-charged metal plates separated by an insulator (dielectric material in the case of capacitors) will have an electric field between them. Depending on the type of dielectric, and its thickness, the potential difference between the plates can be quite high, but at some voltage the electric field will cause the material to break down (ionizing of atoms) and a spark will short the plates. The breakdown voltage of dry air is 3000000 N/C or V/m. For example, plates 0.1 mm apart will spark to each other if the potential difference is 300 V. This could destroy your capacitor! Energy stored in this field can be retrieved safely by connecting the plates through a resistor or other load.
Extensions: The insulating material you use matters. Some materials increase the amount of energy that can be stored in the electric field. Look up “dielectric constants”. The thinner the material, the more energy density you can achieve, but you must be careful not to exceed the breakdown voltage of the material. The maximum voltage allowed is 300 V, and all you have to do is divide by the separation distance between the plates to calculate the maximum field strength: Electric field strength = Potential difference (Volts) divided by separation distance (meters). Look up “dielectric strength” or “breakdown voltage”. Most plastics are at least 5 times better than air. Even paper is better, but it is full of microscopic holes, which are made of… air!
Help/Hints: Try to plan your capacitor using the math and constants for the materials you have first. If you simply try it, and it shorts out at 130 Volts, you have learned something useful, but will have to build it again from scratch!
Quiz Topics: Electric charge, Coulomb’s Law, electric fields, electric potential energy, voltage, capacitance
Online Text: 18.1-18.5 (with math), 18.6-18.8 (no math), 19.1-19.7