Example of a Good First Draft of a Formal Lab Report
Formal Lab Reports
Lab 5: Friction due Friday, June 20…..……Lab 10: Simple Harmonic Motion due Monday, June 30.
Late penalty: 5 points per day. The report is worth 100 points.
In this lab report, you will be trying to report what you have done objectively, explaining your purpose, motivation, procedure, results, and analysis. Your goal is to write a report such that your fellow classmate could read and then be able to repeat your experiment. I expect that one could write an excellent report in 4-5 pages (not including graphs or regression table pages), although there is no required length. Making it longer will not necessarily improve your grade. I will be looking for certain items in each section, as described below, as well as grading on logical flow, clear expression, and orderly presentation. You need to demonstrate to me that you've thoroughly understood the lab!! You may use either the first or third person - definitely not second person.
This report must be word processed. Hand written reports, or any part of it, will not be accepted.Everything in your report should be part of the file- Do not tape on data tables, graphs, etc.
General Guidelines - The Grading Policies handout holds for these formal reports- except for having to show sample calculations (see Data and Graphs description). Be neat!! It makes for easier reading and leaves a good impression (Often in the "real world", packaging is more important than substance. Don't underestimate this.) Practice good writing skills (spelling, etc). Use 9.80 m/s2 for the accepted value for the acceleration due to gravity. As always when writing for a grade, keep in mind that you write for the way your instructor is going to grade!
Title – It should be descriptive.
Abstract - In a paragraph, give your purpose(s), mention your method of discovering the solution to your problem, the fundamental laws guiding you, and the results you obtained. (This probably ought not be more than 3 or 4 sentences.)
Theory - This section should inform the reader as to why you approached the problem as you did. Don't just write down equations, but demonstrate that you know what they mean. This is not a dumping ground for every equation in the lab manual. Equations should be set off from the text and numbered if you refer to them later. This makes it easier to refer to them later. Don't tell me the equations for things like finding an average or percent error. Those are understood. Example:
F= ILB (1)
where F is the force, I represents current, L is the length of the wire, and B is the magnetic field.
Methods and Materials - Don't just copy the lab manual!!! It has much that you don't need and is probably missing some things you do need. For your first draft, I strongly urge you to sit down and write this section without looking at the manual. Only afterwards should you refer to the manual to refresh your memory. Diagrams are often helpful in this section (A picture is worth 1000 words!). I want diagrams of your setup for completeness. I have no problem if you choose to photocopy diagrams from your lab manual and incorporate them into your text. They should be placed in this section and not tacked on to the end. It's often helpful to refer to you data tables, graphs, etc. (This means they need to be labeled.) I do not want a numbered sequence of instructions!! The method should not be presented as a recipe - save it for chemistry!
Data and Graphs - Do not show sample calculations. Incorporate data and graphs into your text pages instead of just dumping them at the end of the report.
Conclusion and Analysis - This section is where you present the results of your experiments and describe whether you were successful in achieving your purpose. (This usually includes numbers!) It is important to include data. How well does the experiment agree with the theory? If they differ, why? I'm not looking for admission that you and your lab partner may have made mistakes - what part of the lab setup could physically explain any discrepancy between measured and predicted/expected results?
Karri Smith, Partner: Sue Wilhelm
Charge!! Discharge!!!
Abstract
The purpose of this lab is to measure the time constant of various resistor-capacitor (RC) circuits. With the measured time constant, the value of the capacitors used was determined and compared to the rated value. The RC circuits studied included combinations of capacitors connected both in parallel and series, and time constants were measured for both charging and discharging circuits.
Theory
Capacitors are devices that are used in electrical circuits to store charge and then used to discharge quickly when connected to a load. They are useful elements in circuits, which require precise timing, and/or large currents, which could not be delivered for long time by a steady state voltage source.
Capacitors come in many shapes and sizes, but all (?) have two conducting components separated by an insulating material. When a capacitor is connected to a voltage source, each component is connected to a terminal of the voltage source and charge flows from the cathode or anode to the respective plate. This creates a potential difference across the gap. Capacitors are rated by the amount of charge they are able to store when connected to a given voltage source,
C = QV (1)
where the charge, Q, is measured in Coulombs, the voltage, V, is measured in Volts, and capacitance, C, is measured in Farads (F).
When a capacitor has become charged, it can then be disconnected from the voltage and applied to the resistive element, which requires the current. The rate at which the charge flows for a charging or discharging RC circuit is determined by the values of the capacitor(s) and resistor(s) in the circuit. Since the capacitance is a constant, the charge remaining on the capacitor can be related to the voltage by Eq. 1. The voltage is measured here because it is an easier quantity to measure experimentally than the charge. The voltage on the capacitor of a discharging RC circuit is given by
V(t) = V0 e-t/ (2)
and for a charging RC circuit by
V(t) = Vo (1-e-t/) (3)
In Eqs. 2 and 3, = R*C and is referred to as the time constant of the circuit, since it determines the rate of the exponential decay or rise of the voltage, and Vo equals the maximum potential difference across the capacitor. One method used in this lab to measure the time constant involved measuring the voltage across the capacitor when the capacitor had 90% and 10% of the maximum voltage. By applying the voltage values with their respective times into Equation 2, a pair of equations can be generated which, when simplified, express the time constant in terms of the time, t, required for the voltage to fall from 90% to 10% of the maximum value:
= t/ln 9 (4)
Capacitors can be connected in different configurations to precisely control the amount of charge delivered to a resistive element. To increase the amount of charge which can be stored for a given voltage source, capacitors can be combined in parallel, as in Figure 1.
Figure 1. Capacitors connected in parallel. Figure 2. Capacitors connected in series.
When capacitors are connected in parallel, the potential difference across each capacitor is the same since each side of the capacitor must be at a common potential at the node. Then by Eq. 1, the total amount of charge is just the sum that each capacitor could store, and the overall capacitance is just the sum of the two capacitors,
Ctotal = C1 + C2(5)
If the capacitors are connected in series, as in Fig. 2, the charge accumulating on the plates connected to the battery is determined by Eq. 1. This induces an equal magnitude - opposite polarity - of charge on the inner plates. Now, since the charge is equal across each capacitor and the capacitance value is intrinsically constant, the voltage across the capacitors must be different. From Eq. 1, the total resistance across capacitors in series must add like:
Ctotal = (1/C1 + 1/C2)-1(6)
Methods and Materials
The circuits used in this lab to measure the time constant were connected on a springboard. The springboard had nodes where two springs were connected together to allow for placing all of the necessary connections at a node in the circuit. A simple schematic of a RC circuit setup with a voltmeter included to monitor the voltage across the capacitor is shown in Figure 3.
(pic from page 50)
Figure 3. Diagram of setup used to monitor a charging RC circuit.
The voltmeter was connected in parallel to measure the voltage across the capacitor. The shunt shown in the circuit was connected when the voltage was first applied. The shunt allows the current to bypass the resistor and charge the capacitor almost immediately. The voltage on the power supply was adjusted to 10.0 V and the shunt removed. When the power supply was turned off, the voltage level dropped slightly (~0.15 V) but then leveled off. This was due to a small leakage through the voltmeter.
The first measurement of the time constant was made measuring the voltage across a discharging capacitor at several points and then graphing the information as a function of time to obtain the time constant. A 100 k resistor and 330 F capacitor were connected in series and the capacitor was "charged" to 10.0V. The shunt was removed and the wire connecting the capacitor to the power supply was disconnected from the power supply and connected to discharge through the resistor. (In Figure 3, the wire from c to the negative power supply terminal was rearranged to connect points c and a.) A stopwatch was used to measure the time when the voltage reached integer values as it discharged, i.e., 9.0V, 8.0V, 7.0V, etc., down to 2.0V. The values are recorded in Table 1. From Eq. 2 it can be seen that a graph of ln(Vc/V) vs. time will result in a linear graph with a slope equal to (-1/). This linear relationship was observed in Graph 1.
The time constant for the remaining circuits was found by measuring the time required for the voltage on a capacitor to fall from 90% to 10% of its initial value. The time constant was then found using Eq. 4. The RC circuits used and the experimental values for the capacitor are listed in Table 2. The resistor values were measured with an ohmmeter.
Data and Graphs:
The voltage values taken for the discharging capacitor are given in Table 1 and the related graph in Graph 1.
Vc(V) / T (s) / Ln (Vc/V)9 / 3.26 / -0.1054
8 / 7.69 / -0.2231
7 / 12.5 / -0.3567
6 / 18.25 / -0.5108
5 / 25.27 / -0.6932
4 / 33.69 / -0.9163
3 / 44.34 / -1.024
2 / 60.06 / -1.6094
Table 1. Voltage across a discharging capacitor.
Graph 1. Voltage across a discharging capacitor.
The value of the time constant from the slope in Graph 1 was found from Eq. 2 to be 37.74 seconds, which represents a 11.9% error with respect to the rated values of the capacitor and resistor. The calculated value of the capacitor from this slope is 369.3 F.
From the second method, the values for the capacitors are listed in Table 2.
Circuit / Vo (V) / t (s) / (s) / Cexp (F) / % error102.2kΩ, 330 μF / 10.0 / 84.31 / 38.37 / 375.5 / 13.8
220 kΩ, 330 μF / 10.0 / 179.2 / 81.56 / 371 / 12.3
102.2 kΩ, series / 10.0 / 18.64 / 8.483 / 83.01 / 8.17
102.2kΩ, parallel / 10.0 / 107.1 / 48.37 / 476.9 / 10.9
102.2kΩ,100μF charging / 10.0 / 24.27 / 11.05 / 108.1 / 8.08
Table 2. t, , and C for different circuits
The equivalent capacitance of the 330 F and 100 F capacitors connected in series was calculated to be 76.7 F, while the equivalent capacitance for those two connected in parallel was calculated to be 430 F.
Conclusion and Analysis:
The time constants of several circuits were calculated and the capacitance values calculated. The values calculated for the 330 F capacitor were 369.3 F, 375.5 F, and 371 F, which compare well with each other but poorly with the rated value of 330 F. The average of the experimental values is 372 F, representing a 12.7% error from 330 F. The measurement of the 100 F capacitor in the charging RC circuit differed by 8.08% from the rated value. The errors for the combination circuits were similar; 8.17% for capacitors in series and 10.9% for thecapacitors connected in parallel. The uncertainty associated with the resistors is less than 1% and not likely significant in the difference in capacitance values. Likewise, the good correlation coefficient and the small y-intercept from the graph indicate a precision in those measurements. While time didn't allow for the direct comparison of charging and discharging circuits with identical resistors and capacitors, the technique was shown to be generally applicable.
It is somewhat curious that all the capacitance values are higher than the rated values for both capacitors, suggesting a systematic error in the method. An unaccounted resistance in the RC circuit would lead to an increased value for the time constant. The combined resistances of the wires and springs involved was not measured, but the expected resistance would be less than 10 and unlikely to explain the > 8% error observed. The presence of the voltmeter would have provided an alternate route for the capacitor to discharge, but as this would have decreased the time constant, cannot explain the discrepancy. Using the values of the capacitors found in Trials 1 and 5 of Table 2, (375.5 F and 108 F) to calculate the equivalent capacitance of the resistors in series by Eq. 6 gives 83.9 F, which compares favorably with the value found experimentally. Together, these results suggest that the actual capacitor values are likely about 10% higher than the rated capacitance.