Methods of measurement and error analysis

There is no such thing as a perfect measurement. The measured value of a physical quantity is never the same as the true value of the quantity. Error is defined as the difference between a physical quantity’s true value and its measured value. It is impossible to eliminate the errors associated with methods of measurement completely.

Introduction to Error

Almost every scientific experiment and theory is predicated on the accuracy of the measurements made during the experiment. Whether you are studying the units and dimensions of a body or conducting research into the theories of electricity and magnetism, precise measurement is required in order to grasp the fundamental concepts involved. Every measurement introduces some level of uncertainty into the experiment’s results.

• Consider the case in which you are measuring the height of a building in order to calculate the velocity of an object when it is thrown vertically upwards at a specific moment. This is known as a height measurement.
• In the event that the type of instrument you use to measure the building is broken or defective, the measurement taken by it will be incorrect.
• The selection of the incorrect instrument was the root cause of the incorrect measurement.

Errors are defined as the uncertainties that occur during the course of experimentation. As a result of experiments, the majority of errors occur, and every measured value may contain some errors. To avoid future issues with our results, it is essential that we eliminate all errors from our calculations and results. Accuracy and precision are two terms used to describe the nature of errors, which are distinguished from one another.

Methods of measurement

Methods of measurement pertain to the following –

• When measuring or expressing a physical quantity, it is important to consider a standardised measurement so that different measurements of the same physical quantity can be compared to one another. As a unit of the specific physical quantity, the standard unit is referred to as the unit of measurement.
• When measuring any physical quantity, we require two components: the numeric value (n) and the unit of measurement (u)
• We can calculate the numerical value by counting the total number of times a physical quantity has been measured in relation to a standard unit. The unit’s name is given in the second part of the sentence.
• Base units: Fundamental or base units are the units used to measure the fundamental or base quantities, respectively.
• Derived units: The units of all other physical quantities are referred to as “combinations of the base units,” which is an abbreviation. The units that are obtained for the derived quantities are referred to as derived units in this context.

Methods of measurement notes necessarily include elaboration on nature and types of errors as well. 

Types of Error

The errors can be classified into two types, which are as follows –

• Systematic errors 
• Random errors 

Systematic errors:

• Systematic errors are errors that occur only in one direction and are distinguished from other types of errors. 
• As a result, systematic errors are also referred to as repetitive errors because they can occur as a result of a malfunctioning machine or as a result of the use of the incorrect experimental apparatus. 
• These errors occur when the device that is being used to take measurements is not functioning properly.

Random errors:

Errors that occur due to any unknown or unpredictable methods in the experiment.

• Even if the instruments are properly designed, they will not produce accurate results in all cases.
• Electronic noise can cause errors
• Irregular changes in the heat loss rate from a solar collector due to changes in the wind can cause errors

Error while calculating physical quantity value

Calculating the value of a physical quantity incorrectly is divided into two parts, which are – 

• Absolute error: The absolute error of measurement refers to the magnitude of variations between the measured and true values of a quantity. The absolute error of measurement is measured in decimal places.
• Percentage error: When the relative error is expressed as a percentage, the term “percentage error” is used to describe it.
• Relative error: The relative error in measuring a physical quantity is defined as the ratio of the absolute error to the true value in the measurement.

Examples of such errors are as follow –

• Instrumental errors occur when the marking of a thermometer is incorrectly described in a document. For example, if the thermometer’s marking reads 108°C instead of 100°C, this is an example of an instrumental error in measurement.
• It is possible to have an instrumental error when the pressure of the atmosphere is 1 bar, and the instrument reads 1.5 bar; this is called an instrument error.
• If the zero of the main scale does not coincide with the zero of the Vernier scale in a Vernier calliper, this is also considered an instrumental error because the design of the Vernier calliper is not proper.

Conclusion 

The general imperfection in technique also has an adverse effect on the results of measurement methods. If an experiment is not carried out in accordance with the guidelines or if the physical conditions are not favourable, it will result in errors that are not desirable. It is possible for these types of errors to occur for a variety of reasons, including improper instrument use, failure to follow instructions according to experiment rules, an unfavourable environment due to external physical conditions, and inaccurate technique.