# Physics 107 - Measurement of Uncertainty

MEASUREMENT UNCERTAINTY IN ANALOG AND DIGITAL MEASURMENTS

You have already seen examples in which random factors give rise to uncertainty in a measured quamtity. In this experiment, you will explore two other common types of measurement and the uncertainty associated with them. One type is an analog measurement, where you read a value from a continuous scale such as a ruler. The other common class of measurement involves digital scales, where the values are divided into discrete steps.

DIGITAL MEASUREMENTS

1. Use one of the digital multimeters to measure the value of a resistor.
2. What is your estimate of the lower limit on the resistance?
3. What is your estimate of the upper limit on the resistance?
4. Invent a pictorial way to show how likely it is that the resistance takes on particular values within this range.

Pause for discussion with the whole class.

ANALOG MEASUREMENTS

5. Use the metre stick to measure the distance between two adjacent blue lines in your laboratory notebook. (Do not measure multiple lines and divide; that comes later)
6. Write down exactly how you did this measurement.
7. What is your estimate of the most likely distance between these two lines?
8. What is your estimate of the lower limit on this distance?
9. What is your estimate of the upper limit on this distance?
10. Work with your partner to invent a pictorial way to show how likely it is that the distance takes on particular values within this range. Explain your reasoning in words as well as a picture.

Pause for discussion with the whole class.

3 COMPARISONS

15. Re-measure your resistor with the digital metre at the front of the lab and compare results. Which do you trust more, and why?

16. Measure the temperature at two different places in the room (near the entrance and near the window) and draw a conclusion as to whether the temperature is significantly different in differnet corners of the room.

17. Use both the analog and digital calipers to measure the diameter of a ball bearing and compare. Which do you trust more and why?

Marking Scheme

a picture or graph for the digital measurement plus explanation.- 2 marks
values for most likely, minimum and maximum distance - 1 mark
a picture or graph for the analog measurement, plus explanation - 2 mark
digital comparfison - 2 marks
temperature comparison - 2 marks
analog-digital comparison - 2 marks