Question

2. You are using a digital multimeter (DMM) to measure the voltage across a resistor. The values displayed on the DMM vary, with five consecutive values being 2.412, 2.432, 2.418, 2.422, and 2.416 V (this happens even though no connections are changing). These fluctuations give rise to an uncertainty in the measured value of resistance.

a) (1 point) One method of quantifying the uncertainty in the measurement is to take half of the range of the largest fluctuating digit. Using this method, what is the uncertainty in the voltage for this measurement?

b) (1 point) A more precise method of quantifying the uncertainty is to find the standard deviation of the data. What is the standard deviation of this data set? (This is usually done with a computer program such as Excel, Matlab, or Wolfram Alpha, that’s fine here as well.)

c) (1 point) Do your results for (a) and (b) agree? In what case could you not use the approximate method described in part (a) (i.e. when would these two methods disagree)?

d) (2 points) The approximate method described in (a) is easier than the more precise method described in (b) so there must be a good reason to use the method described in (b), or else experimenters would always use method (a). Other than precision, why is the method described in (b) preferable to the method described in (a)?

Answer 1

a) larget fluctaing digit range 2 - 8

error = +/- 0.003

b) SD(2.412, 2.432, 2.418, 2.422, 2.416) = 0.0068

c) They do not agree , In the current case it is not the highest digit (3rd after decimal) fluctuating , 2nd digit also fluctating, When only the last digit fluctates the agreement is closer.

d) It is not just precision that matters to get SD, it indicates the spread of the data or the variance in the data. It is computed using the deviations from the mean value. it gives us the true uncertainity in the data when we make a measurement.