Sample Lab Report - PHYS 231
The following is an example of a well-written report that might be submitted by a PHYS 231
student. It begins with a short statement of what is being measured, and why. The procedure and
results are then briefly described for each major part of the exercise. The description of the
procedure need not be lengthy, but must be sufficient for someone familiar with the apparatus to
use it to reproduce your results. A diagram is often useful to convey your setup. Single numbers
may be put into the text, but if several values are needed they should be in a table and perhaps a
graph. Tables and graphs need to be well labeled, and should be mentioned in the text. The report
ends with a summary or conclusion, which must be consistent with the preceding data and
analysis.
This document is typed and uses computer-drawn figures to facilitate posting on the web. You
may prepare any or all portions of your reports by hand, as convenient, but be sure the text is
legible and figures are clear. Graphs should be done on graph paper or by computer, not as rough
sketches.
PHYS 231
Experiment 3.14159 RC circuits
by A. Student
with O. K. Partner
Submitted February 30, 2753
Introduction
We studied the voltage across a capacitor as it charged or discharged through a known
resistor. The goal is to show that the charge/discharge follows an exponential function and that
the time constant is R’C, where R’ is the effective resistance of the voltmeter and resistor in
parallel.
Procedure and Results for charge/discharge curves
The circuits for charging and discharging the capacitor are sketched below. They are
wired so that the initial fully charged or fully discharged state can be quickly reached in one
switch position, and then the discharge or charge starts when the switch is set to the other
position. A stopwatch was started when the switch was thrown, and the DMM read at known
times until the voltage essentially stopped changing.
R
Power
Supply
Red +
b
a
+
C
Black -
-
DMM
Circuit for monitoring charging.
Power
Supply
Red +
Black -
b
a
R
+
C
-
DMM
Circuit for monitoring discharging.
Results for charging and discharging, with marked values R = 1 MΩ and C = 100 µF, are shown
in the attached graphs (from Graphical Analysis). The solid lines are fits to
V*(1-exp(-T*x))+K charging
V*exp(-T*x)+K
discharging
which were derived in the lab manual. These lines fit the data well, confirming that the charge
and discharge are exponential.
Procedure and Results for time constant
Only the discharging circuit was used for this part. The capacitor was charged to 10.0 V
and the time to discharge to 1/e of that value, 3.68 V, was measured with the stopwatch. The
discharge was repeated two or three times and averaged to reduce error. This was done for both
capacitors and again when connected in parallel. Resistor values were measured with the DMM
instead of using the marked values.
Data for the single capacitors is tabulated below
R
(ohm)
55.1K
106.7K
211.1K
.494M
1.062M
τ 100 µF
(sec)
too short
11.58, 11.20, 11.86
21.47, 22.25, 22.50
50.12, 50.35
100.87, 101.23
τ ave 100 µF
(sec)
11.55
22.07
50.24
101.05
τ, 220 µF
(sec)
13.72, 13.87, 13.56
25.95, 26.07, 25.256
50.47, 50.30
113.54, 113.65
too long
τ ave220 µF
(sec)
13.72
25.86
50.38
113.60
and for the parallel combination
R
(ohm)
55.1K
106.7K
211.1K
.494M
τ (100+220) µF
(sec)
19.48, 19.44, 19.48
37.39, 37.28
72.02, 72.10
163.92
τ ave
(sec)
19.47
37.34
72.06
163.92
The average time constant was plotted against the parallel resistance of the resistor and the
meter, assumed to be 10MΩ. The results are in the attached graphs. Since we expect τ = R’C, the
graphs should be straight lines with slope C. This appears to be the case, with values of C from
the slope as tabulated:
nominal capacitance (µF)
from slope (µF)
100
105 ± 0.4
220
240 ± 0.4
320
347 ± 0.6
Note that the sum of the capacitances determined from the individual slopes is in good
agreement with the capacitance from the slope of the parallel combination.
Conclusion
We have measured the charge and discharge of an RC combination. As expected, the
charge/discharge voltage is exponential in time, with a time constant of RC. Capacitors
connected in parallel have the sum of the individual capacitances.
Graph 1
Data Set 1
10.0
9.60
9.20
8.80
8.40
8.00
7.60
7.20
6.80
6.40
V (volts)
6.00
5.60
5.20
4.80
4.40
4.00
3.60
3.20
2.80
2.40
2.00
1.60
1.20
0.800
0.400
0.00
0.00
50.0
100
150
200
Automatic Curve Fit on Data Set 1:
f ( x ) = V*exp(-T*x)
V=
9.89
Mean Square Error:
+K
T= 0.00985
0.000382
K=
0.0812
250
t (sec)
300
350
400
450
500
Graph 1
Data Set 1
9.20
8.80
8.40
8.00
7.60
7.20
6.80
6.40
6.00
5.60
V (volts)
5.20
4.80
4.40
4.00
3.60
3.20
2.80
2.40
2.00
1.60
1.20
0.800
0.400
0.00
0.00
50.0
100
150
200
Automatic Curve Fit on Data Set 1:
f ( x ) = V*(1-exp(-T*x))
V=
8.85
Mean Square Error:
+K
T= 0.00990
0.000333
K=
0.0434
250
t (sec)
300
350
400
450
500
Graph 1
Data Set 1
Data Set 2
Data Set 3
165
160
155
150
145
140
135
130
125
120
115
110
105
100
tau (sec)
95.0
90.0
85.0
80.0
75.0
70.0
65.0
60.0
55.0
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
10.0
0.00
1.00e+05
2.00e+05
3.00e+05
4.00e+05
Statistics:
Slope
Y Intercept
C.O.R.
Data Set 1
0.000105±4.33e-07
0.550±0.237
1.00
Data Set 2
0.000240±3.79e-07
0.582±0.100
1.00
Data Set 3
0.000347±6.23e-07
0.504±0.164
1.00
5.00e+05
6.00e+05
Reff (ohms)
7.00e+05
8.00e+05
9.00e+05
1.00e+06