ON WRITING LAB REPORTS (F96 5LC)

Here are some general guidelines on writing lab reports. These are nothing more than tips and do not suggest a specific format. However, these items are a compendium of ideas that have been compiled by TAs who have previously taught this course.

General Comments:

1. Neatness - an obvious necessity. TAs are only allocated 10-15 minutes to grade each lab writeup. It is very frustrating to try to grade a report that is poorly organized and/or illegibly written.

2. Correctness - make sure that sentences make sense and are reasonable. Do they conform to theoretical expectation.

3. Conciseness - don't spend time or words on unnecessary details, or rewriting sentences that are already in the lab manual.

4. If you are confused by layout or what should be included in writeup, ask the TA first. This is why we are around.

Opening Paragraph - It a good idea to have an introductory paragraph. It should be short, state what you are going to do in the lab, and provide some general overview so a student who has not yet done the lab next year will know what you are doing. If you are susposed to gain familiarity with a piece of equipment, point out how when it should be used and compare to other devices which measure the same properties. Is one more accurate than the other? Does one do more or do things differently?

Example from week 2 of 5LC:

This week we will study the operation of an oscilloscope which measures the time variation of voltage signal, and the function generator that provides a large variaty of time varying voltage waveforms. Specifically, we will look at the detailed functions of the different types of trigger modes, display options, and input coupling. After that, we will use the oscilloscope in differential mode to measure the voltage drop across a circuit component when neither of the voltages (on either side of the resistor) is ground.

Goal - Each section of the lab manual has an objective or goal. You should paraphrase the goal in each section of your lab writeup. Often, it is a good idea to restate the goal in the conclusions when you must state whether the goal was attained.

Some of the labs this quarter consist of a series of related tasks. You can write a separate goal and conclusion for each section or task if that makes more sense to you.

Procedures and Descriptions - Do not waste time and paper by copying the procedures or documenting the equipment. This information is already in the lab manual. Instead, describe any procedure that are not specifically spelled out in the lab manual. Also put a schematic in to show all wire connections between instruments and the circuit, especially if this is not explicitly done in the lab manual. For example, in your schematic of the circuit clearly indicate where your ground connection is located.

Example from week 2 of 5LC:

We noticed that the ground reference was not the same on channel two when we pushed the INVERT button. We had to rezero the ground reference.

Taking Data - It is important to list your original data obtained from the measuring instrument. If you conclusions are wrong, I can go back and find your error. When taking many data points, you would want to present the data in a table. It is critical that you write down the units for everything. To simplify your writing, get used to common shorthand notation (eg. 19.5 mV instead of 1.95 x10-2 V). If you don't know the meaning of k, M, m, m then ask your TA.

Data Reduction and Error Analysis - This is the most signficant aspect of the lab and generally worth the most points. Typically, this is where the students lose the most points as well.

a) When doing data reduction or some other calculation, always indicate which equation(s) you are using, and write them down. Never assume that I know which equation you are using or what you are doing with your data.

b) It is usually necessary to show a sample calculation, especially when doing repetative calculations.

c) When asked to compare two quantities, such as a theoretical value ,T,to an experimental value, E, be sure to calculate the percentage error which is given by the formula

% error = [(E-T)/T] (100)

where T is the theoretical value and E is the experimental value. However this is only part of what you need to do. By itself, the % error is almost meaningless. It becomes meaningful only once you know your EXPERIMENTAL error. Thus, you must estimate the statistical error in all of your measurements. You should consult "An introduction to Error Analysis" by John Taylor to calculate uncertainty or fractional error in your calculated quantities. Often you will be forced to use the chain rule in calculating the experimental fractional error which is defined by the formula

Is your percentage error larger or smaller than your uncertainty? If the percentage error is much larger (usually 2x larger) than the percent experimental error , then there is some reason to suspect that your data is inconsistent with expectation. There could be several reasons for this. Usually, you have calculated the theoretical expectation wrong or you have made an error in determining the experimental value. The first thing you should do is look for a math mistake. If you cannot find anything, then ask your TA to look for the problem. Occasionally, even if you do things as well as you can, the measured values are not very close to what you expect. This may be perfectly OK if your experimental error is large as well. Sometimes, the assumptions which are used to generate a theoretical formula do not reflect the conditions in the experiment very well. Then, you must conclude that your data is inconsistent with expectation. When scientists are confronted with this last case, then they must either improve the theoretical analysis to include the real conditions of the experiment , or improve the experiment to reflect better the theoretical assumptions.

Lets say y_meas is the experimentally measured value of the quantity y, dy_meas is the uncertainty in the measured value of y. Also, lets say y_th is the theoretical expectation for the value of y. Then we say that the measured value is consistent with the theoretical expectation IF

(y_meas - dy_meas) < y_th < (y_meas + dy_meas)

Alternatively, you could compare the % error to the % experimental error. If

% error < % experimental error

then your data is consistent with what you expect theoretically.

For the purposes of this lab, I would only worry if your % error is larger than 2 times the % experimental error.

One of the most difficult things that you must do is evaluate dq, the experimental uncertainty of the measurement of q. The formula on page 73 requires you to evaluate partial derivatives (please ask your TA to show you how to evaluate partial derivatives if you do not know - the recipe is straightforward) and the uncertainty of all independent variables that were measured in order to determine the quantity q.

For example, if I = (1/R) V, then the uncertainty is determined conveniently by

(dI/I)2 = (dR/R)2 + (dV/V)2

So now your task is to determine the uncertainties in the measurement of V, which we call dV, and the uncertainty of R, or dR. See FAQ for a discussion on how determine the uncertainty from an oscilloscope.

Sketches and Graphs: Clearly label your axes on the graph; include units, and point out where the zero point is (if it is on the graph). If two or more curves or lines are included, make sure you indicate which curve is which with some sort of legend. Use multiple colored ink pens to differentiate, or use solid lines or dashes. Graphs are usually constructed with the independent variable (what you are changing, such as frequency or input voltage amplitude to some circuit) on the horizontal axis, and the dependent variable (which is the affected quantity - output voltage across a resistor, for example) on the vertical axis. Draw a curve (or a line) through your data only if you are sure that is form that is suitable for your data. It is not a good idea to simply connect dots. It is a good idea to indicate the uncertainty of each measurement for all of the data if possible, or a representative point if the former would make the plot too cluttered.

For example, if you are testing Ohm's Law where V=IR, your independent variable is usually V (since you can mostly easily control Voltage) and your dependent variable is I (which you measure using a DMM). Typically, the independent variable is placed on the x-axis of a graph. Thus, we rewrite

V=IR to reflect the experimental details. I = (1/R) V. This looks similar to the linear equation y = A+Bx

if you recognize that A is expected to be equal to zero and the slope B= (1/R). After you plot your data, you must determine if the data form a line with the slope equal to (1/R). Try to draw a straight line by eye which goes through most of the data points.

Other rules in graphing data:

Try to put error bars on all data points. If there are too many data points, then put an error bar on several points to indicate the size of the error on all of the rest of the data.

Conclusions: This is also a very important part of the lab report. Essentially, this is the summary section and I use it to tell if you understood what you just did. You should answer this question in your conclusions: Did you accomplish what you set out to do. You might review your goals of each section and state what you learned. If you think you did accomplish what you set out to do, then briefly backup this idea with your measured quantities and errors. Compare your measurements to the expected value. If the percentage error is much larger than your percent experimental error, then you must guess or figure out what went wrong. Try to state the sources of your error and which values might be poorly measured (do to noise glitches, for example). Usually, the critical thing that you should discuss is whether your measurement is consistent or inconsistent with theoretical expectation.

Sometimes your goal is simply to gain experience with a piece of equipment. If so, state some of the things you have learned and perhaps some applications in which this new experience might be helpful.

Example from week 2 of 5LC:

1. We learned that AC coupling changes the displayed signal when the input signal has a non-zero value when we average over time. This feature might be useful when we want to observe a very small signal that has a very large DC offset (a very large average value).

2. DC (Direct coupling) does not distort or change the input signal. It is especially useful at low frequency where AC coupling significantly attenuates the input signal. We observed that the amplitude of the measured signal is smaller than it should be when the frequency of the input signal is less than 10 Hz.

3. If we violate the common ground rules, we seem to remove the second resistor from the circuit since the second resistor now has the same voltage on either end. When this is true, by Ohm's Law, we know that no current can flow through it.