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 s 2 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 9 21 94 1 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 1 1 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 9 21 94 2 least sensitive scale the scale with the largest range Do not use a scale that is 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 V180 volts V180 volts 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 9 21 94 3