# Phys 273 -- Notes on Lab 1

After reading lab reports submitted for this lab in past years, I've noticed a set of common omissions. Most of them are in the Error Analysis section. Here are some hints for this -- and all! -- experiments.

• After you have identified a source of error, ask the question: "How big is this error?" You can go into several layers of detail:
• Which sources of error are the largest? At the very least, name the biggest.
• Quantify the amount of error from each source. If the measurement of time was good to 1 second, and the total time was 2100 seconds, then the percentage uncertainty in the time measurement is (1/2100) = 0.05 percent. That's very small!
• Make a list of the various sources of error, in order from most severe to least.

• Note that some measurements aren't limited by the equipment, but by other factors. For example, if one person closes a switch and other starts a stopwatch, it's possible that the two people don't act at exactly the same time. Even though the stopwatch may read time to 0.01 seconds, the true uncertainty in the measure time may be 0.5 second, or 1 second, due to some mistake in synchronizing the two actions. If you have to guess at the size of some error like this -- go ahead and guess! Just write explicitly, "I'm estimating the uncertainty in the timing process to be 1 second, for the following reason: ..."

If you can come up with some way of measuring such errors, even better.

• Always ask, "What's the effect of this error on the final result?" If you think that you may have cleaned some of the deposited copper off the plate by mistake, then you should follow this to its consequence: if the measured change in mass is too small, then the calculated value for e would be too big (because you have to divide by "change in mass" to get e). Say so.

If you can determine the size of the error in the final result due to an error in the procedure, even better. For example, you might decide that the current was 5 percent larger than you mistakenly measured. This would make the final value for "charge on electron" 5 percent too big.

• If you identify an error, try to figure out a way to eliminate it, or at least minimize it, for future experiments. If the ammeter is the biggest source of error, perhaps you need a better ammeter. Say so.

• If you are able to propagate uncertainties into the final result, check your estimated uncertainty against the difference between your final result and the expected value. For example, if you propagate errors from the stopwatch, ammeter, and balance, and find that the final uncertainty in "e" was 4 percent ... but also determine that your answer differs from the expected value by 10 percent ... then something fishy is going on! Either you underestimated the uncertainty in your measurements, or there was some source of error you didn't consider. You should at least compare these two checks on your answer, and comment on their agreement or disagreement. It would be even better to go back and try to figure out extra sources of error if you need to do so.