Lab #5 FORMAL LAB
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School
Portland State University *
*We aren’t endorsed by this school
Course
215
Subject
Electrical Engineering
Date
Apr 3, 2024
Type
Pages
47
Uploaded by ProfWaterMantis33
Lucas Curtsinger & Tyler & Hussian
2/13/24
TA: Grace Yen
Capacitors and Capacitance
Introduction
In the following three experiments we used capacitors to observe their function, and measure their
voltage and current over a time. Through these experiments I predict that the slope method will be the
most accurate, and that the time constant will decrease if in series and increase when in parallel. The
time constant
𝝉
(tau), the amount of time it takes for a capacitor to charge or discharge to 63.2% of its
maximum voltage, can be calculated by just multiplying the resistance R and the capacitance of the
capacitor C. However, in our experiments we determined
𝝉
by two different means. The first was through
the equation:
𝑙?(𝐼) =−
?
𝝉
+ 𝑙?(
𝑉
0
𝑅
) This equation tells us the slope of our data, natural log of the current vs time is
, which we can use to
1
𝝉
calculate
𝝉
. The other method we will use to calculate
𝝉
was the by finding the time at which our voltage
was the highest multiplying that by 63.2%, then finding the time that corresponds with that new voltage.
With these methods we can find the time constant of a capacitor individually, or in a series or parallel.
Procedure
Setup:
●
Start by neutralizing the capacitors by connecting the positive and negative terminal together and
wait 10 seconds. (This will need to be completed after every trial)
Experiment 1: Light Bulbs and Capacitors
1.
With a single battery, bulb and capacitor connect them on the circuit board as shown in
Figure 1
.
Figure 1:
The circuit board connected to charge a capacitor.
2.
Once the bulb has stopped glowing, disconnect it from the battery source and connect the
positive and negative wires together that were previously connected to the power source,
completing the circuit as shown in
Figure 2
.
Figure 2:
The circuit board connected to discharge a capacitor.
3.
Add a second battery to the circuit board and complete steps 1 and 2 again.
Experiment 2: RC Circuit
1.
Start by connecting the voltage and current probe into LoggerPro, and zero the probes by
connecting the positive and negative ends of the respective probes together.
2.
Neutralize the capacitor.
3.
Setup the circuit as shown in
Figure 3
. Make sure to include a resistor in the circuit, and that the
negative end of the capacitor with the two black lines is connected to the negative end of the
circuit.
`
Figure 3:
Resistor-Capacitor (RC) circuit configuration to measure the current and voltage.
4.
Start by applying power to the circuit, then hit collect on LoggerPro and wait for data collection to
complete.
Experiment 3: Capacitors in Series and Parallel
A)
Capacitor in Series
1.
Start by neutralizing the capacitors.
2.
Connect the circuit as shown in
Figure 4
. This time we will only be using the current
probe so you can disconnect the voltage probe from LoggerPro.
Figure 4:
Resistor-Capacitor (RC) circuit in series to measure the current.
3.
Start by applying power to the circuit, then hit collect on LoggerPro and wait for data
collection to complete.
A)
Capacitor in Parallel
1.
Start by neutralizing the capacitors.
2.
Connect the circuit as shown in
Figure 5
.
Figure 5:
Resistor-Capacitor (RC) circuit in parallel to measure the current.
3.
Start by applying power to the circuit, then hit collect on LoggerPro and wait for data
collection to complete.
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Data & Analysis
Experiment 1: Light Bulbs and Capacitors
In this experiment we watched the process of a capacitor charging and discharging through a light bulb.
The setup of the experiment was easy, at this point though we were still getting used to the negative and
positive poles of the capacitor, as well as the necessity to discharge the capacitor. While no graphs or
tables were created during this experiment, we did try our best to collect some data. We had used a timer
on our phone to time the time it took for the bulb to lose its glow for charge and discharge of 1 battery and
2 batteries. For the 1 battery experiment the bulb was not very bright, but we did note that it took 8.876
seconds for the bulb to turn off while charging the capacitor and 7.22 seconds to turn off when the
capacitor was discharged. For the 2 battery experiment the bulb was much brighter. During charging of
the capacitor the bulb turned off after 22.11 seconds, and while discharging turned off after 15.47
seconds. The results of this experiment tell us that the rate at which a capacitor charges and discharges
are different. Also, if you increase the voltage, which in turn increases the current, the more charge is
forced into the capacitor.
Experiment 2: RC Circuit
In experiment 2 we set set up a RC circuit to find the time constant
𝝉
using two different methods, the
one-over-e method and from the slope. Setting up the circuit was easy since we have the experience, but
again trying to remember to discharge the capacitor was a challenge to make sure we didn't skew the
results. Before starting the experiment we used this equation to find our time constant:
𝝉 = 𝑅𝐶
R being the resistance and C being the capacitance. With using a 10 Ohm resistor and 1 Farad capacitor
our time constant came out to be 10 seconds. We then completed the experiment and found the results
that are shown in
Appendix A
. Before we graphed the data we used the one-over-e method to find the
time constant for the capacitor by applying the equation:
𝑉(?) = 𝑉
0
(1 − 𝑒
−
?
𝝉
)
If we set t and
𝝉
equal in the equation above we get 1-.3678=.632. So by multiplying our max voltage by
.632 we will get the the voltage value that correlates to both t and
𝝉
. For our experiment our max voltage
was 2.757, then by multiplying it by .632 we get 1.742, the point at when the capacitor is 63% charged.
Then we found the value that correlates to this value which was 10.8 seconds, which was very close to
our expected value of 10 seconds. Finally we used the slope method to try to find our time constant. By
taking the equation that describes the current through an RC circuit and taking the natural log of both
sides we get:
𝑙?(𝐼) =−
?
𝝉
+ 𝑙?
𝑉
0
𝑅
So by taking the natural log of the current values we got in the experiment and graphing them with the
time, shown in
Figure 6
, we can find the value for
𝝉
by taking the inverse of the slope.
Figure 6:
RC circuit results showing relationship between ln(current) (A) and time (s).
These results show us that as time progresses the current decreases through the circuit as the capacitor
is charged and that the slope is -.0846. Now to find
𝝉
we use this equation:
𝝉 =−
1
?𝑙??𝑒
Which gets us a value of 11.8 seconds. Out of the two methods it seems the one-over-e method is more
accurate. For the one-over-e method our it is 8% from our accepted value, which we get from this
calculation:
10.8 ? −10 ?
|
|
10 ?
100% = 8%
which falls within the acceptable range. But for our slope method it is 18% from our accepted value, which
we get from this calculation:
11.8 ? −10 ?
|
|
10 ?
100% = 18%
Which does not fall within the acceptable range. Sources of error within the experiment would have come
from turning on the circuit too soon or too late, which at this point were not sure when the right time to turn
the circuit on would be. In conclusion, our results for the one-over-e method supported the equation
related to it, but our hypothesis was not supported because the one-over-e method was more accurate
than the slope method.
Experiment 3: Capacitors in Series and Parallel
In experiment 3 we set up a RC circuit in series and in parallel to find the time constant
𝝉
from the slope of
the graph showing the relationship between the natural log of the current and time. Setting up the circuit
was easy since we have the experience, but by this time we were well aware of needing to neutralize our
capacitors. Before starting the experiment we used the following equations to find the time constant for
the series circuit:
𝐶
?𝑒?
= (
1
𝐶
1
+
1
𝐶
2
)
−1
𝝉 = 𝑅𝐶
With R being resistance and C being capacitance. And we used this equation to find the net capacitance
of the parallel circuit to find the time constant:
𝐶
?𝑒?
= 𝐶
1
+ 𝐶
2
As a result we got .5 seconds for the RC series circuit, and 2 seconds for the parallel RC circuit. First we
collected data for the RC circuit in series, which can be found in
Appendix B
, and graphed our results to
show the correlation of the natural log of the current and time, shown in
Figure 7
.
Figure 7:
RC circuit in series results showing relationship between ln(current) (A) and time (s).
By taking the same equation from experiment 2 that describes the current through an RC circuit and
taking the natural log of both sides:
𝑙?(𝐼) =−
?
𝝉
+ 𝑙?
𝑉
0
𝑅
We were able to find the time constant by taking the inverse of the slope which gives us 7.69 seconds.
We then needed to find the capacitance of the circuit from our found time constant by using this equation:
𝐶 =
𝝉
𝑅
Which we calculated out to be .769 Farads. This is approximately 54% from the accepted value. Which
we get from this calculation:
.769 𝐹 −.5 𝐹
|
|
.5 𝐹
100% = 54%
Which shows that the experiment we conducted does not fall within the acceptable range.
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For the next experiment we collected data for the RC circuit in parallel, which can be found in
Appendix
C
, and graphed our results to show the correlation of the natural log of the current and time, shown in
Figure 7
.
Figure 8:
RC circuit in parallel results showing relationship between ln(current) (A) and time (s).
By taking the same equation from the trial of the RC circuit in series that describes the current through an
RC circuit and taking the natural log of both sides:
𝑙?(𝐼) =−
?
𝝉
+ 𝑙?
𝑉
0
𝑅
We found the time constant by taking the inverse of the slope which gives us 27.5 seconds. Then we
calculated the capacitance of the circuit from the time constant by using this equation:
𝐶 =
𝝉
𝑅
Which calculated out to be 2.75 Farads. This result is approximately 38% from the accepted value. Which
we get from this calculation:
2.75 𝐹 −2 𝐹
|
|
2 𝐹
100% = 38%
Which shows that the experiment we conducted does not fall within the acceptable range. Sources of
error within the experiment would have come loose wires not making complete contact, and turning on the
circuit too soon or late, or not discharging the capacitors fully. We did end up repeating the experiment
multiple times because we thought we were getting bad results when instead we were just graphing the
time on the y-axis instead of the x-axis. Even though the data supports our hypothesis that the time
constant will decrease if in series and increase when in parallel it is well outside the range of acceptance
for both the experiment of the RC circuit in series and in parallel.
Conclusion
In conclusion, we see that as we increase the voltage of an RC circuit it takes longer to charge and
discharge, as well as how the time constant is related to the current, and how to find the time constant
with the one-over-e method and the slope method. We also came across the finding that by increasing
the capacitance we increase the time constant. For example when we put the RC circuit into a parallel
circuit we see an increase in the time constant from 7.69 F to 27.5 F. For experiment 1 we saw the time of
charging the capacitor increased from 8.87 seconds when using one battery increased to 22.11 seconds
when using two. For experiment 2 we found the time constant using the one-over-e method was 8% from
our actual value, and was 18% using the slope method. This means that the one-over-e method was
more accurate than the slope method because the percent of error is smaller, which does not support our
hypothesis that the slope method is more accurate. For experiment 3 we saw the time constant was
larger in a parallel RC circuit than in series. We ended up seeing the time constant for the RC circuit in
series was 7.69 seconds, and was 27.5 seconds for an RC circuit in parallel, which supports our
hypothesis that the RC circuit in parallel will have a larger time constant. Even though the time constant
we got was for the RC circuit in series was 54% from our expected value, and the RC circuit that was in
parallel was 38% from our expected value we still see that patterns that arise from the experiment that
can be confirmed with the equation for the equivalent capacitance for each circuit and with the equation
𝝉
=RC.
Appendices
Appendix A
Data Collection for Experiment 2
Voltage
Current
time (s)
ln(Current)
0.018311
-0.00063
0.1
#NUM!
0.018311
0.000286
0.2
-8.159518747
0.018311
-0.00032
0.3
#NUM!
0.094223
0.24559
0.4
-1.4040918
0.148964
0.240726
0.5
-1.424095922
0.17643
0.238895
0.6
-1.431731154
0.191498
0.236778
0.7
-1.440632286
0.227928
0.234032
0.8
-1.452297421
0.252342
0.230694
0.9
-1.466663122
0.270653
0.228577
1
-1.475882145
0.294876
0.226746
1.1
-1.483924831
0.316238
0.224609
1.2
-1.493394166
0.340462
0.222797
1.3
-1.501494236
0.361824
0.220051
1.4
-1.513895941
0.386047
0.219746
1.5
-1.515282945
0.404358
0.217323
1.6
-1.526370553
0.431633
0.215492
1.7
-1.534831493
0.449944
0.213375
1.8
-1.544704098
0.471115
0.210934
1.9
-1.556209991
0.486374
0.210018
2
-1.560562038
0.507545
0.207901
2.1
-1.570693274
0.535011
0.205765
2.2
-1.581020538
0.544167
0.204563
2.3
-1.586879282
0.56839
0.202732
2.4
-1.595870369
0.592613
0.201206
2.5
-1.60342602
0.607872
0.199089
2.6
-1.614003318
0.629234
0.197868
2.7
-1.620155137
0.644302
0.195122
2.8
-1.634130275
0.668716
0.194225
2.9
-1.638737998
0.683784
0.191479
3
-1.652977137
0.695992
0.190563
3.1
-1.65777243
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0.723457
0.188141
3.2
-1.670563597
0.738525
0.186615
3.3
-1.678707608
0.750732
0.185699
3.4
-1.683628196
0.774956
0.182972
3.5
-1.698422143
0.793266
0.181751
3.6
-1.705117661
0.814629
0.180531
3.7
-1.711852771
0.832748
0.179634
3.8
-1.716833831
0.851059
0.176888
3.9
-1.732238515
0.863266
0.175667
4
-1.739165122
0.881386
0.174465
4.1
-1.746031131
0.893593
0.172939
4.2
-1.754816348
0.917816
0.171719
4.3
-1.761895859
0.933075
0.168991
4.4
-1.77790982
0.948334
0.168076
4.5
-1.783339021
0.963402
0.166855
4.6
-1.790630107
0.981712
0.165653
4.7
-1.79786004
0.993919
0.164127
4.8
-1.807114761
1.008987
0.162601
4.9
-1.816455932
1.03035
0.161686
5
-1.822099096
1.045609
0.159264
5.1
-1.837192076
1.060677
0.157433
5.2
-1.848755308
1.072884
0.156212
5.3
-1.85654122
1.088142
0.15501
5.4
-1.864265648
1.10321
0.15379
5.5
-1.872167244
1.118469
0.152569
5.6
-1.880138326
1.127625
0.151062
5.7
-1.89006493
1.145744
0.150146
5.8
-1.896147125
1.170158
0.148926
5.9
-1.904305741
1.182365
0.14679
6
-1.918752285
1.197433
0.145283
6.1
-1.929071715
1.209641
0.144367
6.2
-1.93539661
1.221848
0.143147
6.3
-1.943883205
1.239967
0.142231
6.4
-1.950302783
1.246071
0.141335
6.5
-1.95662232
1.264381
0.139809
6.6
-1.967478074
1.282501
0.137978
6.7
-1.980661027
1.291656
0.136471
6.8
-1.991643141
1.306915
0.13586
6.9
-1.996130335
1.322174
0.13464
7
-2.005150729
1.328087
0.134029
7.1
-2.009699085
1.346397
0.132504
7.2
-2.021142445
1.361656
0.130997
7.3
-2.032580857
1.36776
0.130081
7.4
-2.039597946
1.382828
0.129166
7.5
-2.04665688
1.398087
0.126743
7.6
-2.065593865
1.407242
0.126743
7.7
-2.065593865
1.410294
0.125828
7.8
-2.072839384
1.434517
0.123386
7.9
-2.092437626
1.443672
0.123386
8
-2.092437626
1.458931
0.122776
8.1
-2.097393722
1.467896
0.121269
8.2
-2.10974406
1.473999
0.120354
8.3
-2.117317879
1.495361
0.118523
8.4
-2.132648244
1.501465
0.118523
8.5
-2.132648244
1.516533
0.1161
8.6
-2.15330339
1.519585
0.11549
8.7
-2.158571333
1.540947
0.114269
8.8
-2.169199961
1.550102
0.113964
8.9
-2.17187267
1.56517
0.112438
9
-2.18535332
1.577377
0.110626
9.1
-2.201600136
1.589584
0.110626
9.2
-2.201600136
1.59874
0.109711
9.3
-2.209905643
1.607704
0.10849
9.4
-2.221097276
1.622963
0.107574
9.5
-2.229576296
1.629066
0.106678
9.6
-2.237940328
1.644325
0.105762
9.7
-2.246563992
1.650238
0.104847
9.8
-2.255253134
1.662445
0.103931
9.9
-2.264028062
1.6716
0.103016
10
-2.272870963
1.680756
0.101814
10.1
-2.28460766
1.692772
0.100594
10.2
-2.296662665
1.701927
0.099983
10.3
-2.302755107
1.711082
0.099068
10.4
-2.311948796
1.717186
0.098457
10.5
-2.318135374
1.729393
0.097561
10.6
-2.327277456
1.738358
0.096645
10.7
-2.336710808
1.744461
0.09573
10.8
-2.34622355
1.762772
0.095425
10.9
-2.34941468
1.771927
0.093594
11
-2.368789
1.774979
0.093288
11.1
-2.372063797
1.783943
0.092697
11.2
-2.378419169
1.799202
0.091476
11.3
-2.391678636
1.805305
0.090561
11.4
-2.401731622
1.805305
0.090256
11.5
-2.405105202
1.823616
0.088425
11.6
-2.425600544
1.832581
0.088425
11.7
-2.425600544
1.841736
0.086918
11.8
-2.442790134
1.850891
0.087223
11.9
-2.439287221
1.856995
0.085697
12
-2.45693746
1.856995
0.085697
12.1
-2.45693746
1.872253
0.084476
12.2
-2.471287809
1.88427
0.083256
12.3
-2.485835081
1.88427
0.083256
12.4
-2.485835081
1.896477
0.082359
12.5
-2.496667539
1.905632
0.081444
12.6
-2.507839611
1.917839
0.080223
12.7
-2.522945022
1.9207
0.080528
12.8
-2.519150329
1.923752
0.079918
12.9
-2.52675417
1.939011
0.078392
13
-2.546033398
1.951218
0.077801
13.1
-2.553600994
1.957321
0.076885
13.2
-2.56544448
1.966286
0.076275
13.3
-2.573410048
1.975441
0.07597
13.4
-2.577416753
1.978493
0.074749
13.5
-2.593619445
1.987648
0.074444
13.6
-2.597708114
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1.999855
0.074139
13.7
-2.601813569
2.002907
0.072327
13.8
-2.626557776
2.011871
0.072327
13.9
-2.626557776
2.017975
0.071411
14
-2.63930336
2.024078
0.071411
14.1
-2.63930336
2.033234
0.069885
14.2
-2.660904245
2.039337
0.06958
14.3
-2.665278109
2.048492
0.06958
14.4
-2.665278109
2.051544
0.068378
14.5
-2.682704144
2.054596
0.068073
14.6
-2.68717462
2.066612
0.066853
14.7
-2.7052591
2.06356
0.066853
14.8
-2.7052591
2.078819
0.066242
14.9
-2.714440576
2.084923
0.065937
15
-2.719055538
2.091026
0.065022
15.1
-2.733029605
2.100182
0.063801
15.2
-2.751986415
2.103043
0.064106
15.3
-2.747217316
2.112198
0.06321
15.4
-2.761292762
2.118301
0.062599
15.5
-2.771005975
2.124405
0.061073
15.6
-2.795685409
2.127457
0.061989
15.7
-2.780798329
2.130508
0.061378
15.8
-2.790703814
2.142715
0.060463
15.9
-2.805723671
2.148628
0.059853
16
-2.815863723
2.15168
0.059547
16.1
-2.820989362
2.157784
0.058937
16.2
-2.831286202
2.163887
0.058346
16.3
-2.841364474
2.169991
0.058041
16.4
-2.846605622
2.176094
0.05743
16.5
-2.857188464
2.182198
0.05682
16.6
-2.867866903
2.185249
0.05682
16.7
-2.867866903
2.194214
0.056515
16.8
-2.873249189
2.200317
0.054684
16.9
-2.906184117
2.203369
0.054684
17
-2.906184117
2.212524
0.054379
17.1
-2.911777229
2.215576
0.054379
17.2
-2.911777229
2.22168
0.053177
17.3
-2.934129307
2.224731
0.052872
17.4
-2.939881381
2.233887
0.053177
17.5
-2.934129307
2.233887
0.051956
17.6
-2.957358072
2.239799
0.051651
17.7
-2.963245723
2.245903
0.051346
17.8
-2.969168242
2.245903
0.050735
17.9
-2.981139271
2.25811
0.04982
18
-2.999338769
2.25811
0.050125
18.1
-2.993235393
2.264214
0.04921
18.2
-3.011658424
2.273369
0.049515
18.3
-3.005479625
2.276421
0.048618
18.4
-3.023761446
2.282524
0.047703
18.5
-3.04276099
2.285385
0.048313
18.6
-3.030054603
2.288437
0.047092
18.7
-3.055652144
2.29454
0.046482
18.8
-3.068690138
2.297592
0.045567
18.9
-3.088571509
2.306747
0.046482
19
-3.068690138
2.303696
0.045872
19.1
-3.08190037
2.312851
0.045261
19.2
-3.095309544
2.312851
0.044651
19.3
-3.108878575
2.318954
0.044346
19.4
-3.115732766
2.322006
0.043755
19.5
-3.129149387
2.32811
0.043755
19.6
-3.129149387
2.340126
0.043144
19.7
-3.143211921
2.343178
0.042534
19.8
-3.157451523
2.34623
0.042229
19.9
-3.16464809
2.352333
0.041924
20
-3.171896824
2.358437
0.041924
20.1
-3.171896824
2.358437
0.041313
20.2
-3.186578059
2.36454
0.041313
20.3
-3.186578059
2.370644
0.041008
20.4
-3.193988109
2.373695
0.038891
20.5
-3.246992418
2.376747
0.039482
20.6
-3.231910407
2.379608
0.039196
20.7
-3.239180578
2.385712
0.039787
20.8
-3.224215053
2.388763
0.037365
20.9
-3.287020842
2.391815
0.03828
21
-3.262827712
2.391815
0.03828
21.1
-3.262827712
2.40097
0.037365
21.2
-3.287020842
2.40097
0.03706
21.3
-3.295217058
2.407074
0.035839
21.4
-3.328718593
2.410126
0.036755
21.5
-3.303481008
2.416229
0.035534
21.6
-3.337265294
2.416229
0.035839
21.7
-3.328718593
2.422333
0.035229
21.8
-3.345885672
2.425194
0.035229
21.9
-3.345885672
2.428246
0.034332
22
-3.371677415
2.431297
0.034618
22.1
-3.363381501
2.434349
0.033417
22.2
-3.398690526
2.428246
0.034332
22.3
-3.371677415
2.440453
0.033417
22.4
-3.398690526
2.443504
0.032501
22.5
-3.426484421
2.440453
0.033112
22.6
-3.407859525
2.449608
0.032806
22.7
-3.417143853
2.45266
0.032196
22.8
-3.435913058
2.455711
0.032501
22.9
-3.426484421
2.458763
0.032196
23
-3.435913058
2.461815
0.031586
23.1
-3.455041295
2.464867
0.031586
23.2
-3.455041295
2.470779
0.03006
23.3
-3.504559895
2.476883
0.03067
23.4
-3.484470301
2.476883
0.030975
23.5
-3.474574851
2.476883
0.03067
23.6
-3.484470301
2.473831
0.03006
23.7
-3.504559895
2.476883
0.029755
23.8
-3.514758094
2.479935
0.029755
23.9
-3.514758094
2.482986
0.029469
24
-3.524416416
2.486038
0.029469
24.1
-3.524416416
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2.492142
0.028858
24.2
-3.545368028
2.498245
0.028858
24.3
-3.545368028
2.504349
0.028858
24.4
-3.545368028
2.504349
0.027637
24.5
-3.588599824
2.507401
0.027332
24.6
-3.599697102
2.507401
0.027332
24.7
-3.599697102
2.507401
0.027332
24.8
-3.599697102
2.516365
0.027332
24.9
-3.599697102
2.513504
0.027027
25
-3.610918913
2.519417
0.027027
25.1
-3.610918913
2.522469
0.025806
25.2
-3.657148256
2.522469
0.026112
25.3
-3.6453603
2.516365
0.026112
25.4
-3.6453603
2.531624
0.025501
25.5
-3.669037612
2.531624
0.025196
25.6
-3.681070027
2.531624
0.025196
25.7
-3.681070027
2.537727
0.025501
25.8
-3.669037612
2.537727
0.024891
25.9
-3.693248987
2.540779
0.024891
26
-3.693248987
2.546883
0.023994
26.1
-3.72995148
2.543831
0.023994
26.2
-3.72995148
2.546883
0.024605
26.3
-3.704805605
2.549934
0.023689
26.4
-3.742744474
2.546883
0.023689
26.5
-3.742744474
2.552986
0.022774
26.6
-3.782135745
2.552986
0.023079
26.7
-3.768832166
2.55909
0.022469
26.8
-3.795618698
2.55909
0.022774
26.9
-3.782135745
2.565002
0.021553
27
-3.837240261
2.556038
0.022774
27.1
-3.782135745
2.565002
0.022163
27.2
-3.809331047
2.571106
0.022774
27.3
-3.782135745
2.571106
0.022163
27.4
-3.809331047
2.574158
0.020638
27.5
-3.880621242
2.574158
0.021553
27.6
-3.837240261
2.574158
0.021248
27.7
-3.851492506
2.580261
0.020027
27.8
-3.910673916
2.580261
0.021248
27.9
-3.851492506
2.583313
0.020638
28
-3.880621242
2.586365
0.020332
28.1
-3.895559279
2.586365
0.020332
28.2
-3.895559279
2.583313
0.020332
28.3
-3.895559279
2.592468
0.020332
28.4
-3.895559279
2.589417
0.020027
28.5
-3.910673916
2.59552
0.019131
28.6
-3.956445223
2.598572
0.019131
28.7
-3.956445223
2.601624
0.020027
28.8
-3.910673916
2.59552
0.019741
28.9
-3.925057588
2.601624
0.019131
29
-3.956445223
2.601624
0.019131
29.1
-3.956445223
2.604675
0.018826
29.2
-3.972516386
2.604675
0.01852
29.3
-3.98890405
2.610588
0.01791
29.4
-4.022396063
2.610588
0.017605
29.5
-4.039572326
2.61364
0.0173
29.6
-4.057048777
2.616692
0.01791
29.7
-4.022396063
2.619743
0.01791
29.8
-4.022396063
2.616692
0.01791
29.9
-4.022396063
2.622795
0.017605
30
-4.039572326
2.622795
0.016689
30.1
-4.093005459
2.622795
0.016384
30.2
-4.11145003
2.625847
0.016079
30.3
-4.130241206
2.625847
0.016384
30.4
-4.11145003
2.625847
0.016079
30.5
-4.130241206
2.625847
0.016384
30.6
-4.11145003
2.628899
0.016689
30.7
-4.093005459
2.628899
0.016689
30.8
-4.093005459
2.628899
0.016384
30.9
-4.11145003
2.635002
0.016689
31
-4.093005459
2.635002
0.016384
31.1
-4.11145003
2.638054
0.015163
31.2
-4.188897029
2.638054
0.015774
31.3
-4.149392264
2.638054
0.015774
31.4
-4.149392264
2.63195
0.015469
31.5
-4.168917258
2.647209
0.015774
31.6
-4.149392264
2.647209
0.015469
31.7
-4.168917258
2.644157
0.015163
31.8
-4.188897029
2.644157
0.015163
31.9
-4.188897029
2.650261
0.015774
32
-4.149392264
2.650261
0.014877
32.1
-4.207938883
2.650261
0.014877
32.2
-4.207938883
2.653122
0.015163
32.3
-4.188897029
2.656174
0.014267
32.4
-4.249806101
2.653122
0.014572
32.5
-4.2286534
2.659225
0.014877
32.6
-4.207938883
2.659225
0.014267
32.7
-4.249806101
2.653122
0.014267
32.8
-4.249806101
2.659225
0.012741
32.9
-4.362930139
2.659225
0.013657
33
-4.293503068
2.662277
0.014267
33.1
-4.249806101
2.662277
0.013657
33.2
-4.293503068
2.662277
0.013657
33.3
-4.293503068
2.668381
0.013046
33.4
-4.339273706
2.659225
0.013351
33.5
-4.316163991
2.668381
0.012436
33.6
-4.387159787
2.668381
0.013351
33.7
-4.316163991
2.671432
0.012131
33.8
-4.411991119
2.668381
0.013046
33.9
-4.339273706
2.674484
0.011826
34
-4.437454782
2.668381
0.012741
34.1
-4.362930139
2.674484
0.012436
34.2
-4.387159787
2.674484
0.013046
34.3
-4.339273706
2.674484
0.012436
34.4
-4.387159787
2.677536
0.01152
34.5
-4.463670624
2.677536
0.012131
34.6
-4.411991119
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2.68364
0.011826
34.7
-4.437454782
2.68364
0.012436
34.8
-4.387159787
2.680588
0.011826
34.9
-4.437454782
2.68364
0.011215
35
-4.490503111
2.68364
0.012131
35.1
-4.411991119
2.68364
0.01152
35.2
-4.463670624
2.686691
0.01152
35.3
-4.463670624
2.692795
0.011826
35.4
-4.437454782
2.686691
0.01152
35.5
-4.463670624
2.689743
0.01091
35.6
-4.518075479
2.692795
0.0103
35.7
-4.575611384
2.692795
0.01152
35.8
-4.463670624
2.692795
0.01091
35.9
-4.518075479
2.692795
0.01091
36
-4.518075479
2.692795
0.010014
36.1
-4.603771165
2.692795
0.01091
36.2
-4.518075479
2.695847
0.01091
36.3
-4.518075479
2.695847
0.010605
36.4
-4.546429691
2.698708
0.010014
36.5
-4.603771165
2.698708
0.0103
36.6
-4.575611384
2.695847
0.010605
36.7
-4.546429691
2.698708
0.0103
36.8
-4.575611384
2.698708
0.010014
36.9
-4.603771165
2.698708
0.010014
37
-4.603771165
2.701759
0.009403
37.1
-4.666726492
2.704811
0.009098
37.2
-4.69970067
2.707863
0.0103
37.3
-4.575611384
2.701759
0.0103
37.4
-4.575611384
2.701759
0.010014
37.5
-4.603771165
2.707863
0.009708
37.6
-4.634804991
2.707863
0.009403
37.7
-4.666726492
2.707863
0.009403
37.8
-4.666726492
2.707863
0.009403
37.9
-4.666726492
2.710915
0.009403
38
-4.666726492
2.713966
0.009403
38.1
-4.666726492
2.713966
0.008793
38.2
-4.733799329
2.710915
0.008183
38.3
-4.805696447
2.713966
0.008183
38.4
-4.805696447
2.713966
0.008183
38.5
-4.805696447
2.717018
0.008183
38.6
-4.805696447
2.717018
0.008183
38.7
-4.805696447
2.723122
0.008183
38.8
-4.805696447
2.717018
0.008488
38.9
-4.769101878
2.717018
0.009098
39
-4.69970067
2.717018
0.008793
39.1
-4.733799329
2.723122
0.008793
39.2
-4.733799329
2.723122
0.008488
39.3
-4.769101878
2.723122
0.008488
39.4
-4.769101878
2.710915
0.008488
39.5
-4.769101878
2.723122
0.008488
39.6
-4.769101878
2.729225
0.008488
39.7
-4.769101878
2.729225
0.006962
39.8
-4.96728849
2.729225
0.007267
39.9
-4.924411727
2.729225
0.007877
40
-4.843808158
2.729225
0.008183
40.1
-4.805696447
2.729225
0.008183
40.2
-4.805696447
2.732277
0.008183
40.3
-4.805696447
2.732277
0.007572
40.4
-4.883298046
2.732277
0.006962
40.5
-4.96728849
2.732277
0.007877
40.6
-4.843808158
2.735329
0.007877
40.7
-4.843808158
2.732277
0.008183
40.8
-4.805696447
2.735329
0.006657
40.9
-5.012086346
2.735329
0.007572
41
-4.883298046
2.735329
0.007572
41.1
-4.883298046
2.735329
0.007877
41.2
-4.843808158
2.73838
0.006351
41.3
-5.059142998
2.735329
0.007267
41.4
-4.924411727
2.735329
0.007267
41.5
-4.924411727
2.741432
0.007572
41.6
-4.883298046
2.741432
0.006962
41.7
-4.96728849
2.744293
0.006962
41.8
-4.96728849
2.744293
0.007572
41.9
-4.883298046
2.744293
0.006962
42
-4.96728849
2.744293
0.006962
42.1
-4.96728849
2.744293
0.007572
42.2
-4.883298046
2.741432
0.006962
42.3
-4.96728849
2.744293
0.006962
42.4
-4.96728849
2.744293
0.006657
42.5
-5.012086346
2.744293
0.006657
42.6
-5.012086346
2.73838
0.006962
42.7
-4.96728849
2.747345
0.005436
42.8
-5.214711783
2.744293
0.006657
42.9
-5.012086346
2.747345
0.006962
43
-4.96728849
2.747345
0.005741
43.1
-5.160121868
2.747345
0.006657
43.2
-5.012086346
2.750397
0.006962
43.3
-4.96728849
2.747345
0.006351
43.4
-5.059142998
2.741432
0.006657
43.5
-5.012086346
2.750397
0.005436
43.6
-5.214711783
2.750397
0.006046
43.7
-5.108358383
2.7565
0.006657
43.8
-5.012086346
2.750397
0.005741
43.9
-5.160121868
2.750397
0.006351
44
-5.059142998
2.750397
0.005741
44.1
-5.160121868
2.744293
0.006351
44.2
-5.059142998
2.753448
0.005741
44.3
-5.160121868
2.747345
0.006351
44.4
-5.059142998
2.7565
0.005741
44.5
-5.160121868
2.747345
0.006657
44.6
-5.012086346
2.7565
0.005741
44.7
-5.160121868
2.7565
0.006046
44.8
-5.108358383
2.7565
0.005436
44.9
-5.214711783
2.753448
0.006046
45
-5.108358383
Table 1:
Data for experiment 2 showing current, voltage and time.
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Appendix B
Data Collection for RC Circuit in Series from Experiment 3
Current (A)
Time (s)
ln(current)
-1.91E-05
0.1
#NUM!
0.000286
0.2
-8.159161137
2.86E-04
0.3
-8.159161137
-1.91E-05
0.4
#NUM!
2.36E-01
0.5
-1.441920889
2.30E-01
0.6
-1.470640392
0.224915
0.7
-1.492034723
0.220966
0.8
-1.509744901
2.17E-01
0.9
-1.527774392
0.21307
1
-1.546134924
0.209427
1.1
-1.563380623
0.20607
1.2
-1.579539623
0.202122
1.3
-1.598885116
0.198784
1.4
-1.615537102
0.195122
1.5
-1.634131479
0.191479
1.6
-1.652978551
0.188141
1.7
-1.670564293
0.185394
1.8
-1.68527044
0.182056
1.9
-1.703438601
0.178719
2
-1.721942962
0.175972
2.1
-1.737430474
0.172939
2.2
-1.75481461
0.170212
2.3
-1.770711782
0.16716
2.4
-1.788803637
0.164738
2.5
-1.803400758
0.161381
2.6
-1.823988689
0.158958
2.7
-1.839112526
0.155621
2.8
-1.860334446
0.153179
2.9
-1.876147005
0.150452
3
-1.894113441
0.14801
3.1
-1.910473724
0.145588
3.2
-1.926975106
0.142841
3.3
-1.946020781
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0.140724
3.4
-1.960953459
0.138283
3.5
-1.97845459
0.13586
3.6
-1.996127074
0.134029
3.7
-2.009696186
0.131607
3.8
-2.027934647
0.129166
3.9
-2.046659594
0.127029
4
-2.063336574
0.125217
4.1
-2.077703551
0.122776
4.2
-2.097393466
0.120964
4.3
-2.112261883
0.118828
4.4
-2.130079726
0.116405
4.5
-2.150675605
0.11488
4.6
-2.163870585
0.112438
4.7
-2.185351525
0.110626
4.8
-2.201598141
0.108795
4.9
-2.218288376
0.107288
5
-2.232235111
0.105457
5.1
-2.249449091
0.103626
5.2
-2.266964591
0.101814
5.3
-2.284605008
0.100288
5.4
-2.299705332
0.098457
5.5
-2.318131957
0.096951
5.6
-2.33355442
0.095119
5.7
-2.352621532
0.093594
5.8
-2.368793302
0.092087
5.9
-2.385023755
0.090561
6
-2.401732582
0.08873
6.1
-2.422158824
0.087223
6.2
-2.439286614
0.086002
6.3
-2.453380659
0.084476
6.4
-2.471282234
0.083256
6.5
-2.485837869
0.082054
6.6
-2.500376028
0.080528
6.7
-2.519147109
0.079308
6.8
-2.534421869
0.077496
6.9
-2.557534442
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0.076275
7
-2.573411729
0.075054
7.1
-2.589545177
0.073833
7.2
-2.605943187
0.072632
7.3
-2.622351942
0.071411
7.4
-2.6393015
0.069885
7.5
-2.660900612
0.068665
7.6
-2.678522213
0.067768
7.7
-2.691663742
0.066853
7.8
-2.705265538
0.065632
7.9
-2.723693932
0.064411
8
-2.742468317
0.063515
8.1
-2.756483755
0.062599
8.2
-2.771003066
0.061378
8.3
-2.79069601
0.060463
8.4
-2.805724471
0.059242
8.5
-2.826120334
0.058346
8.6
-2.841367993
0.05743
8.7
-2.857183809
0.056515
8.8
-2.87325379
0.055599
8.9
-2.889586239
0.054684
9
-2.906189872
0.054073
9.1
-2.917414121
0.052872
9.2
-2.939886977
0.051956
9.3
-2.95735467
0.051346
9.4
-2.969171647
0.05043
9.5
-2.987163137
0.049515
9.6
-3.00548426
0.048923
9.7
-3.01749758
0.048008
9.8
-3.036388343
0.047092
9.9
-3.055642848
0.046482
10
-3.068688284
0.045567
10.1
-3.08858119
0.044651
10.2
-3.10887787
0.044346
10.3
-3.11573602
0.043449
10.4
-3.136158194
0.042534
10.5
-3.157454473
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0.042229
10.6
-3.164655224
0.041313
10.7
-3.18657391
0.040703
10.8
-3.201457906
0.040092
10.9
-3.216566786
0.038891
11
-3.246996567
0.03828
11.1
-3.262814989
0.03767
11.2
-3.27888766
0.03706
11.3
-3.295222888
0.036449
11.4
-3.311829393
0.035839
11.5
-3.328716338
0.035229
11.6
-3.345893357
0.034618
11.7
-3.363370591
0.034027
11.8
-3.380598025
0.033722
11.9
-3.389607094
0.032806
12
-3.417131768
0.032501
12.1
-3.42647763
0.031891
12.2
-3.445435544
0.031281
12.3
-3.464759817
0.030975
12.4
-3.474563817
0.030365
12.5
-3.494464971
0.03006
12.6
-3.504566067
0.029469
12.7
-3.524432148
0.029163
12.8
-3.534842132
0.028553
12.9
-3.555992953
0.027943
13
-3.577600816
0.027637
13.1
-3.588582395
0.027027
13.2
-3.610914098
0.026722
13.3
-3.622269791
0.026112
13.4
-3.645375512
0.026112
13.5
-3.645375512
0.025196
13.6
-3.681067033
0.025196
13.7
-3.681067033
0.024605
13.8
-3.70481384
0.024605
13.9
-3.70481384
0.023689
14
-3.742733075
0.023689
14.1
-3.742733075
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0.023079
14.2
-3.768835699
0.022774
14.3
-3.782147044
0.022469
14.4
-3.795637973
0.021858
14.5
-3.82317844
0.021858
14.6
-3.82317844
0.021248
14.7
-3.851498917
0.020943
14.8
-3.865965716
0.020638
14.9
-3.880644878
0.020332
15
-3.895542733
0.020027
15.1
-3.910665894
0.019741
15.2
-3.925054632
0.019131
15.3
-3.95646055
0.019131
15.4
-3.95646055
0.01852
15.5
-3.988884869
0.01852
15.6
-3.988884869
0.018215
15.7
-4.005499997
0.01791
15.8
-4.022395858
0.01791
15.9
-4.022395858
0.0173
16
-4.057068888
0.0173
16.1
-4.057068888
0.016689
16.2
-4.092987451
0.016384
16.3
-4.111442416
0.016384
16.4
-4.111442416
0.016079
16.5
-4.13024438
0.015774
16.6
-4.149406643
0.015774
16.7
-4.149406643
0.015163
16.8
-4.188869223
0.015163
16.9
-4.188869223
0.014877
17
-4.207917418
0.014572
17.1
-4.228643548
0.014267
17.2
-4.24980836
0.014267
17.3
-4.24980836
0.013962
17.4
-4.271430824
0.013962
17.5
-4.271430824
0.013657
17.6
-4.293531171
0.013351
17.7
-4.316131003
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0.013046
17.8
-4.33925342
0.013046
17.9
-4.33925342
0.012741
18
-4.362923164
0.012741
18.1
-4.362923164
0.012436
18.2
-4.387166776
0.012131
18.3
-4.412012774
0.011826
18.4
-4.43749186
0.011826
18.5
-4.43749186
0.01152
18.6
-4.46363714
0.01152
18.7
-4.46363714
0.01152
18.8
-4.46363714
0.01091
18.9
-4.518072346
0.011215
19
-4.49048439
0.010605
19.1
-4.546443043
0.010605
19.2
-4.546443043
0.0103
19.3
-4.575642198
0.0103
19.4
-4.575642198
0.0103
19.5
-4.575642198
0.010014
19.6
-4.603813075
0.010014
19.7
-4.603813075
0.009708
19.8
-4.634763321
0.009403
19.9
-4.666702164
0.009403
20
-4.666702164
0.009098
20.1
-4.699694847
0.009403
20.2
-4.666702164
0.009098
20.3
-4.699694847
0.009098
20.4
-4.699694847
0.008793
20.5
-4.733813295
0.008793
20.6
-4.733813295
0.008488
20.7
-4.769137055
0.008183
20.8
-4.805754419
0.008183
20.9
-4.805754419
0.007877
21
-4.843763745
0.008183
21.1
-4.805754419
0.007877
21.2
-4.843763745
0.007877
21.3
-4.843763745
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0.007877
21.4
-4.843763745
0.007572
21.5
-4.883275057
0.007572
21.6
-4.883275057
0.007267
21.7
-4.924411963
0.007267
21.8
-4.924411963
0.006962
21.9
-4.967313984
0.006962
22
-4.967313984
0.006962
22.1
-4.967313984
0.006657
22.2
-5.012139415
0.006657
22.3
-5.012139415
0.006657
22.4
-5.012139415
0.006351
22.5
-5.059068848
0.006657
22.6
-5.012139415
0.006351
22.7
-5.059068848
0.006351
22.8
-5.059068848
0.006046
22.9
-5.108309564
0.006046
23
-5.108309564
0.006046
23.1
-5.108309564
0.005741
23.2
-5.160101073
0.005741
23.3
-5.160101073
0.005741
23.4
-5.160101073
0.005741
23.5
-5.160101073
0.005436
23.6
-5.214722157
0.005436
23.7
-5.214722157
0.005741
23.8
-5.160101073
5.44E-03
23.9
-5.214722157
0.005436
24
-5.214722157
0.00515
24.1
-5.268789379
0.00515
24.2
-5.268789379
0.005436
24.3
-5.214722157
0.00515
24.4
-5.268789379
0.00515
24.5
-5.268789379
0.00515
24.6
-5.268789379
0.004845
24.7
-5.329877071
0.00515
24.8
-5.268789379
0.004539
24.9
-5.394940664
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0.004845
25
-5.329877071
0.004539
25.1
-5.394940664
0.004845
25.2
-5.329877071
0.004845
25.3
-5.329877071
0.004234
25.4
-5.464533956
0.004539
25.5
-5.394940664
0.004234
25.6
-5.464533956
0.004539
25.7
-5.394940664
0.004539
25.8
-5.394940664
0.004234
25.9
-5.464533956
0.004234
26
-5.464533956
0.004234
26.1
-5.464533956
0.004234
26.2
-5.464533956
0.004234
26.3
-5.464533956
0.003929
26.4
-5.539335169
0.003929
26.5
-5.539335169
0.003624
26.6
-5.620187265
0.003929
26.7
-5.539335169
0.003624
26.8
-5.620187265
0.003624
26.9
-5.620187265
0.003624
27
-5.620187265
0.003624
27.1
-5.620187265
0.003624
27.2
-5.620187265
3.32E-03
27.3
-5.708156038
0.003319
27.4
-5.708156038
0.003319
27.5
-5.708156038
0.003319
27.6
-5.708156038
0.003014
27.7
-5.804616305
0.003319
27.8
-5.708156038
0.003319
27.9
-5.708156038
0.003014
28
-5.804616305
0.003319
28.1
-5.708156038
0.003014
28.2
-5.804616305
0.003014
28.3
-5.804616305
0.003014
28.4
-5.804616305
0.003014
28.5
-5.804616305
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0.003014
28.6
-5.804616305
0.003014
28.7
-5.804616305
0.003014
28.8
-5.804616305
0.003014
28.9
-5.804616305
0.002708
29
-5.91138428
0.003014
29.1
-5.804616305
0.002708
29.2
-5.91138428
3.01E-03
29.3
-5.804616305
0.002708
29.4
-5.91138428
2.71E-03
29.5
-5.91138428
0.002708
29.6
-5.91138428
0.002708
29.7
-5.91138428
0.002403
29.8
-6.030929431
2.71E-03
29.9
-5.91138428
0.002098
30
-6.166730972
0.002708
30.1
-5.91138428
2.71E-03
30.2
-5.91138428
0.002403
30.3
-6.030929431
0.002708
30.4
-5.91138428
0.002403
30.5
-6.030929431
0.002403
30.6
-6.030929431
0.002403
30.7
-6.030929431
0.002098
30.8
-6.166730972
0.002708
30.9
-5.91138428
0.002098
31
-6.166730972
0.002098
31.1
-6.166730972
0.002403
31.2
-6.030929431
0.002098
31.3
-6.166730972
0.002098
31.4
-6.166730972
0.002098
31.5
-6.166730972
0.002098
31.6
-6.166730972
0.002098
31.7
-6.166730972
0.001793
31.8
-6.323916555
0.002098
31.9
-6.166730972
0.002098
32
-6.166730972
0.002098
32.1
-6.166730972
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0.002098
32.2
-6.166730972
0.001793
32.3
-6.323916555
0.002098
32.4
-6.166730972
0.001793
32.5
-6.323916555
0.001793
32.6
-6.323916555
0.001793
32.7
-6.323916555
0.001793
32.8
-6.323916555
0.001793
32.9
-6.323916555
0.001793
33
-6.323916555
0.001793
33.1
-6.323916555
0.002098
33.2
-6.166730972
0.001793
33.3
-6.323916555
0.001793
33.4
-6.323916555
0.001793
33.5
-6.323916555
0.001793
33.6
-6.323916555
0.001793
33.7
-6.323916555
0.001793
33.8
-6.323916555
0.001793
33.9
-6.323916555
0.001793
34
-6.323916555
0.001793
34.1
-6.323916555
0.001793
34.2
-6.323916555
0.001793
34.3
-6.323916555
0.001793
34.4
-6.323916555
0.001793
34.5
-6.323916555
0.001793
34.6
-6.323916555
0.001793
34.7
-6.323916555
0.001793
34.8
-6.323916555
0.001793
34.9
-6.323916555
0.001488
35
-6.510502511
1.49E-03
35.1
-6.510502511
0.001793
35.2
-6.323916555
0.001488
35.3
-6.510502511
0.001793
35.4
-6.323916555
0.001488
35.5
-6.510502511
0.001488
35.6
-6.510502511
0.001488
35.7
-6.510502511
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0.001793
35.8
-6.323916555
0.001488
35.9
-6.510502511
1.18E-03
36
-6.740076953
1.18E-03
36.1
-6.740076953
0.001183
36.2
-6.740076953
1.18E-03
36.3
-6.740076953
0.001183
36.4
-6.740076953
0.001488
36.5
-6.510502511
0.001793
36.6
-6.323916555
1.49E-03
36.7
-6.510502511
0.001488
36.8
-6.510502511
0.001183
36.9
-6.740076953
0.001488
37
-6.510502511
0.001488
37.1
-6.510502511
0.001183
37.2
-6.740076953
0.001183
37.3
-6.740076953
0.000877
37.4
-7.038569941
0.001183
37.5
-6.740076953
0.001183
37.6
-6.740076953
1.18E-03
37.7
-6.740076953
0.001183
37.8
-6.740076953
0.001488
37.9
-6.510502511
0.001183
38
-6.740076953
0.001488
38.1
-6.510502511
0.001183
38.2
-6.740076953
0.001183
38.3
-6.740076953
0.001183
38.4
-6.740076953
0.001488
38.5
-6.510502511
0.001183
38.6
-6.740076953
0.001183
38.7
-6.740076953
0.001183
38.8
-6.740076953
0.001183
38.9
-6.740076953
0.001183
39
-6.740076953
0.001183
39.1
-6.740076953
0.001183
39.2
-6.740076953
0.001183
39.3
-6.740076953
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0.001183
39.4
-6.740076953
0.000877
39.5
-7.038569941
0.001183
39.6
-6.740076953
0.001183
39.7
-6.740076953
0.001183
39.8
-6.740076953
8.77E-04
39.9
-7.038569941
0.001183
40
-6.740076953
0.000877
40.1
-7.038569941
0.000877
40.2
-7.038569941
0.000877
40.3
-7.038569941
1.18E-03
40.4
-6.740076953
0.001183
40.5
-6.740076953
0.000877
40.6
-7.038569941
0.000877
40.7
-7.038569941
0.000877
40.8
-7.038569941
1.18E-03
40.9
-6.740076953
0.000877
41
-7.038569941
0.001183
41.1
-6.740076953
0.000877
41.2
-7.038569941
0.000877
41.3
-7.038569941
0.001183
41.4
-6.740076953
0.000877
41.5
-7.038569941
0.001183
41.6
-6.740076953
0.000877
41.7
-7.038569941
0.001183
41.8
-6.740076953
0.000877
41.9
-7.038569941
0.001183
42
-6.740076953
0.000877
42.1
-7.038569941
0.000877
42.2
-7.038569941
8.77E-04
42.3
-7.038569941
0.000877
42.4
-7.038569941
0.000877
42.5
-7.038569941
0.000877
42.6
-7.038569941
0.000877
42.7
-7.038569941
0.001183
42.8
-6.740076953
0.000877
42.9
-7.038569941
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Table 1:
Data for experiment 3 of RC Circuit in series.
0.000877
43
-7.038569941
0.000877
43.1
-7.038569941
0.000877
43.2
-7.038569941
0.000877
43.3
-7.038569941
0.000877
43.4
-7.038569941
0.000877
43.5
-7.038569941
0.000877
43.6
-7.038569941
8.77E-04
43.7
-7.038569941
0.001183
43.8
-6.740076953
0.000877
43.9
-7.038569941
8.77E-04
44
-7.038569941
0.000877
44.1
-7.038569941
0.000877
44.2
-7.038569941
0.000877
44.3
-7.038569941
0.000877
44.4
-7.038569941
0.000572
44.5
-7.466013956
0.000877
44.6
-7.038569941
0.000572
44.7
-7.466013956
0.000877
44.8
-7.038569941
0.000877
44.9
-7.038569941
0.000877
45
-7.038569941
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Appendix C
Data Collection for RC Circuit in Parallel from Experiment 3
Current (A)
Time (s)
ln(current)
0.0002861
0.1
-8.1591611
0.0005722
0.2
-7.466014
0.0005722
0.3
-7.466014
0.0002861
0.4
-8.1591611
0.0002861
0.5
-8.1591611
0.2428627
0.6
-1.415259
0.24133682
0.7
-1.4215617
0.24011612
0.8
-1.4266326
0.23889542
0.9
-1.4317294
0.23769379
1
-1.436772
0.23647308
1.1
-1.4419209
0.23555756
1.2
-1.4458
0.23374557
1.3
-1.453522
0.23283005
1.4
-1.4574465
0.23160934
1.5
-1.4627032
0.23038864
1.6
-1.4679877
0.22916794
1.7
-1.4733002
0.22827148
1.8
-1.4772196
0.22735596
1.9
-1.4812384
0.22644043
2
-1.4852734
0.22521973
2.1
-1.4906788
0.2243042
2.2
-1.4947521
0.22310257
2.3
-1.5001237
0.22218704
2.4
-1.5042357
0.22096634
2.5
-1.5097449
0.22005081
2.6
-1.5138968
0.21915436
2.7
-1.517979
0.21823883
2.8
-1.5221653
0.21701813
2.9
-1.5277744
0.21640778
3
-1.5305908
0.21518707
3.1
-1.5362475
0.21429062
3.2
-1.5404222
0.21337509
3.3
-1.5447037
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0.21215439
3.4
-1.550441
0.21123886
3.5
-1.5547657
0.21032333
3.6
-1.5591092
0.20942688
3.7
-1.5633806
0.20851135
3.8
-1.5677618
0.20759583
3.9
-1.5721622
0.20637512
4
-1.5780598
0.20545959
4.1
-1.5825059
0.20484924
4.2
-1.585481
0.20395279
4.3
-1.5898667
0.20273209
4.4
-1.5958699
0.20212173
4.5
-1.5988851
0.20090103
4.6
-1.6049429
0.1999855
4.7
-1.6095104
0.19908905
4.8
-1.6140031
0.19817352
4.9
-1.6186123
0.19756317
5
-1.6216969
0.19634247
5.1
-1.6278949
0.19573212
5.2
-1.6310083
0.19422531
5.3
-1.6387364
0.19330978
5.4
-1.6434613
0.19269943
5.5
-1.6466236
0.19147873
5.6
-1.6529786
0.1905632
5.7
-1.6577714
0.18997192
5.8
-1.660879
0.18936157
5.9
-1.664097
0.18814087
6
-1.6705643
0.18722534
6.1
-1.6754424
0.18661499
6.2
-1.6787077
0.18569946
6.3
-1.6836257
0.18480301
6.4
-1.6884648
0.18358231
6.5
-1.6950922
0.18327713
6.6
-1.6967559
0.18205643
6.7
-1.7034386
0.18175125
6.8
-1.7051163
0.18053055
6.9
-1.7118553
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0.17993927
7
-1.7151359
0.17902374
7.1
-1.7202368
0.17810822
7.2
-1.725364
0.17749786
7.3
-1.7287967
0.17688751
7.4
-1.7322413
0.17566681
7.5
-1.7391662
0.17538071
7.6
-1.7407962
0.17446518
7.7
-1.7460301
0.17354965
7.8
-1.7512915
0.1729393
7.9
-1.7548146
0.17202377
8
-1.7601226
0.17110825
8.1
-1.7654589
0.17051697
8.2
-1.7689205
0.16960144
8.3
-1.7743041
0.16868591
8.4
-1.7797168
0.16838074
8.5
-1.7815276
0.16716003
8.6
-1.7888036
0.16654968
8.7
-1.7924616
0.16593933
8.8
-1.796133
0.16504288
8.9
-1.80155
0.1647377
9
-1.8034008
0.163517
9.1
-1.8108383
0.16260147
9.2
-1.816453
0.1622963
9.3
-1.8183316
0.16138077
9.4
-1.8239887
0.16078949
9.5
-1.8276593
0.16017914
9.6
-1.8314625
0.15926361
9.7
-1.8371945
0.15865326
9.8
-1.8410342
0.15804291
9.9
-1.8448887
0.15712738
10
-1.8506985
0.15592575
10.1
-1.8583753
0.1553154
10.2
-1.8622974
0.15439987
10.3
-1.8682095
0.15378952
10.4
-1.8721704
0.15317917
10.5
-1.876147
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0.15256882
10.6
-1.8801395
0.15165329
10.7
-1.8861584
0.15106201
10.8
-1.8900649
0.15045166
10.9
-1.8941134
0.14953613
11
-1.9002172
0.14892578
11.1
-1.9043072
0.14862061
11.2
-1.9063585
0.14770508
11.3
-1.9125377
0.14678955
11.4
-1.9187553
0.14619827
11.5
-1.9227915
0.14558792
11.6
-1.9269751
0.14497757
11.7
-1.9311762
0.14436722
11.8
-1.9353951
0.14375687
11.9
-1.9396318
0.14314651
12
-1.9438866
0.14223099
12.1
-1.9503029
0.14162064
12.2
-1.9546034
0.14072418
12.3
-1.9609535
0.14041901
12.4
-1.9631244
0.13980865
12.5
-1.9674805
0.1391983
12.6
-1.9718557
0.13858795
12.7
-1.9762501
0.1379776
12.8
-1.9806639
0.13736725
12.9
-1.9850973
0.1367569
13
-1.9895504
0.13616562
13.1
-1.9938833
0.13586044
13.2
-1.9961271
0.13494492
13.3
-2.0028886
0.13463974
13.4
-2.0051527
0.13372421
13.5
-2.0119757
0.13311386
13.6
-2.0165504
0.13219833
13.7
-2.023452
0.13189316
13.8
-2.0257631
0.13130188
13.9
-2.0302562
0.13069153
14
-2.0349155
0.129776
14.1
-2.0419454
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0.12947083
14.2
-2.0442997
0.12886047
14.3
-2.0490251
0.12825012
14.4
-2.0537728
0.12763977
14.5
-2.0585433
0.12702942
14.6
-2.0633366
0.12702942
14.7
-2.0633366
0.12613297
14.8
-2.0704186
0.12552261
14.9
-2.0752693
0.12491226
15
-2.0801437
0.12430191
15.1
-2.0850419
0.12369156
15.2
-2.0899642
0.12338638
15.3
-2.0924345
0.12247086
15.4
-2.0998822
0.12216568
15.5
-2.1023771
0.12126923
15.6
-2.1097422
0.12096405
15.7
-2.1122619
0.1203537
15.8
-2.1173204
0.11974335
15.9
-2.1224046
0.11943817
16
-2.1249564
0.11882782
16.1
-2.1300797
0.11852264
16.2
-2.1326512
0.11760712
16.3
-2.1404057
0.11640549
16.4
-2.1506756
0.11610031
16.5
-2.1533007
0.11548996
16.6
-2.1585717
0.11518478
16.7
-2.1612176
0.11487961
16.8
-2.1638706
0.11396408
16.9
-2.171872
0.11365891
17
-2.1745534
0.11274338
17.1
-2.182641
0.11274338
17.2
-2.182641
0.1124382
17.3
-2.1853515
0.11154175
17.4
-2.1933563
0.1109314
17.5
-2.1988433
0.11032104
17.6
-2.2043606
0.11001587
17.7
-2.2071307
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0.10971069
17.8
-2.2099084
0.10910034
17.9
-2.2154873
0.10818481
18
-2.2239143
0.10787964
18.1
-2.2267391
0.10757446
18.2
-2.229572
0.10728836
18.3
-2.2322351
0.10667801
18.4
-2.2379402
0.10606766
18.5
-2.2436781
0.10545731
18.6
-2.2494491
0.10515213
18.7
-2.2523471
0.10454178
18.8
-2.2581685
0.10393143
18.9
-2.264024
0.10393143
19
-2.264024
0.10332108
19.1
-2.2699139
0.10271072
19.2
-2.2758387
0.10211945
19.3
-2.2816121
0.10181427
19.4
-2.284605
0.10120392
19.5
-2.2906178
0.10059357
19.6
-2.296667
0.10059357
19.7
-2.296667
0.10028839
19.8
-2.2997053
0.09937286
19.9
-2.3088762
0.09937286
20
-2.3088762
0.09845734
20.1
-2.318132
0.09784698
20.2
-2.3243504
0.09784698
20.3
-2.3243504
0.09725571
20.4
-2.3304116
0.09664536
20.5
-2.3367071
0.09664536
20.6
-2.3367071
0.09572983
20.7
-2.3462253
0.09542465
20.8
-2.3494183
0.09542465
20.9
-2.3494183
0.09450912
21
-2.3590589
0.09420395
21.1
-2.3622932
0.0935936
21.2
-2.3687933
0.09328842
21.3
-2.3720593
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0.09298325
21.4
-2.375336
0.09239197
21.5
-2.3817152
0.09208679
21.6
-2.3850238
0.09178162
21.7
-2.3883433
0.09117126
21.8
-2.3950155
0.09086609
21.9
-2.3983684
0.09056091
22
-2.4017326
0.09025574
22.1
-2.4051081
0.08964539
22.2
-2.4118935
0.08903503
22.3
-2.4187253
0.08872986
22.4
-2.4221588
0.08811951
22.5
-2.4290614
0.08811951
22.6
-2.4290614
0.08752823
22.7
-2.4357939
0.08722305
22.8
-2.4392866
0.0866127
22.9
-2.4463088
0.08630753
23
-2.4498385
0.08600235
23.1
-2.4533807
0.08569717
23.2
-2.4569354
0.08508682
23.3
-2.4640831
0.08478165
23.4
-2.4676762
0.08447647
23.5
-2.4712822
0.0841713
23.6
-2.4749013
0.08356094
23.7
-2.482179
0.08325577
23.8
-2.4858379
0.08296967
23.9
-2.4892802
0.08235931
24
-2.4966637
0.08205414
24.1
-2.500376
0.08174896
24.2
-2.5041022
0.08144379
24.3
-2.5078422
0.08083344
24.4
-2.5153646
0.08083344
24.5
-2.5153646
0.07991791
24.6
-2.5267553
0.07991791
24.7
-2.5267553
0.07961273
24.8
-2.5305813
0.07930756
24.9
-2.5344219
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0.07810593
25
-2.5496893
0.07810593
25.1
-2.5496893
0.07749557
25.2
-2.5575344
0.07749557
25.3
-2.5575344
0.07688522
25.4
-2.5654416
0.07658005
25.5
-2.5694187
0.07627487
25.6
-2.5734117
0.0759697
25.7
-2.5774208
0.0759697
25.8
-2.5774208
0.07505417
25.9
-2.5895452
0.07474899
26
-2.5936195
0.07413864
26.1
-2.6018184
0.07413864
26.2
-2.6018184
0.07383347
26.3
-2.6059432
0.07352829
26.4
-2.6100851
0.07324219
26.5
-2.6139837
0.07293701
26.6
-2.6181591
0.07232666
26.7
-2.6265625
0.07232666
26.8
-2.6265625
0.07202148
26.9
-2.6307908
0.07141113
27
-2.6393015
0.07141113
27.1
-2.6393015
0.07080078
27.2
-2.6478852
0.07080078
27.3
-2.6478852
0.07019043
27.4
-2.6565433
0.06988525
27.5
-2.6609006
0.06958008
27.6
-2.665277
0.0692749
27.7
-2.6696726
0.06896973
27.8
-2.6740876
0.06866455
27.9
-2.6785222
0.06837845
28
-2.6826976
0.06837845
28.1
-2.6826976
0.0677681
28.2
-2.6916637
0.06746292
28.3
-2.6961771
0.06746292
28.4
-2.6961771
0.06685257
28.5
-2.7052655
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0.06654739
28.6
-2.7098409
0.06624222
28.7
-2.7144373
0.06593704
28.8
-2.7190549
0.06563187
28.9
-2.7236939
0.06532669
29
-2.7283546
0.06502151
29.1
-2.7330371
0.06441116
29.2
-2.7424683
0.06441116
29.3
-2.7424683
0.06410599
29.4
-2.7472175
0.06410599
29.5
-2.7472175
0.06351471
29.6
-2.7564838
0.06320953
29.7
-2.7613001
0.06290436
29.8
-2.7661398
0.06290436
29.9
-2.7661398
0.06229401
30
-2.7758901
0.06229401
30.1
-2.7758901
0.06198883
30.2
-2.7808011
0.06168365
30.3
-2.7857363
0.06137848
30.4
-2.790696
0.0610733
30.5
-2.7956804
0.0610733
30.6
-2.7956804
0.06046295
30.7
-2.8057245
0.06046295
30.8
-2.8057245
0.0598526
30.9
-2.8158704
0.05954742
31
-2.8209822
0.05954742
31.1
-2.8209822
0.05924225
31.2
-2.8261203
0.05893707
31.3
-2.831285
0.05865097
31.4
-2.8361512
0.05865097
31.5
-2.8361512
0.05804062
31.6
-2.8466122
0.05804062
31.7
-2.8466122
0.05773544
31.8
-2.851884
0.05712509
31.9
-2.8625118
0.05712509
32
-2.8625118
0.05681992
32.1
-2.8678684
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0.05651474
32.2
-2.8732538
0.05651474
32.3
-2.8732538
0.05620956
32.4
-2.8786684
0.05559921
32.5
-2.8895862
0.05529404
32.6
-2.8950902
0.05529404
32.7
-2.8950902
0.05498886
32.8
-2.9006246
0.05468369
32.9
-2.9061899
0.05437851
33
-2.9117862
0.05437851
33.1
-2.9117862
0.05407333
33.2
-2.9174141
0.05407333
33.3
-2.9174141
0.05378723
33.4
-2.9227192
0.05348206
33.5
-2.9284091
0.05348206
33.6
-2.9284091
0.05317688
33.7
-2.9341316
0.05256653
33.8
-2.9456757
0.05226135
33.9
-2.9514981
0.05195618
34
-2.9573547
0.05195618
34.1
-2.9573547
0.051651
34.2
-2.9632457
0.051651
34.3
-2.9632457
0.05134583
34.4
-2.9691716
0.05104065
34.5
-2.9751329
0.05073547
34.6
-2.9811299
0.0504303
34.7
-2.9871631
0.0504303
34.8
-2.9871631
0.04981995
34.9
-2.9993398
0.04981995
35
-2.9993398
0.04981995
35.1
-2.9993398
0.04920959
35.2
-3.0116667
0.04920959
35.3
-3.0116667
0.04920959
35.4
-3.0116667
0.04892349
35.5
-3.0174976
0.04892349
35.6
-3.0174976
0.04831314
35.7
-3.0300517
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0.04831314
35.8
-3.0300517
0.04770279
35.9
-3.0427654
0.04770279
36
-3.0427654
0.04739761
36.1
-3.0491834
0.04709244
36.2
-3.0556428
0.04709244
36.3
-3.0556428
0.04678726
36.4
-3.0621443
0.04648209
36.5
-3.0686883
0.04648209
36.6
-3.0686883
0.04617691
36.7
-3.0752754
0.04617691
36.8
-3.0752754
0.04587173
36.9
-3.0819062
0.04587173
37
-3.0819062
0.04556656
37.1
-3.0885812
0.04556656
37.2
-3.0885812
0.04526138
37.3
-3.0953011
0.04495621
37.4
-3.1020664
0.04434586
37.5
-3.115736
0.04434586
37.6
-3.115736
0.04434586
37.7
-3.115736
0.04405975
37.8
-3.1222085
0.04375458
37.9
-3.129159
0.0434494
38
-3.1361582
0.0434494
38.1
-3.1361582
0.0434494
38.2
-3.1361582
0.04314423
38.3
-3.1432067
0.04283905
38.4
-3.1503052
0.04253387
38.5
-3.1574545
0.0422287
38.6
-3.1646552
0.0422287
38.7
-3.1646552
0.0422287
38.8
-3.1646552
0.04192352
38.9
-3.1719082
0.04192352
39
-3.1719082
0.04131317
39.1
-3.1865739
0.04131317
39.2
-3.1865739
0.04131317
39.3
-3.1865739
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0.041008
39.4
-3.1939882
0.041008
39.5
-3.1939882
0.04070282
39.6
-3.2014579
0.04070282
39.7
-3.2014579
0.04039764
39.8
-3.2089838
0.04009247
39.9
-3.2165668
0.04009247
40
-3.2165668
0.03948212
40.1
-3.2319075
0.03919601
40.2
-3.2391802
0.03919601
40.3
-3.2391802
0.03858566
40.4
-3.2548745
0.03889084
40.5
-3.2469966
0.03858566
40.6
-3.2548745
0.03828049
40.7
-3.262815
0.03828049
40.8
-3.262815
0.03797531
40.9
-3.270819
0.03767014
41
-3.2788877
0.03736496
41.1
-3.2870219
0.03736496
41.2
-3.2870219
0.03736496
41.3
-3.2870219
0.03736496
41.4
-3.2870219
0.03705978
41.5
-3.2952229
0.03675461
41.6
-3.3034917
0.03675461
41.7
-3.3034917
0.03644943
41.8
-3.3118294
0.03614426
41.9
-3.3202372
0.03614426
42
-3.3202372
0.03583908
42.1
-3.3287163
0.03583908
42.2
-3.3287163
0.03583908
42.3
-3.3287163
0.03553391
42.4
-3.337268
0.03522873
42.5
-3.3458934
0.03522873
42.6
-3.3458934
0.03492355
42.7
-3.3545938
0.03492355
42.8
-3.3545938
0.03461838
42.9
-3.3633706
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0.03433228
43
-3.3716694
0.03433228
43.1
-3.3716694
0.0340271
43.2
-3.380598
0.03433228
43.3
-3.3716694
0.0340271
43.4
-3.380598
0.03372192
43.5
-3.3896071
0.03372192
43.6
-3.3896071
0.03372192
43.7
-3.3896071
0.03341675
43.8
-3.3986981
0.03341675
43.9
-3.3986981
0.03311157
44
-3.4078724
0.03311157
44.1
-3.4078724
0.0328064
44.2
-3.4171318
0.03250122
44.3
-3.4264776
0.03219604
44.4
-3.4359117
0.03219604
44.5
-3.4359117
0.03219604
44.6
-3.4359117
0.03219604
44.7
-3.4359117
0.03219604
44.8
-3.4359117
0.03189087
44.9
-3.4454355
0.03158569
45
-3.455051
Table 1:
Data for experiment 3 of RC Circuit in parallel.
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