Wave Measurement & Ohm s Law Marking scheme : Methods & diagrams : 2 Graph plotting : 1 Tables & analysis : 2 Questions & discussion : 3 Performance : 2 Aim: Various types of instruments are used by engineers and scientists to measure different aspects of an input signal. This experiment will help give an indication to the type of instrument to use depending on the measurement and accuracy required. This experiment will also help give a general overview about various computer-base types of measurements, as like in the PHASE, RLC and NiSCOPE experiments. In this case, a PCI Ni-FGEN 5401 waveform generator card is incorporated into a PC. The PCI card is a single channel device for generating analog waveforms. It functions like a conventional function generator, except that it is controlled via LabView on a PC. After investigating the various types of instruments available for measurement taking, the best suited instrument is now used to investigate the relationship between current and potential difference in a circuit. Equipment List: Tektronics digital real time oscilloscope with two probes Tektronics AFG3021 Circuit board with Load resistors Multimeter Voltmeter PC Preliminary Theory: In the first part of this experiment, multiple measurements of one signal will be made using different types of instruments. Measurements to be taken are the frequency, voltage level and resistance. The voltage level is not always a single fixed value. For time-varying signals (ie AC signals), the value measured will depend on the time and method of measurement. This value can be voltage at a single point, average of several points or the root-mean-square (rms) value or the peak-topeak value (pk-pk). A multimeter gives the rms value of an AC signal when set to measure in the AC mode and the mean value when set to measure in the DC mode, while the voltmeter will 101
measure the average value. A multimeter can also be used to check the continuity of the flow of current in any circuit. Read the IO experiment for further details on V mean, V pp and V rms. Ohm s law, named after Georg Ohm, defines the relationship between power, voltage, current and resistance. The principles apply to AC, DC or RF (radio frequency). At a fixed temperature, the current (I) flowing through a conductor and the potential difference (V ) across it are related through Ohm s Law: V = IR where R is the total resistance of the material in the circuit. If the above law is satisfied, then the material is said to be ohmic. The AC analog to Ohm s law is: V = IZ where Z is the impedance of the circuit and V and I are the rms or effective values of the voltage and current. The impedance, Z, represents the combined opposition of all the reactances (of capacitors and inductors) and/or resistances in the circuit. See PHASE and RLC experiments for further reading on impedance in an AC circuit. Only DC circuits will be considered here. For a conductor with a uniform cross section A and of length l, the resistance is given as R = ρ l A where the quantity ρ is a constant called the resistivity and is a measure of how difficult it is for current to flow in the material. The value for the resistivity is a characteristic of the material and is always positive. What are the units for resistivity? The resistance of a material is based on the number of collisions between the electrons constituting the current and the atoms in the material. As the temperature (energy) is raised, the atoms in the material move around more and increase the frequency of these collisions thereby impeding the progress of the current carriers. Consequently the resistance (and resistivity) of a simple material increases with increasing temperature and vice versa. Why is the resistance of a material directly proportional to its length? Why is the resistance of a material inversely proportional to its cross sectional area? Experimental Tasks: 1. Waveform Measurements Carefully wire up the circuit drawn below and use one of the resistors provided as your unknown resistance. Draw and label clearly the experimental set-up. 102
Connect the Arbitrary Function Generator AFG3021 across the resistors as shown in the diagram. The values can be set using the buttons on the AFG3021. Set the function generator to output the following waveforms: 8 khz Sine wave with amplitude of 5 V pp 1 khz Sine wave with amplitude of 5 V pp 1 khz Sine wave with amplitude of 5 V pp and 2.5 V Offset 1 khz Square wave with amplitude of 5 V pp and 2.5 V Offset 1 khz Triangle wave with amplitude of 5 V pp and 2.5 V Offset DC input with amplitude 5 V pp DC input with amplitude 5 V pp and 2.5 V Offset DC input with amplitude 0 V pp and 2.5 V Offset For each of the output waveform, measure and record using the following devices: oscilloscope (OSC) multimeter (DMM) in both AC and DC mode voltmeter (VM) REMEMBER to check the polarities of your set-up before beginning the experiment. If unsure, please check with the demonstrators first. Before taking any measurements with the OSC, remember to set the Coupling mode to DC and also set the MEASURE menu boxes to : CH2 Freq, CH2 Pk-Pk, CH2 CycRMS, CH2 Mean 103
When using the DMM, please do NOT rotate the dial while the meter is connected to a circuit. Disconnect first before a different measurement is taken as you may chort circuit the probes. Set both the DMM and the VM ranges to the highest before taking any initial measurements. Further readings may be required if the chosen range is not at its most sensitive for that measurement. Signal Type Measurement OSC DMM VM Value Mode Frequency V pp V rms V mean Resistance R 1 Resistance R 2 Record the measurements and the relevant units in a table like the above for each waveform. Indicate also the measurement mode for the DMM. Mark the column X if the value cannot be measured. Note down any unstable reading. Sketch the V output against time curves for each of the waveforms. What is the difference between a DC and an AC waveform? Which of the test equipment(s) used gives the most accurate reading for V mean of an AC signal? Which of the test equipment(s) should be used to measure a DC signal? Explain the method used to measure the value of the resistors. 2. Ohm s law The previous circuit set-up is again used here. Set a 0 V DC waveform as the output from the AFG3021. Vary the DC Offset voltage (V in ) from 0 V to 8 V in steps of about 0.5 V. Record the values for V 1 and I in a table. It is important to ensure that the probe earths for both the channels are connected to 0V of the function generator and all the polarities are connected as shown in the diagram. 104
Record the results in a table. Plot the graphs (by HAND) of V 1 and V in against I for the resistor. Choose a scale that will make full use of the page. What type of curve do you expect to get and why? Can you explain any deviations from the expected curve? Draw straight line of best fit through your data and calculate the values for both R 1 and R 2. Draw straight line of minimum slope that go through at least two out of every three data points. From their slopes calculate the minimum values for R 1 and R 2. Draw straight line of maximum slope that go through at least two out of every three data points. From their slope calculate the maximum values for R 1 and R 2. Hence record your value for R 1 and R 2 with its associated error. How does this value for R 1 and R 2 compare with the values measured previously? Conclusions: Summarize your results and conclusions from this series of experiments. 105