Errors and Uncertainties in physics experiments and measurement and their solutions?

a)Errors

The difference between standard and experimental values is error.

There are two types of errors:-

i)Systematic error

ii)Random error

i)Systematic error :-

• ·         Also known as assignable error

• ·         Usually follow same trend of variations

Causes:-

• ·         Zero error in measuring instrument

• ·         Poor calibration of instrument

• ·         Incorrect calibration on the measuring instrument

EXAMPLE:-

Error occurring due to L.C of the measuring instrument

SOLUTION TO SOLVE ERROR:-

• ·         By comparing the instrument with other instrument which is more accurate

• ·         By carefully monitoring the measurement process

ii)Random error:-

• ·         Also known as Un Assignable error

• ·         Do not follow the same trend of variation

Causes:-

• ·         Due to some unknown reasons

• ·         Deviation in results

EXAMPLE:-

During measurement ,there are different  values of result of same measuring quntity.

SOLUTION TO SOLVE ERROR:-

• ·         Cannot be controlled experimentally.

• ·         By taking several reading of same measuring quantity  and then taking their mean value.

Uncertainties:-

Uncertainty is the situation which involves imperfect  or unknown  information.

There are three kinds of uncertainties commonly known today.

I)Absolute uncertainty

ii)Fractional uncertainty

iii)Percentage uncertainty

i)Absolute Uncertainty:-

• ·         Usually called absolute error

• ·         Usually the range of values in which the” true value” lies.

• ·         It is related to the least count of the measuring instrument.

• ·         Has the same unit as that of the value.

Least Count of the some measuring instrument is given as;

i)                    L.C of Meter Rod is 0.1cm

ii)                   L.C of Vernier  caliper is 0.01cm

iii)                 L.C of Screw Gauge is 0.001cm

Precision:-

• It is the minimum value that the device can measure.

• A device with less precision is more precise

e.g :Screw Gauge has least precision ,so it is more precise device

ii)Fractional Uncertainty:-

• ·         Also known as percentage uncertainty

• ·         It is the ratio of L.C to the mean value or measured value

• ·         It has no unit

Formula:-

Fractional Uncertainty= L.C/M.V

iii)Percentage Uncertainty:-

The percentage uncertainty can be interpreted as describing the uncertainty that would result if the measured value had been 100 units.

• ·         It has no units

• ·         It is the ratio of L.C to the mean value or measured value multiply by 100

Formula:-

Percentage Uncertainty= L.C/M.V * 100