Download Lab06_La_Juan

Physics 102
Comparison of Capacitances
Phuc La, Juan Guerrero
February 29, 2006
Abstract:
The purpose of this lab is to determine the permittivity of air, plastic, mica and
wood. This laboratory is also used to explain the effect of the distance on the
capacitance of the capacitor.
Equipment:








AC generator
decade capacitance box
decade resistance box
decade resistance box
digital voltmeter
micrometer
parallel plate capacitor apparatus
Micrometer Calipers
Procedure:
The circuit is set up as in the picture:




Picture 01
Set C1 to 0.01 μF
R3 is set to 10 Ω
Measure the diameter of the plate with a ruler. Next measure the
thickness of the dielectrics with a micrometer caliper. The radius and
thickness of the dielectrics are used to find the permittivity of C4 in each
situation.
Next set the AC generator to 1kHz.

Set the dial of VOM to V~. The VOM connects like in the picture.
Part One
1. The dielectric in this section is air. The capacitive distance (d) is the
thickness of mica chips. Three small mica pieces are placed on the
capacitor plate in a triangle to make a tripod base to give distance
between the two plates of capacitor.
2. Next adjust R4 until the voltage (V) is at a minimum and record it. (If R4
gets too big then the voltage will go back up.)
3. Repeat this with the capacitive distances of 2d, 3d and 4d. R4 is adjusted
until the voltage V is at a minimum and record it.
Part Two
1. The dielectric is replaced by cardboard.
2. Adjust R4 until the voltage V is at a minimum and record it with each
dielectric. (If R4 gets too big then the voltage will go back up.)
3. The experiment repeats with other dielectrics which are plastic, mica and
wood. R4 is adjusted until the voltage V is at a minimum and record it.
Data:
The diameter of the plate is 14.82 cm
In the first part of the experiment
Distance
mm
0.76
1.52
2.28
3.04
C1
μF
R3
Ω
0.01
0.01
0.01
0.01
R4
Ω
10
10
10
10
510
1030
1540
2050
Table 01: Increasing the capacitive distance
In the second part of the experiment
Dielectric
Air
Cardboard
Plastic
Mica
Wood
Distance
mm
0.76
0.51
0.81
0.80
0.52
C1
μF
R3
Ω
0.01
0.01
0.01
0.01
0.01
Table 02: Changing dielectric material
R4
Ω
10
10
10
10
10
510
100
420
116
300
Analysis
calculations:
1. In the first part of the experiment
Find C2
The equation below illustrates a Wheatstone bridge circuit theory and Ohm’s law.
C 2 R3

C1 R4
 C2 
R3
C1
R4
R3, R4 and C1 are substituted into the equation above to find the values of C 2.
Table 03 gives the values of C2.
Distance (d)
Mm
0.76
1.52
2.28
3.04
C1
μF
R3
Ω
0.01
0.01
0.01
0.01
R4
Ω
10
10
10
10
510
1030
1540
2050
C2
μF
1.96E-04
9.71E-05
6.49E-05
4.88E-05
Table 03: Calculating C2 with different capacitive distance
Data to be graphed
The capacitance equation is
C   0
A
d
In the first part of the experiment, κ, ε0 and A are constant. The independent
variable is 1/d. C is the dependent variable. Therefore, the relationship between
1/d and C is linear. The slope of the line is κε0 A. Table 04 gives data to be
graphed.
Distance (d)
mm
0.76
1.52
2.28
1/d
1/m
1316
658
439
C2
μF
1.96E-04
9.71E-05
6.49E-05
C2
F
1.96E-10
9.71E-11
6.49E-11
3.04
329
4.88E-05
4.88E-11
Table 04: Data for graphing
2. In the second part of the experiment
Find C2
The equation below illustrates a Wheatstone bridge circuit theory and Ohm’s law.
C 2 R3

C1 R4
 C2 
R3
C1
R4
R3, R4 and C1 are substituted into the above equation to find the value of C 2.
Table 05 gives the values of C2.
Dielectric
Air
Cardboard
Plastic
Mica
Wood
C1
μF
R3
Ω
0.01
0.01
0.01
0.01
0.01
R4
Ω
10
10
10
10
10
510
100
420
116
300
C2
μF
1.96E-04
1.00E-03
2.38E-04
8.62E-04
3.33E-04
Table 05: the values of C2
Finding the permittivity of various materials
The capacitance equation is
A
d
Cd
  2
A
C2  
Also
The diameter of the plate is 14.82 cm. The area of the plate of capacitor is
A   r2
=> A =  (14.82/(100*2))2 = 1.72E-2 (m2)
C2, A and d are substituted into the above equation to find the value of ε. Table
06 gives the values of ε.
Dielectric
Air
Cardboard
Plastic
Mica
Wood
Distance (d)
m
7.6E-04
5.1E-04
8.1E-04
8.0E-04
5.2E-04
Area
m2
1.72E-02
1.72E-02
1.72E-02
1.72E-02
1.72E-02
Experimental ε
C2/Nm2
8.66E-12
2.97E-11
1.12E-11
4.01E-11
1.01E-11
C2
F
1.96E-10
1.00E-09
2.38E-10
8.62E-10
3.33E-10
Table 06: Caculating ε
graphs:
Capacitance versus 1/distance
2.50E-10
C = 1.49E-13 (1/d) - 6.56E-13
C (F)
2.00E-10
1.50E-10
1.00E-10
5.00E-11
0.00E+00
0
200
400
600
800
1000
1200
1400
1/distance (1/m)
Graph 01: Capacitance versus 1/distance
Error analysis:
There are some variations in the data. These variations have come from several
sources:
 Reading errors



Device variation
Instructions
Calculating
Reading error is a common error. In the experiment, the data is read from the
device. The device shows a variant number. Therefore the recorded data is an
estimate or average of the fluctuation quantity.
The device used in the experiment also contributed to errors. Each device has a
deviation, so it adds to the affects of the result of the experiment. In the
experiment, there is resistance in wires and devices, so the result is different
from the theory result.
Not following instructions can affect the data in the experiment. If an experiment
is done incorrectly then the, data may come out incorrect. With incorrect data, a
person’s conclusion will be incorrect.
Calculating errors are also made. When the results are rounded off early in
calculations, it affects the following steps. In the experiment, the theoretical
voltage and current are rounded off so when total voltage and current are
calculated they are not going to come out perfect.
In the experiment, there are errors in the results. The percent error shows the
difference between experimental values and theoretical values.
In the first part of the experiment
In graph 01, the experimental slope of the line is 1.49E-13. The theoretical slope
of the line is κε0 A. The dielectric of air is κ = 1.
The theoretical slope of the line is
8.85E-12 C2/Nm2 * 1.72E-2 m = 1.52E-13 C2/Nm
The percent error is
1.49 *10 13 1.52 *10 13
% error 
100% 1.97%
1.52 *10 13
In the second part of the experiment
Dielectric materials don’t have theoretical values so the percent error is
impossible.
Conclusion:
The laboratory shows the effect of the distance between the plates to the
capacitance of the capacitor. The relationship between the capacitance and
reversed distance between two plates is a line. The slope of the line is κε0 A.
Also, the laboratory shows the dielectric materials affect on the capacitance of a
capacitor. Finally, the capacitance of a capacitor depends on an area of plate,
dielectric material and capacitive distance.
Grade 95/100