Understand instruments, their uses and their resolution

Resolution and instrument choice

Resolution is the smallest change in the measured quantity needed to change an instrument's reading; for an instrument with a scale, its resolution is its smallest division. Choose an instrument that can measure the required quantity. Make the final digit of a recorded value match the smallest division of the measuring instrument; do not estimate an extra digit. For example, if a metre rule has millimetre divisions, record a length as 18.2 cm or 182 mm, not 182.3 mm. If a protractor has 1° divisions, record an angle as 32°, not 32.5°. (Manual stopwatch timing is the exception here: although the stopwatch has a 0.01 s resolution, human reaction time is not precise to 0.01 s, so record manually timed measurements to 0.1 s.)

Typical resolutions listed in the lecture

Length: metre rule 1 mm, vernier calipers 0.1 mm, micrometer 0.01 mm. Mass: top-pan balance 0.01 g. Angle: protractor 1°. Time: stopwatch 0.01 s. Temperature: thermometer 1 °C. Potential difference: voltmeter 1 mV–0.1 V. Current: ammeter 1 mA–0.1 A. Vernier calipers may also have a resolution of 0.02 or 0.05 mm; follow the scale on the actual instrument. Know the English names of all the instruments listed above.

Reading a micrometer

Use a micrometer for small widths, thicknesses or diameters, such as the diameter of a copper wire. First read the sleeve's main scale, then read the thimble division aligned with the reference line, and add the two readings. In the diagram, each main-scale division is 0.5 mm and each thimble division is 0.01 mm: 2.50+17×0.01=2.67 mm. The other two examples are 2.50+26×0.01=2.76 mm and 3.00+24×0.01=3.24 mm. Refer to the first image below for the detailed reading method.

Reading a vernier caliper

Vernier calipers can measure diameters, thicknesses and small lengths. First read the main-scale value to the left of the vernier zero. Then find the vernier division that lines up with a main-scale mark, multiply its division number by the resolution, and add the result to the main-scale reading. The example is 13 mm+3×0.1 mm=13.3 mm (1.33 cm). Digital vernier calipers can reduce parallax error when reading conventional vernier calipers. Refer to the second image below for the detailed reading method.

Examples