2) Measurement and techniques

Contents: i) measurementii) errors and uncertainties

i) measurement

quantity instrument precisionlength 1)ruler

2)vernier caliper3)micro metre screw gauge

mass Weighing scalecurrent AmmeterVoltage Voltmeter

temperature Thermometer in glasstime 1)analogue stop watch

2)digital stop watch

ii) errors and uncertainties

-Errors are uncertainties in measured quantities which arise from different source due toi) limitation of the observerii) instrumentiii) the method used

-systematic errors are errors of measurements which occurs according to some fix pattern and always one sided-e.g:

-systematic error are not reducible by repeating the reading and obtain the average

1

-can be avoided by calibration curves.-random errors are errors with different magnitude and signs in repeated measurement- e.g:

-can be avoided by taking the average of a few readings.-precision refers to the extent or limit of sensitivity of a given measuring instrument to obtain the reading of the physical quantity being measured.

-e.g:

-Accuracy is the ability to obtain the true value.

-Actual uncertainty is obtained from the instrument used by taking the smallest graduation . -e.g: 1) ruler – 0.1cm 2)vernier -0.01cm-Generally all readings can be recorded in the form of R R- must be one significant figure and same decimal point with R.-e.g: i) 123.23 cm ii) 235.2 N

-fractional uncertainty=

-e.g:

2

-percentage uncertainty=

-e.g:

-consequential uncertaintiesi) Addition: if A= B+ C, so -e.g:

ii) substraction: if A= B-C, so -e.g:

iii) product: if A=BxC, so

-e.g:

iv) Quotient: if A=B/C, so

-e.g:

v)

3

-e.g:

cathode-ray oscilloscope (c.r.o).

-The cathode-ray oscilloscope (CRO) is a common laboratory instrument that provides accurate time and amplitude measurements of voltage signals over a wide range of frequencies. Its reliability, stability, and ease of operation make it suitable as a general purpose laboratory instrument. The heart of the CRO is a cathode-ray tube .

-The Y AMPLIFIER (VOLTS/CM) control determines the height of the trace. Choose a setting so the trace occupies at least half the screen height, but does not disappear off the screen. The TIMEBASE (TIME/CM) control determines the rate at which the dot sweeps across the screen. Choose a setting so the trace shows at least one cycle of the signal across the screen..

-Measuring voltage and time period

The trace on an oscilloscope screen is a graph of voltage against time. The shape of this graph is determined by the nature of the input signal.

In addition to the properties labelled on the graph, there is frequency which is the number of cycles per second.

The diagram shows a sine wave but these properties apply to any signal with a constant shape.

Amplitude is the maximum voltage reached by the signal. It is measured in volts, V.

Peak voltage is another name for amplitude. Peak-peak voltage is twice the peak voltage (amplitude). When reading an

oscilloscope trace it is usual to measure peak-peak voltage.

4

Time period is the time taken for the signal to complete one cycle. It is measured in seconds (s), but time periods tend to be short so milliseconds (ms) and microseconds (µs) are often used. 1ms = 0.001s and 1µs = 0.000001s.

Frequency is the number of cycles per second. It is measured in hertz (Hz), but frequencies tend to be high so kilohertz (kHz) and megahertz (MHz) are often used. 1kHz = 1000Hz and 1MHz = 1000000Hz.

frequency  =          1        

    and     time period  =          1        

time period frequency

5