PHYS351001 Contemporary Physics Laboratory Laboratory Exercise: LAB 01 Resistivity, Root-mean-square Voltage, Potentiometer (updated 1/25/2017) PART I: SOME FUNDAMENTAL CONCEPTS: 1. Limits on accuracy and precision: Nearly all measurements in experimental physics involve the determination of one or more of a few fundamental quantities: force, mass, distance, time, charge, EMF, current, and temperature. Usually it is not necessary to measure each of these quantities separately because modern measuring instruments are designed to indicate either fundamental or derived quantities directly. With all measurements, however, there are associated uncertainties, the importance of which depends on the degree of precision and accuracy demanded by the experiment. They are caused by calibration errors, by noise within the measurement environment, by statistical fluctuations in the source or in the meter itself. Ultimately, limitations to the accuracy occur because of the obvious fact that it is always necessary to disturb a system in order to acquire information from it, i.e., to make it do work on the measuring instrument, or at the very least to have its entropy increased. For example, work has to be exerted against a restraining spring to move the needle of an analog meter. Even in a digital meter which has no moving parts power is required to provide the information for the measuring system, usually in the form of I 2 R (joule) heating of the input circuit. The energy to perform this work can only come from the system being measured. Even in cases where there is no direct connection between measurer and measurement, for example in observing light reflected from an object, there is momentum transfer to the object that reflects incident rays. Whenever possible one should choose instruments and conditions so that none of these limitations is significant within the practical limits of accuracy. But, at the margin of information accessibility, they can be critical. Q1. If a voltmeter has an input resistance of 10 7 what is the power required to measure one volt? What would it be if the resistance were 1000? 1 Q2. Calculate the visible light power incident on a 1 cm square receptor at 1 meter from a 100 watt incandescent lamp which is 30% efficient for visible light (assuming the lamp is a point source). Modern voltmeters, i.e. digital meters, are accurate within their specified tolerance limits and remain reliable for years. Digital voltage measuring systems rely on conversion of the input value from an analog quantity to a digital quantity which is then displayed in 1 All questions or problems printed in boldface represent written exercises to be solved and submitted to your instructor one week after they are assigned.
analog form on a digital indicator. Later we shall be more specific about the digitizing system. At this point, we wish to consider a cause of common inaccuracies. All dc sources of electrical signals are represented by the diagram illustrated below (Fig.1). The source is always within a black box and, therefore, its internal terminals cannot be accessed. In the diagram, Ri is the internal resistance of the device. Therefore, whenever any current is drawn from the source, the terminal voltage is less than the generated voltage by the ir drop across the internal resistance. The voltmeter is in series with the source and its internal resistance and, therefore, it could contribute to the deviation from the true load free supply value. Fig. 1 Voltage source with internal resistance Q3. To what extent can you believe what the voltmeter tells you? PART II: DC MEASUREMENTS Before attempting this exercise review the "Resistance Band Markings" distributed with this handout. Select 5 resistors from the resistors available in the back of the room that have color codes. Do not take duplicate resistors. 1. Using the multimeter as an Ohm meter measure the resistance of each of the resistors. 2. Make a table in your notebook for your data. For each of the resistors, record in your lab books the color code of the resistors and using the "Resistance Band Markings" chart determine what values you should have by the color code.
Resistor Band Markings Color 1 st /2 nd band 3 rd band --------------------------------------------- ------------ Black 0 10 0 Brown 1 10 1 Red 2 10 2 Orange 3 10 3 Yellow 4 10 4 Green 5 10 5 Blue 6 10 6 Violet 7 10 7 Gray 8 10 8 White 9 10 9 Gold N/A 10-1 Silver N/A 10-2 Using band color guide note the number associated with the colored bands on your resistor. The first band is the one closest to the end of the resistor. The 1 st and 2 nd bands correspond to a 2 digit number, e.g. 47, for yellow-violet. The 3 rd number is the decimal multiplier e.g. 10 6 for blue. Equivalent to 47 x 10 6 Ohms. The forth band is a tolerance of resistance. (+/- 5 or 10 %) 1 st /2 nd band yellow=4 1 st /2 nd band violet=7 47 x 10 6 ohms 10%-tolerance +/-4700000 ohms 51700000 ohms 42300000 ohms 3 rd band blue=10 6 4 th band tolerance 10%-silver 5%=gold
Q4. How well do the resistances from the color code agree within tolerance with the measured resistance in each case? Calculate a % difference for each case. Record your results. 3. Select 4 resistors having approximately the following values 10 6, 10 5, 5 x10 5, 5 x 10 4 ohms. By approximately, a 470 k- ohm resistor is close enough to 5 x10 5. Measure and record the resistance values of the resistors. Connect wires to your power supply so that it will produce between 5-15 volts, measure and record its value, but do not connect it to your breadboard yet. 4. Connect the first four of your selected resistors in series on your breadboard as illustrated below (Fig. 2 and as on breadboard hand out) starting with R 1 = 1 x 10 6 Ohms followed by each successively smaller resistor with the 5.6 x 10 4 Ohm resistor to the left. Wire the series resistors to the power supply with the terminal of the highest value resistor connected to the negative side of the power supply (black/ground) and the lowest value resistor to the positive side of the supply (red/voltage side). Calculate the current that will flow through the four resistors. Calculate the voltage drop that should appear across each resistor. Record your reading from the multimeter and the value as indicated by the color code. R 1 R 2 R 3 R 4 Fig. 2 Series Resistors Turn on the power supply. Q6. Measure and record the supply voltage and the voltage across each resistor. Q7. What would you expect the sum of the voltages across each resistor be equal to in each case? What do you find? Calculate a % difference for these expected and measured quantities. Part 2. RMS Values: Compare AC voltage recorded by a Digital Oscilloscope (DO) and multimeter. 1. Turn on your DO and Function Generator. 2. Insert a (BNC) "T" connecter on the Function Generator. 3. Set the Function Generator frequency to about 100 Hz and waveform to a sign-wave.
4. Connect one arm of the "T" to Channel one of the DO (BNC connectors both ends) and the other side of the "T" to a multimeter set at AC volts (BNC to alligator/micro-clip cable). See Figure 5. 5. Using the DO screen scale and the gain settings adjust the signal to exactly 2 volts peak-to-peak. (Peak to peak voltage refers to the voltage read from the top of the waveform to the bottom of the wave-form or twice the wave amplitude on the DO. The peak voltage is the amplitude or one half of the peak to peak value.) Record or calculate all the following in your laboratory notebook: 6. Record the AC volts reading on the multimeter. V RMS =. 7. Calculate and record the ratio of V RMS to the peak voltage reading on the DO. (The peak voltage reading refers to the wave-form amplitude.) This ratio should equal approximately one-half the square root of 2. The peak reading divided by the square root of 2 is the RMS (Root Mean Square) value. 8. Divide the peak voltage by the square root of 2. Compare the V RMS to the value you just calculated. 9. Calculate the % difference between your multimeter V RMS reading and the peak reading divided by the by the square root of 2. Display the V RMS value of the signal on your oscilloscope to compare to your calculated value. The meter reading is the RMS (Root Mean Square) value of the AC voltage, or the effective value of the voltage, the equivalent of the DC value. Q8. Record the % difference between the mutlimeter V RMS reading and the oscilloscope V RMS value for 10 different input frequencies from 10Hz to 1kHz. Plot this % difference vs. frequency. (Use the oscilloscope V RMS as the ideal value.) Calculation of % difference = [100% * (measured value ideal value)]/(ideal value) Part 3: The Use and Measurement of a Trimpot: A trimpot is a three terminal device that can be adjusted to supply a particular resistance or obtain a particular voltage drop across a particular resistance. The second purpose mentioned is much more common. 1) Obtain a 5 K or 10K trimpot (5000 Ohm or 10,000 Ohm) from the back of the room. 1 3 2
2) Place trimpot into bread board. Use wires inserted in the bread board and a multimeter to measure resistance value from 1 to 2, 2 to 3, 1 to 3. Record these values. 3) Adjust the resistance set screw so that resistance from 1 to 2 is exactly 1000 ohms. Measure resistance from 2 to 3, and 1 to 3 and record. 4) Attach 5 VDC to 1 and Gnd to 3. Measure voltage between 1 to 2, 2 to 3, 1 to 3 and record. 5) Adjust the set screw one complete turn to increase the resistance in 1 to 2. Repeat #4 above. 6) Repeat #5 above and record result. Q9: What is the resistance and voltage pattern that emerges when you complete steps 3 to 6 using a trimpot? % Difference Calculation: 1 amplitude 2 amplitude peak to peak 1 to 3 peak voltage is 2 to 1 3 Fig. 3
Oscilloscope Operation: volts/div The divisions for volts/div are the centimeter by centimeter grid covering the oscilloscope screen. time/div time/div volts/div Figure 4 ----------------------------------------------------------------------------------- multimeter DVM Signal Generator output * 0 0 oscilloscope Channel 1 input: * Channel 2 input: * Figure 5
Name: PH409 Contemporary Physics Laboratory Laboratory Exercise: LAB 01-SEC 01, 02 Resistivity, Root-mean-square Voltage, Potentiometer Q1. If a voltmeter has an input resistance of 107 what is the power required to measure one volt? What would it be if the resistance were 1000? Q2. Calculate the visible light power incident on a 1 cm square receptor at 1 meter from a 100 watt incandescent lamp which is 30% efficient for visible light (assuming the lamp is a point source). Q3. How accurate is a voltmeter and what makes it accurate? Explain your answer. Which voltmeter would be better, one with an input resistance of 10 8 or 10 12 ohms? Why? Q4. After measuring the resistors individually, how well do the resistances from the color code agree within tolerance with the measured resistance in each case? Calculate a % difference for each case. Give a sample calculation, and record all your results. Q6. Measure and record the terminal voltage and the voltage across each resistor. Q7. What would you expect the sum of the voltages across each resistor be equal to in each case? What do you find? Calculate a % difference for these expected and measured quantities. Q8. Record the % difference between the mutlimeter V RMS reading and the oscilloscope V RMS value for 10 different input frequencies from 10Hz to 1kHz. Plot this % difference vs. frequency. (Use the oscilloscope V RMS as the ideal value.) Calculation of % difference = [100% * (measured value ideal value)]/(ideal value)
Q9: What is the resistance and voltage pattern emerges when you complete steps 3 to 6 using a trimpot?