EXPERIMENT 4: MEASURING POTENTIAL DIFFERENCE WITH A DIGITAL MULTIMETER
AN EXERCISE IN SYSTEMATIC ERROR
Prior to Lab: Solve the following problem to hand in at the beginning of lab: A simple
pendulum is constructed from a mass and a string. The pendulum is determined to be
30.0 cm long  0.50 cm.
a. If the acceleration of gravity is 980.0 cm/s2  0.10 cm/s2, what is the measurement
uncertainty in the period of the pendulum?
b. In lab the period of the pendulum is determined to be 1.11 s, 1.09 s, 1.11 s, 1.10 s,
1.10 s, 1.14 s, 1.11 s, 1.08 s, 1.10 s, 1.10 s in 10 trials. Determine the standard
deviation for this data.
c. How does the measurement uncertainty found in part a compare with the statistical
uncertainty in part b?
Object: To determine the potential difference across a resistor, and determine which scale
provides the most accurate reading.
Discussion: Instrumentation is a necessity for making any kind of measurement in
experimental science. However, the measurement is only as good as the accuracy and
sensitivity of the instrument. In any measurement there are two sources of possible
error. First is the accuracy of the instrument itself. This accuracy is determined by the
calibration of the instrument which is done either by the manufacturer or by a
calibration lab. In the case of general physics lab, we use the manufacturer’s
calibration. The second source of error is the experimenter’s ability to read the
instrument (or data).
A digital multimeter (DMM) is a good instrument to use to explore this aspect of
measurement because of the availability of several scales of sensitivity. In this lab, we
will consider the accuracy of this common electrical measuring instrument with relation
to choice of scale, and ability to read the instrument. Both these aspects are important
to obtaining the most accurate measurement. We will use the DCV ranges of the
multimeter to obtain potential difference readings across two resisters supplied with a
nominal 3 volts from a battery eliminator. The manufacturer claims an accuracy for
the DMM of ±0.5% of the reading for the DMM. In addition we don’t know whether
the meter is rounding up or down the last decimal position, so our reading error is ±0.5
digit in the last decimal place for both our zero reading and our voltage reading for a
combined reading error of ±1 digit.
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Figure 1. A wiring diagram for the experimental apparatus. The 3
volts is generated by the battery eliminator with the switch on it set
for 3 v. The zig-zag lines represent resistors, the rectangle marked
DMM is the digital multimeter, and the other lines represent wires
connecting the various elements of the apparatus.
3 volts


DMM
Figure 2. The apparatus and wiring
arrangement for the experiment. The DMM is
connected to the resistor board to measure the
potential difference (voltage) 180  resistor.
Figure 3. The same apparatus as Figure 1,
however, the DMM is now properly connected
to measure the potential difference (voltage)
across the 1000  resistor.
Experimental Procedure:
1. Attach the battery eliminator to the end terminals of the board containing the 1000 
and 180  resistors.
2. After checking with your instructor, plug in the battery eliminator.
3. Measure the potential difference across each resistor on the 200 V, 20 V, and 2 V
ranges as necessary to fill in the following table. Begin measurement with the least
sensitive scale (the scale with the largest range). Do not use a scale that is
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smaller than the measured potential difference determined on a less sensitive
scale.
4. Determine the uncertainty of each measurement and record it. (Instrumental
uncertainty plus reading uncertainty: V = 0.5%  reading + 1 unit in the smallest
displayed decimal position.) For example if your reading is 2.46 v, your uncertainty is
(0.005  2.46 v + 0.01v = 0.02 v). Your value for the voltage is then 2.46 v ± 0.02 v.
5. Determine the fractional uncertainty of each measurement.
Range
Volts
V1000
(volts)
V1000
(volts)
V1000
V1000
(%)
V180
(volts)
V180
(volts)
V180
V180
(%)
200 volt
20 volt
2 volt
Report: What do you conclude about the use of the DMM to measure voltage (potential
difference)? What can you conclude about systematic error?
What can you conclude about the voltages across the resistors?
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