Andrew Tomasch University of Michigan AAPT Summer Meeting July 24, 2006 An Apparatus to Demonstrate the Energy Stored in a Capacitor AAPT Summer Meeting Syracuse New York July 24, 2006 Andrew Tomasch
Jan 21, 2016
Andrew TomaschUniversity of Michigan
AAPT Summer MeetingJuly 24, 2006
An Apparatus toDemonstrate the Energy
Stored in a Capacitor
AAPT Summer MeetingSyracuse New York
July 24, 2006
Andrew Tomasch
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Experimental Goals
• To demonstrate that capacitors store energy that can be retrieved as mechanical work
• To deduce from the experimental data that the energy stored in a capacitor is proportional to the square of the potential to which it has been charged
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Overview
Power Supply
1 FaradCapacitor
2 Meter LongAluminum Rule 300 g Mass
Servo
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Experiment Design• Servo mounted
directly to measuring scale attached to support rail
• Slotted support rail clamped to table via corner brackets
• Power supply, DVM and Capacitor on table
• Banana jacks for all connections
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Experiment Construction• Based on inexpensive, high-quality
hobby industry motor/gearbox• Design requires a minimum of
skilled fabrication—most parts are adapted with little or no modification
• Parts readily available from commercial sources
• Screwdriver assembly suitable for student labor
• Minimal machine shop time required to reduce cost
Futaba S3003 Radio Control Servo
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Theory of Operation
21
2
ln( ) ln 2ln( )2
mgh CV
Ch V
mg
Work Done Against Gravity = Efficiency x Stored Energy
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Data (Linear Plot)
y = 0.0276x2.2221
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4 5 6 7
V_0 (V)
h (
m)
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Data (Log Plot)
Typical Efficiency for Motor/gearbox is ~25%
y = 2.2224x - 3.5888
-1.4
-1.2
-1-0.8
-0.6
-0.4
-0.2
00.2
0.4
0.6
0 0.5 1 1.5 2
ln V_0
ln h
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Data (Student Worksheet Plot)
2 Volts
3 Volts
Lower Efficiency at LowVoltages SteepensExponent Slightly
6 Volts
AAPT Summer MeetingJuly 24, 2006
Andrew TomaschUniversity of Michigan
Summary and Conclusions
• The apparatus is easy to construct from commercial parts with minimal fabrication
• The experiment is robust and has been successfully tested in the undergraduate labs during the 2006 winter semester
• The data tend to yield exponents slightly steeper than 2 due to lower motor efficiency at low potentials. The effects are small enough to neglect