Errors in Measurement
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Errors will always be involved during the measurement process. No measurement is perfect, as the error involved in a measurement cannot be removed completely, and understanding the types and sources of errors is crucial for ensuring accuracy and reliability. Measured value is always somewhat different from true value (standard value).
The difference between true value and measured value is known as errors.
Error = True Value тАУ Measured Value.
Errors in measurement can occur due to various factors, leading to deviations between the measured value and the true value.
Different types of Error:
(1) Constant Error:
The error which affects each observation by same amount. These errors arises due to faulty calibration of instrument. It can be detected and eliminated by using number of different methods, apparatus and technique or calibrating the instrument against a standard.
Table of Contents
(2) Systematic Errors:
Systematic errors are consistent and predictable, affecting measurements in a consistent direction. These errors come into existence by virtue of a definite rule, which tends to occur in one direction, either positive or negative. We can eliminate such errors once we know the rule which govern them. These can be further classified as,
a) Instrumental Error:
This error is arises due to defect in measuring instrument. These errors can be detected by measuring same physical quantities with different instrument or by different method. eg. Wearing of meter scale. Zero error in Vernier callipers and Screw gauge.
Instrumental errors can be avoided by:-
- Selecting a suitable instrument for the particular measurement applications.
- Appling correction factors after determining the amount of instrumental error.
b) Error due to imperfection in Experimental Technique:
This error is arises due to limitation of experimental arrangement, imperfection of apparatus used. eg. Temperature Loss to surrounding in its measurement however insulation may be, error due to buoyancy of air when weight of a body is measured in air.
c) Personal Errors:
This error is arises due to taking improper precautions, carelessness of an observer. Can be minimized by taking repeated observation.eg. error in measurement of time period of simple pendulum while one might stop the stop-watch earlier or a bit later than exactly on completion of one oscillation, parallax error while reading a meter scale.
d) Errors due to External Cause/ Natural Error:
This error is arises due to change in physical condition like temperature, pressure, humidity etc. eg. In ohmтАЩs law experiment resistance measurement is influenced by variation in temperature, expansion of meter scale due to increase in temperature, Temperature change causes clock drift.
(3) Least Count Error:
Due to limitation imposed by least count of measuring instrument. The minimum measuring capability of a measuring instrument is known as least count.
(4) Gross Error or Mistakes:
These errors are mainly due to human mistakes in taking reading or improper adjustment of the apparatus, due to casual approach of observer, computational error. These errors can be avoided by careful working.
(5) Random Errors:
Random errors, also known as Statistical errors or By chance error, are unpredictable and occur randomly during the measurement process. The exact cause of random error may not be traced. They can arise from various sources, such as fluctuations in environmental conditions, due to slight variation in the attentiveness of the observer while taking observations, or inherent variability in the quantity being measured.
Random Error cannot be removed but minimized by taking number of observation and finding its mean value. eg. Slight variation in null point every time in potentiometer experiment.
Measurement of Errors
- Mean /True value – Arithmetic mean of all experimentally observed values.
- Absolute error: The difference between true value and individual measured value of a quantity.
- Mean Absolute Error: The arithmetic mean of magnitude of all values of absolute error.
A measured physical quantity can be represented with limits of absolute error as a = am ┬▒ тИЖam
- Relative Error/Fractional Error: The ratio of Mean Absolute Error to the mean value.
- Percentage Error: Relative error expressed in terms of percentage.
Video Lecture ЁЯШК Errors in Measurement
Combination of Error
For Addition or Subtraction:
For expression like, Y = A + B or Y = A – B
Absolute error in measurement of Y is given by тИЖY = тИЖ A + тИЖ B
For Multiplication or Division:
For expression like, Y = AB or Y = A/B
Relative error in measurement of Y is given by
For expression like, Y = An B / Cm
Relative error in measurement of Y is given by
Percentage error in measurement of Y is given by
What are errors in measurement?
Answer: Errors in measurement refer to the discrepancies or variations between the measured value and the true value of a quantity being measured. These errors can occur due to various factors and can affect the accuracy and precision of measurements.
What is the difference between accuracy and precision?
Answer: Accuracy refers to how close a measured value is to the true value or the accepted reference value. Precision, on the other hand, relates to the degree of consistency or reproducibility of repeated measurements. Accuracy indicates the absence of systematic errors, while precision reflects the absence of random errors.
What are random errors?
Answer: Random errors are unpredictable variations in measured values that occur due to various uncontrollable factors, such as environmental conditions, human limitations, or equipment limitations. These errors cause measurements to scatter around the true value, and they can be reduced by repeating measurements and applying statistical analysis to estimate the average value.
What is the difference between zero error and zero correction?
Answer: Zero error refers to a deviation in a measuring instrument where it does not read zero when it should. It can be positive (when the instrument indicates a value greater than zero when it should read zero) or negative (when the instrument indicates a value less than zero when it should read zero). Zero correction, on the other hand, is the adjustment made to the measured value to account for the zero error and obtain the true value.
What is parallax error?
Answer: Parallax error occurs when the observer’s eye is not directly aligned with the scale of the measuring instrument. This misalignment leads to an apparent shift in the position of the scale markings, causing an incorrect reading. Parallax error can be minimized by ensuring that the eye is positioned perpendicular to the scale and by using instruments with anti-parallax mirrors or scales.
Can errors in measurement be completely eliminated?
Answer: In practice, it is nearly impossible to completely eliminate errors in measurement. However, through careful calibration, proper measurement techniques, error analysis, and statistical methods, the impact of errors can be minimized, and measurements can be made more accurate and precise.
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