Ch 1

The measurement of a given quantity is essentially an act or the result of comparison between the quantities and a predefined standard.

The device used for comparing the unknown quantity with the unit of measurement or standard quantity is called a Measuring Instrument.

Ch:1 Philosophy of Measurement

Direct method: compare the quantity directly with the primary or secondary standard.

Indirect method: in this method measurement involve the use of instruments as a physical means of determining quantities or variables.

Methods of measurement

Electrical instruments may be divided into two categories, that are;

1. Absolute instruments,2. Secondary instruments.

-Absolute instruments gives the quantity to be measured in term of instrument constant & its deflection. e.g. galvanometer- In Secondary instruments the deflection gives the magnitude of electrical quantity to be measured directly. These instruments are required to be calibrated by comparing with another standard instrument before putting into use.

Classification of Instruments

CLASSIFICATION OF SECONDARY INSTRUMENTS Secondary instruments can be classified into three types;

i. Indicating instrumentsii. Recording instrumentsiii. Integrating instruments

Indicating Instruments:It indicate the magnitude of an electrical quantity at the time when it is being measured. The indications are given by a pointer moving over a graduated dial.

Recording Instruments:The instruments which keep a continuous record of the variations of the magnitude of an electrical quantity to be observed over a defined period of time.

Integrating Instruments:The instruments which measure the total amount of either quantity of electricity or electrical energy supplied over a period of time. For example energy meters

In these types of instruments, pointer of the electrical measuring instrument deflects to measure the quantity. The value of the quantity can be measured by measuring the net deflection of the pointer from its initial position. In order to understand these types of instruments let us take an example of deflection type permanent magnet moving coil ammeter .

Deflection Type Instruments

It has two permanent magnets which are called the stationary part of the instrument and the moving part which is between the two permanent magnets that consists of pointer. Thus the torque is proportional to the current which is given by the expression Td = K.I

In opposite to deflection type of instruments, the null or zero type electrical measuring instruments tend to maintain the position of pointer stationary. They maintain the position of the pointer stationary by producing opposing effect. Thus for the operation of null type instruments following steps are required:

Value of opposite effect should be known in order to calculate the value of unknown quantity.

Detector shows accurately the balance and the unbalance condition accurately.

The detector should also have the means for restoring force.

Null Type Instruments

ACCURACY: Accuracy is the agreement between a measured value and the true value.

It is the closeness with which an instrument reading approaches the true value of the quantity being measured.

TRUE VALUE: The true value of quantity to be measured may be defined as the average of an infinite number of measured values.

DEFINATIONS

PRECISION : Precision also called reproducibility or repeatability, the degree to which further measurements or calculations show the same or similar results.

Instrument precision is usually associated with the number of digits displayed on the output, i.e., its resolution.

High accuracy, but low precision

High precision, but low accuracy

STATIC ERROR: static error is defined as the difference between the measured value and the true value of the quantity.

δa=Am-Atwhere δa=error

Am=measured value At=true value

DRIFT: if the quantity has perfect reproducibility the we can say there is no drift

Reproducibility is the closeness with which a given value may be repeatedly measured.

DEAD ZONE: it is defined as the largest change of input quantity for which there is no output present.

If we are making physical measurements, there is always error involved. The error is notated by using the delta, Δ, symbol followed by the variable representing the quantity measured.

A simple way of looking at the error is as the difference between the true value and the approximate value.i.e: Error (e) = True value – Approximate value

WHAT IS ERROR?

Limiting errors(guarantee errors) The accuracy of measuring instrument is guaranteed within a

certain percentage (%) of full scale reading E.g manufacturer may specify the instrument to be accurate at

±2 % with full scale deflection

There are three types of errors1. Gross errors2. Systematic errors3. Random errors

TYPES OF ERROR

cause by human mistakes in reading/using instruments may also occur due to incorrect adjustment of the

instrument and the computational mistakes cannot be treated mathematically cannot eliminate but can minimize Eg: Improper use of an instrument.

This error can be minimized by taking proper care in reading and recording measurement parameter.

In general, indicating instruments change ambient conditions to some extent when connected into a complete circuit.

Therefore, several readings (at three readings) must be taken to minimize the effect of ambient condition changes.

GROSS ERRORS

Systematic error is caused by any factors that systematically affect measurement of the variable across the sample.

For instance, if there is loud traffic going by just outside of a classroom where students are taking a test, this noise is liable to affect all of the children's scores -- in this case, systematically lowering them.

There are 3 types of systematic error :-

(i) Instrumental error

(ii) Environmental error

(iii) Observational error

SYSTEMATIC ERROR

(i) Instrumental error

- inherent while measuring instrument because of their mechanical structure (eg: irregular spring tension, stretching of spring, etc)

- error can be avoid by:(a) selecting a suitable instrument for the particular measurement application(b) apply correction factor by determining instrumental error (c) calibrate the instrument against standard

(ii) Environmental error- due to external condition effecting the measurement including surrounding area

condition such as change in temperature, humidity, barometer pressure, etc

- to avoid the error :- (a) use air conditioner (b) sealing certain component in the

instruments (c) use magnetic shields

(iii) Observational error- introduce by the observer

- most common : parallax error and estimation error (while reading the scale)

- Eg: an observer who tend to hold his head too far to the left, while reading the position of the needle on the scale.

It occur due to unknown causes, occur when all systematic error has accounted

- accumulation of small effect, require at high degree of accuracy

- can be avoid by

(a) increasing number of reading

(b) use statistical means to obtain best approximation of true value

RANDOM ERRORS