Instrumentation & Measurement: Error and Its Types
- 1. Error and Types of error
- 2. What is an error? Deviation from actual or true value is known as error. For example, if a resistor has a value 10KΩ and a meter reads the value 9.5KΩ, then there is an error of 0.5KΩ in the measurement.
- 3. Types of Errors There are different sources of errors and are classified as Gross Errors Systematic Errors Random Errors
- 4. Gross errors These errors occur mostly due to human mistakes and are classified as Reading Errors Recording Errors Calculation Errors Improper use of instrument (Loading Effect) Zero Error removal
- 5. Systematic errors These errors are classified as Instrumental Errors These errors occurs mostly Due to mechanical structure of instrument. Due to calibration of errors
- 6. Environmental errors These errors occur due to environmental effects. e.g. temperature, pressure etc. These errors can be avoided i. By selecting suitable instrument according to the measurement requirement. ii. Correction factor for instrument error can be applied. iii. Instruments can be calibrated against a standard instrument.
- 7. Random errors These errors occur due to unknown causes. e.g. A voltmeter read at half-hour intervals and voltmeter Is operated under ideal environment conditions and has been accurately calibrated before the measurement, it will be found that the readings vary slightly over the period of observation.
- 8. Error calculations When a quantity is calculated from the measurements made on more than one instruments. It must be assumed that error will combine in worst possible way. It means the resulting error will be larger than the error in any one instrument.
- 9. Error calculations Sum of quantities When a quantity is calculated as the sum of two measured quantities, the total error will be sum of absolute error in each quantity. E = (A ± ΔA) + (B ± ΔB) E = (A + B) ± (ΔA + ΔB) ∆A will be the absolute error in A and ∆B will be absolute error in B.
- 10. Error calculations Difference of quantities when a quantity is calculated as the difference of two measured quantities, the total error will be sum of absolute errors in each quantity. E = (A ± ΔA) - (B ± ΔB) E = (A - B) ± (ΔA + ΔB) ∆A will be the absolute error in A and ∆B will be absolute error in B.
- 11. Error calculations Product of quantities when a quantity is calculated as the product of two or more measured quantities, the total %age error will be the sum of %age error in each quantity. e.g. Power is the product of V and I. P = VI ± (V.ΔI + I.ΔV) % error in P = (% error in I) + (% error in V)
- 12. Error calculations Quotient of quantities when a quantity is calculated as the quotient of two or more measured quantities, the %age error will be the sum of %age error in each quantity. e.g. Resistance is the quotient of V and I. R = V/I % error in R = (% error in V) + (% error in I)
- 13. Error calculations Quantity Raised to a Power when a quantity is raised to a power, the %age error will be % error in AB = B(% error in A) e.g. error calculation of I2.