# Measurements and Errors of Instruments

Posted on at

### Measurement Errors

Errors may come from different sources and are usually classified under three main headings.

#### Gross errors

Gross errors are essentially human mistakes that are the result of carelessness

–      Wrong computation

#### Systematic errors

Systematic errors are divided into two categories

–      Instrumental Errors: Due to shortcomings of the instrument

–      Environmental Errors: Due to external conditions affecting the measurement

#### Instrumental errors

–      Friction in bearings of various moving components

–      Zero setting not adjusted properly

–      Calibration error due to aging

–      Faulty display circuit in digital instruments

#### Environmental errors

–      Ambient parameters such as temperature, pressure, humidity, magnetic and electric fields, dust and other such external parameters can affect the performance of the instrument.

#### Random errors

–      Though gross errors and systematic errors can be avoided by taking proper care, some errors of unexplainable origin can also occur in measurements.

–      These errors are classified as random errors.

–      Random errors can be minimized by taking many readings and determining the mean value.

### Absolute errors and relative errors

–      If a resistor is known to have a resistance of 500 Ω with a possible error of ±50 Ω, the ±50 Ω is an absolute error. This is because 50 Ω is stated as an absolute quantity, not as a percentage or fraction of the 500 Ω resistance

–      When the error is expressed as a percentage or as a fraction of the total resistance, it becomes a relative error. Thus the ±50 Ω is ±10 % relative to 500 Ω or ±1/10 of 500 Ω. So the resistance can be specified as R = 500 Ω ± 10 %.

–      Another method of expressing an error is to refer to it in ppm relative to the total quantity.

–      For example, the temperature coefficient of 1 MΩ resistor might be stated as hundred ppm/Co, which means 100 parts per million / degree Celsius. One millionth of 1 MegaΩ is 1 Ω. Consequently, 100 ppm of 1 MΩ is 100 Ω. Therefore, a 1 Co change in temperature may cause the 1 MΩ resistance to increase or decrease by 100 Ω.