Werry
Partners: Christopher Lexi Baker, Alex Mara, Michael Kreisman
1/30/12
Lab 2
Wed 9AM
Data
Variable Capacitor:
# of pages
Distance
(mm)
25
0.725
50
1.45
100
2.9
150
4.35
200
5.8
250
7.25
Capacitance
(nF)
0.18
Area (m2)
0.0302
0.163
0.12
0.092
0.07
0.066
RC Circuit (qualitative):
Graph for charge and discharge of a lightbulb in an RC circuit
RC Circuit (quantitative):
Capacitance
Resistance
run # (F)
()
expected meas amplitude (Vo)
% error for
1
93.8
100.5 0.009427
0.01
2.993 6.079411047
2
93.8
561.7 0.052687
0.06
2.994 13.87909001
3
93.8
1001 0.093894
0.09
2.992 4.147025682
4
93.8
10030 0.940814
0.93
2.936 1.149430174
5
325
100.5 0.032663 0.009
2.997 72.44546498
6
325
561.7 0.182553
0.19
2.991
4.07964832
7
325
1001 0.325325
0.32
2.963 1.636824714
8
325
10030
3.25975
3.2
2.919 1.832962651
Methods
Variable Capacitor:
Page widths were of what was in the lab instructions.
RC Circuit (qualitative):
4F capacitor instead of a 10F capacitor
used resistor board instead of individual resistors
used a light bulb of resistance 1.7 0.1 ohms
Instead of a 10 ohm resistor used a resistor board of 1 ohms, and then 2 ohms
Start voltage was 3V
Analysis
Capacitor Basics:
Yes, it would still be a capacitor
It was 0.9 pF, this is smaller than what I would expect
Yes, the capacitance is additive because the wires have a capacitance that isnt negligible,
and the wires are in series with the capacitor plates
The crackling is caused by the aluminum foil crunching together. They are attracted to
each other because of equal and opposite charge being distributed to each piece of foil.
Thus, charging the capacitor creates an attraction between the plates.
The amount of energy required to move one charge from one plate to the other is zero,
because the plates have equal and opposite charge.
The energy stored in a capacitor is: CV2, in this case with C = 0.9 pF and V = 5 kV, the
stored energy is 11 micro Joules. The strength of the electric field is F = qE, where q =
2E/V = 5nC. So F = 5x10-14N
Construction of Capacitor:
The capacitance of the dielectric capacitor is larger. This is to be expected; assuming the
dielectric constant of acrylic is above 1.
A potential difference is created between the plates as well as an electric field.
Fringing of the fields occurs when like charges gathered on a plate of a capacitor repel
each other, causing the charge density to be greater on the edges of the plate. The
standard equations for capacitance are an approximation because fringing effects
significantly increase the capacitance.
If a semiconductor was placed in-between capacitor plates, the capacitance would
probably drop. The semiconductor would have charge separation due to attraction to the
plates, this would create more a neutral electric field.
Variable Capacitor:
How do you expect the slope of this line relates to physical characteristics of the
capacitor?
The slope of the plot of Capacitance vs. 1/d would be directly proportional. This is
because of the relationship between C and d for parallel plates:
Our value is not what
Id expect due to the following experimental error.
Reason for discrepancy: We measured our pages as page numbers, not actual pages. So
all of our values for page width were one half of the suggest width. This allowed for extra
noise caused by the measuring equipment.
Calculating permittivity of paper:
A is area of the capacitor plates, D is the distance
between the plates, is the permittivity of free space, and is the permittivity of the paper.
RC Circuit (qualitative):
The time to dim the bulb decreases as the resistance increases.
The current is greatest when it first starts flowing at the light bulb is brightest. The
current is lowest when the bulb is completely out. The current is zero because of the
resistors present.
The current slowly drops to zero as the capacitor charges. When the capacitor discharges,
the current flows immediately again at the same original magnitude and in the same
direction.
RC Circuit (quantitative):
For % errors for tao, see data
If a larger DC voltage had been used, our measurements of would have decreased.
Plot is in data. The slope of tao vs resistance for the 93uF capacitor is 10810, for the
325uF capacitor the slope is 3128.5.
The voltage across a capacitor AND its capacitance increases the amount of charge it can
store.
Q(t) could be determined by multiplying V(t) by the capacitance
I(t) is the derivative of Q(t) with respect to time
The energy stored in a fully charged capacitor with C = 325uF: E= CV2 = 0.00146 J.
Discussion/Conclusion
In section 4, the demonstration was faulty in that the charges between the foil wasnt enough to
attract them together and cause a crinkling noise. This was most likely the fault of the charge
generator. In section 6 we measured the page numbers wrong and used half of the width values.
This led to more noticeable noise caused by the measuring devices, which caused the graph of C
vs 1/d to be off. This could have been solved by using the correct page widths. T-values could
not be determined because there was no value for measurement uncertainty of the devices used.
Instead, percent error was used to evaluate the correctness of the values of tao. The permittivity
of paper was found to be 1.5, when this value should have been higher (Wikipedia estimates 3.4).
Once again the page widths may have thrown off this result. In addition, the glossy pages of the
textbook may have a lower permittivity than regular printer paper.