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Measurements

Introduction

Making Measurements

A measurement should always be regarded as an estimate. The precision of the final result of an experiment cannot be better than the precision of the measurements made during the experiment, so the aim of the experimenter should be to make the estimates as good as possible.

There are many factors which contribute to the accuracy of a measurement. Perhaps the most obvious of these is the level of attention paid by the person making the measurements: a careless experimenter gets bad results! However, if the experiment is well designed, one careless measurement will usually be obvious and can therefore be ignored in the final analysis. In the following discussion of errors and level of precision we assume that the experiment is being performed by a careful person who is making the best use of the apparatus available.

Systematic Errors

If a voltmeter is not connected to anything else it should, of course, read zero. If it does not, the "zero error" is said to be a systematic error: all the readings of this meter are too high or too low. The same problem can occur with stop-watches, thermometers etc. Even if the instrument can not easily be reset to zero, we can usually take the zero error into account by simply adding it to or subtracting it from all the readings. (It should be noted however that other types of systematic error might be less easy to deal with.) Similarly, if 10 ammeters are connected in series with each other they should all give exactly the same reading. In practice they probably will not. Each ammeter could have a small constant error. Again this will give results having systematic errors.

For this reason, note that a precise reading is not necessarily an accurate reading. A precise reading taken from an instrument with a systematic error will give an inaccurate result.

Random Errors

Try asking 10 people to read the level of liquid in the same measuring cylinder. There will almost certainly be small differences in their estimates of the level. Connect a voltmeter into a circuit, take a reading, disconnect the meter, reconnect it and measure the same voltage again. There might be a slight difference between the readings. These are random (unpredictable) errors. Random errors can never be eliminated completely but we can usually be sure that the correct reading lies within certain limits.

To indicate this to the reader of the experiment report, the results of measurements should be written as

Result 盪ncertainty

For example, suppose we measure a length, to be 25cm with an uncertainty of 0.1cm. We write the result as

= 25cm 񵩕cm

By this, we mean that all we are sure about is that is somewhere in the range 24.9cm to 25.1cm.

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