Measurement Techniques | 9702 Physics Summary Notes

• 2. Measurement Techniques | 9702 Physics Summary Notes

Quantity	Accuracy	Instrument
Length	1 cm	Tape
	0.1 cm	Ruler
	0.01 cm	Vernier caliper
	0.001 cm	Micrometer screw gauge
Volume	1 cm3	Measuring cylinder
	0.05 cm3	Pipette/burette
Angle	0.5o	Protractor
Time	1 min	Clocks
	0.01 sec	Stopwatch
	-axis scale	Time base of c.r.o
Temperature	1oC	Thermometer
	0.5oC	Thermocouple
P.d.	0.01 V	Voltmeter
Current	0.01 A	Ammeter
	0.0001 A	Galvanometer

2.1 Using a Cathode Ray Oscilloscope

Example: A supply of peak value 5.0 V and of frequency 50 Hz is connected to a c.r.o with time-base at 10 ms per division and Y-gain at 5.0V per division. Which trace is obtained?

2.2 Systematic and Random Errors

·  Systematic error:

o Constant error in one direction; too big or too small

o Cannot be eliminated by repeating or averaging

o If systematic error small, measurement accurate

o Accuracy: refers to degree of agreement between result of a measurement and true value of quantity.

·  Random error:

o Random fluctuations or scatter about a true value

o Can be reduced by repeating and averaging

o When random error small, measurement precise

o Precision: refers to degree of agreement of repeated measurements of the same quantity (regardless of whether it is correct or not)

2.3 Calculations Involving Errors

For a quantity x = (2.0±0.1)mm

· Absolute uncertainty = ∆x = ±0.1mm

· Fractional uncertainty = ∆x/x =0.05  

· Percentage uncertainty =  (∆x/x) × 100% = 5%

· Combining errors:

o When values added or subtracted, add absolute error

If p = (2x+y) / 3 or p = (2x-y) / 3, then ∆p = (2∆x+∆y) / 3

o When values multiplied or divided, add % errors

o When values are powered (e.g. squared), multiply percentage error with power

If r = 2xy³ or r = 2x / y³, then ∆r/r = ∆x/x+ 3 (∆y/y)

2.4 Treatment of Significant Figures

· Actual error: recorded to only 1 significant figure

· Number of decimal places for a calculated quantity is equal to number of decimal places in actual error.

· During a practical, when calculating using a measured quantity, give answers to the same significant figure as the measurement or one less

2.5 Micrometer Screw Gauge

·  Measures objects up to 0.01mm

·  Place object between anvil & spindle

·  Rotate thimble until object firmly held by jaws

·  Add together value from main scale and rotating scale

2.6 Vernier Scale

Measures objects up to 0.1mm

·  Place object on rule

·  Push slide scale to edge of object.

·  The sliding scale is 0.9mm long & is divided into 10 equal divisions.

·  Check which line division on sliding scale matches with a line division on rule

·  Subtract the value from the sliding scale (0.09×Divisions) by the value from the rule.