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An Apparatus to Demonstrate the Energy Stored in a Capacitor. AAPT Summer Meeting Syracuse New York July 24, 2006. Andrew Tomasch. Experimental Goals. To demonstrate that capacitors store energy that can be retrieved as mechanical work - PowerPoint PPT Presentation
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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
