1. Complete Table 1. (small) Trial Average Current, i Area V*s Total Charge, Q=a
ID: 3162190 • Letter: 1
Question
1. Complete Table 1. (small)
Trial
Average Current, i
Area V*s
Total Charge, Q=area/10000
Final Voltage, V
Capacitance, C1 = Q/V
1
-5.385E-4
239.89
0.023989
2.979275
8.05E-3
2
-5.385E-4
229.26
0.022926
2.984456
7.68E-3
3
-5.385E-4
183.26
0.018326
2.984456
6.14E-3
Average Capacitance
7.32E-3
Standard Deviation
0.001013
(2 points x 8 = 16 points)
2. Complete Table 2. (large)
Trial
Average Current, i
Area V*s
Total Charge,
Q=area/10000
Final Voltage, V
Capacitance, C2 = Q/V
1
-5.385E-4
523.86
0.052386
2.766839
0.01893
2
-5.385E-4
404.11
0.040411
2.792746
0.01447
3
-5.385E-4
347.28
0.034728
2.797927
0.01241
Average Capacitance
0.01527
Standard Deviation
0.00333
(2 points x 8 = 16 points)
3. Complete Table 3.
Configuration
Average Current, i
Area V*s
Total Charge,
Q=area/10000
Final Voltage, V
Capacitance, Ceff = Q/V
Parallel
-5.385E-4
456.43
0.045643
2.792746
0.01634
Series
-5.385E-4
188.74
0.018874
2.979275
0.00634
(2 points x 4 = 8 points)
a. Using the relation for parallel capacitors, Ceff = C1 + C2, calculate the effective capacitance of C1 and C2 in parallel with uncertainty based on data in Table 1 and 2. Statistically compare this effective capacitance to that measured in Table 3, comment as necessary. Show all work. (30 points)
b. Using the relation for series capacitors, 1/Ceff = 1/C1 + 1/C2, calculate the effective capacitance of C1 and C2 in series with uncertainty based on data in Table 1 and 2. Statistically compare this effective capacitance to that measured in Table 3, comment as necessary. Show all work. (30 points)
Trial
Average Current, i
Area V*s
Total Charge, Q=area/10000
Final Voltage, V
Capacitance, C1 = Q/V
1
-5.385E-4
239.89
0.023989
2.979275
8.05E-3
2
-5.385E-4
229.26
0.022926
2.984456
7.68E-3
3
-5.385E-4
183.26
0.018326
2.984456
6.14E-3
Average Capacitance
7.32E-3
Standard Deviation
0.001013
Explanation / Answer
standared deviation C1 = 0.001013
C2 = 0.00333
C1 = 7.32e-3 +/- 0.001013
C2 = 15.27 +/- 0.00333
when C1 and C2 are in parallel
Ceff = C1 + C2 = 7.32e-3 +15.27e-3 +/- (0.001013 +0.00333)
Uncertainity in sum or difference adds up, hence
Ceff = 22.59e-3 +/- 0.004343
lower limit = 18.153e-3 , upper limit = 26.933 e-3
measured value = 0.01634 = 16.34e-3 is outside the expected range
b) when C1 and C2 are in series
Ceff = 1/[1/C1 + 1/C2] = C1C2/(C1 + C2) = 7.32e-3 *15.27e-3 /22.59e-3
= 4.95e-3
for a quotient fractional uncertinities add up
fractional uncertainity Ceff = (1.013/7.73) + (3.33/15.27) + (4.343/22.59)
= 0.5487
uncertainity = 0.5487 * 4.95e-3 = 2.72e-3
measured value = 6.34e-3
expected value 4.95 +/- 2.72e-3
measured value is within the range of expected value.
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