2006 AAPT Summer Meeting
A Simple Apparatus to Demonstrate the
Energy Stored in a Capacitor
A. Tomasch, D. Gerdes, R. Armen, and M. Love
Department of Physics
The University of Michigan
450 Church Street
Ann Arbor, MI 48109-1040
atomasch ‘at’ umich ‘dot’ edu
We describe a simple apparatus to quantitatively demonstrate the energy U stored in a capacitor of capacitance C charged to a potential difference V, by directly extracting mechanical work. The work delivered by a small motor and gearbox can be obtained directly by measuring the distance a known mass is lifted vertically in the earth's gravitational field. Students can quantitatively measure the relationship between the energy stored in the capacitor and the extracted mechanical work and calculate the efficiency for the system. The apparatus has been developed for use in introductory E&M laboratory courses, and is constructed from readily obtained commercial parts requiring a minimum amount of skilled labor for fabrication and assembly.
The apparatus is constructed from readily available commercial parts. The heart of the experiment is a high quality motor and gearbox assembly adapted from a radio control servo mechanism sold for hobby applications. The servo is modified by removing the supplied amplifier card and wiring banana jack leads directly to the motor. A small spool is attached to the output arm of the unit creating a small motorized winch which can lift a mass by winding fishing line onto the spool as the motor turns. The resulting winch assembly is then attached to a two meter aluminum ruler mounted to a slotted aluminum support rail. The rail is attached vertically to a table by means of C-clamps and steel corner brackets. Finally, a 300 gram mass is constructed from a small plastic container filled with lead shot and hardware store fittings. A one Farad Capacitor is charged to a known potential with an external power supply and then discharged through the winch assembly. The change in height measured for the mass can then be compared to the predicted stored energy in the capacitor and the power law dependence for the stored energy determined from measurements at different charging potentials. The efficiency of the winch motor can also be estimated. A photo of the apparatus appears below.