PH4705 & ET4305: Measurements

1. PH4705 & ET4305: Measurements • Measurement: assign numbers to property of object or event to describe it • The absolute true value of a measurement can’t be known (our measurement method or system will affect the object or event). We measure the conventional true value accepting the there is some uncertainty. • A measurement is a number with appropriate units • A measuring system must be calibrated against some standard

2. PH4705 & ET4305: Measurements • Units: a quantity in terms of which other quantities may be expressed (e.g. length in metres) • Ideally units should be related to a standard which is permanent and unchangeable • Many standards were originally material – properties of same physical object kept in one location • Portable secondary standards copied from this were/are used for calibration, or a “recipe” for generating a standard given. • All precision measurements are traceable back to secondary standard maintained in an official standards lab

3. PH4705 & ET4305: Measurements • There are three independent fundamental qualities: mass, length and time* • We use the SI –Systems International system of units this defines seven base units: Mass, Length, Time (independent base units) Ampere, Kelvin, Mole, Candela (derived base units) *ignoring relativity. Mass is still a material standard

4. PH4705 & ET4305: Measurements • Errors: When we measure a quantity there are always errors, we aim to reduce them to an acceptable level. • Two types: Intrinsic or systematic error associated with the measurement instrument or method. Extrinsic or Influence error arising from sources external to the instrument or generated by it

5. PH4705 & ET4305: Measurements • Intrinsic errors are usually determinate, they can be compensated for • Dynamic error: the measuring instrument can’t respond fast enough to changes in the measurand • Law error: The instrument deviates from the stated (or assumed) relationship linking the measurand and the measured value (non linearity or zero errors are common) • Loading error: the instrument, when connected, causes a change in the measurand

6. PH4705 & ET4305: Measurements • Extrinsic errors: Random, they cannot be assigned a definite value • Every effort is made to minimise the effect of extrinsic errors through using the “right” instrument, selection of appropriate measurement technique, and estimate of expected results. • Random errors are assumed to be Gaussian

7. PH4705 & ET4305: Measurements • For Gaussian random errors 68.3% of reading lie within ±one standard deviation, σ, and 95.4% lie within ±2σ • A common way of expressing the uncertainty is to quote the result as the mean value ±α, where α = 0.675σ • Alternatively, the meaurement ± a value related to the % accuracy expressed in terms of least significant figures is given