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Accuracy, Precision of Instruments and Errors in Measurement

There is only a limit up to which measurements can be made with a measuring instrument. This limit is called the least count of the instrument.

For example, a metre rod can measure length accurately up to 0.1 cm, whereas vernier caliper can measure length accurately up to 0.01 cm. However, when we make use of various measuring instruments, various types of errors creep into the observations.

In the study of physics, there is a need to measure various physical parameters. The simplest of all measurements is that of length.

No measurement of a physical quantity can be correct in an absolute sense. The numerical value of a measured quantity can only be approximate.

How precise the measurement is, depends upon the instrument employed to make that measurement.

A brief account of the possible types of errors in measurements is as below:
  1. Constant Errors
When the results of a series of observations are in error by the same amount, the error is said to be a constant one.

For example, in measuring the length of a cylinder by vernier callipers, whose graduations are faulty, say one centimetre on the scale is actually 0.9 centimetre: the measured length will always be greater than the true value by a constant amount.

In order to avoid constant error, physical measurements are made by as many different methods as possible.
  1. Systematic Errors
A systematic error is one that always produces an error of the same sign. These are due to known causes.

Detecting the source of the error and the rule governing this error eliminates this type of error. Systematic error may be subdivided into the following four main types:
  1. Instrumental Errors
    These are inherent errors of the apparatus and the measuring instruments used. A simple example is the ‘zero-error’ of a measuring instrument. All instrumental errors come under this category. The instrumental error, if any, can be detected by interchanging two similar instruments or by using different methods for measuring the same physical quantity.
  2. Observational or Personal Errors
    The errors due to the personal peculiarities of the experiment are known as personal errors. For example, parallax error while reading the position of uprights on the optical bench. The more experienced the experimenter is, the lesser it is.
    Obtaining several readings carefully and then taking their arithmetical mean can minimize these errors.
  3. Errors Due to External Causes
    These errors are caused by external conditions (pressure, temperature, wind, etc). For example, expansion of a scale due to increase in temperature. These errors can be taken care of by applying suitable corrections.
  4. Errors Due to Imperfection
    Sometimes, even when we know the nature of error, it cannot be eliminated due to imperfection in experimental arrangement.
    For example, in calorimetry, loss of heat due to radiation, the effect on weighing due to buoyancy of air, etc. These errors will always exist but observations can be corrected for them.
  1. Random Errors
These errors are due to unknown causes and are sometimes termed as chance errors. In an experiment, even the same person repeating an observation may get different readings every time. For example, while measuring diameter of a wire with a screw gauge, one may get different readings and different observations. It may happen due to many reasons.

For example, due to non-uniform area of section of the wire at different places, the screw might have been tightened unevenly in the different observations, etc.

In such a case, it may not be possible to indicate, which observation is most accurate. However, if we repeat the observation a number of times, the arithmetic mean of all the readings is found to be most accurate or very close to the most accurate reading for that observation.

That is why in the experiment, it is recommended to repeat an observation a number of times and then to take the arithmetical mean.

If a
1, a2, a3……..an are the n different readings in an experiment, then their arithmetical means given by
or =
  1. Gross Errors
These are the results of sheer carelessness or mistake on the part of the person performing the experiment. No correction can be applied for them. They are of the following three types:
  1. Neglect of the Sources of Error
    This type of gross error results due to negligence towards source errors, e.g., for plotting the field of a magnet, improper setting of the magnet along NS-line presence of magnetic in the vicinity of the magnet etc.
  2. Reading the Instruments Incorrectly
    Sometimes, over a metre-scale, one cm is divided in 20 parts instead of 10 parts. In a voltmeter or ammeter 1 volt or 1 ampere might have been divided into 20 or 15 parts instead of 10. The experimenter may read the instrument without paying due attention to the value of 1 division.
  3. Improper Recording of the Reading
    This type of mistake is committed by the experimenter, when he records the reading wrongly. For example, he may record 21.3 in place of 23.1. This happens due to undue haste or when the experimenter mentally carries the reading for a long time.
  4. Least count error
    The smallest value that can be measured by the measuring instrument is called its least count. All the readings or measured values are good only up to this value.
    The least count error is the error associated with the resolution of the instrument.
    For example, a vernier callipers has the least count as 0.01 cm; a spherometer may have a least count of 0.001 cm. Least count error belongs to the category of random errors but within a limited size; it occurs with both systematic and random errors. If we use a metre scale for measurement of length, it may have graduations at 1 mm division scale spacing or interval. Using instruments of higher precision, improving experimental techniques, etc., we can reduce the least count error. Repeating the observations several times and taking the arithmetic mean of all the observations, the mean value would be very close to the true value of the measured quantity.

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