ELECTRICAL MEASUREMENTS

Transcription

1 Physics Department Electricity and Magnetism Labratry ELECTRICAL MEASUREMENTS 1. Aim. Learn t use measuring instruments: Digital multimeter. Analg scillscpe. Assembly f simple elementary circuit. Cllectin and interpretatin f LISSAJOUS patterns.. Overview. Many cmmn electrical measurement instruments are based n electrical current. This first lab exercise seeks t give yu sme understanding f these instruments and t demnstrate their crrect use. Generally, in an electric circuit we can get tw electric measurements: current measurements (I) and vltage measurement (V). T measure V with a multimeter: Cnnect the vltmeter in parallel with the element, i.e. the black-test lead is cnnected t the negative terminal f the element being measured, and the red-test lead is cnnected t the psitive terminal f the element, as shwn in the figure. V I (current) can be measured by cnnecting a multi-meter in series with the element. Multi-meter can be damaged by wrng measurement cnnectin. Measuring a large current while the DMM is prepared t measure a small ne will certainly harm the DMM. Fr example, measuring a 1 ampere current while the DMM is n the milliamp scale will definitely blw a fuse! A.1 Resistr clr cde guide. A resistr is a circuit element manufactured t have a cnstant resistance. The resistance f a resistr can be determined by the clr bands (see the chart belw) printed n the resistr accrding t the fllwing rule: 1

2 R = (first clr number)(secnd clr number) x 10 (third clr number) Ω The furth clr band tells yu the tlerance f the resistr: gld means ±5% tlerance, silver means ±10% tlerance and n furth band means ±0%. High-precisin resistrs have five bands. The first three bands indicate the first three significant figures f the resistance; the furth band indicates the number f zers; the fifth band is the percent tlerance. Digit (X, Y, Z) Clr 0 Black 5 Green 1 Brwn 6 Blue Red 7 Vilet 3 Orange 8 Grey 4 Yellw 9 White tlerance multiplicatr (Z) nd digit (Y) 1 st digit (X) Resistr Value: Clr Cde: R = XY x 10 Z Ω - First band crrespnd t first digit X. - Secnd band crrespnd t secnd digit Y. - Third band crrespnd t the (expnent) Z. - Furth band indicates the precisin: 5% gld and 10 % silver. Example: One resistr with red-green-red-gld cde has a value f, R=5 x 10 Ω=500Ω=.5 kω, 5% f precisin, it is, 500 x 0.05 = 15. The result is, R ± R =.50 ± 0.13 kω.. Multimeter. Multimeter is an electrnic measuring instrument that cmbines several measurement functins in ne unit. A typical multimeter may include features such as the ability t measure. Current and vltage at statinary regime, DC= direct current, AC alternating current. Resistrs Capacitrs Electric Cntinuity Hybrid parameters f transistrs..1 Hw t measure with a digital multimeter (DMM). Measuring Vltage: 1. Set the DMM selectin dial t read DC vlts (V). Insert ne wire int the scket labeled 'V' and a secnd wire int the scket labeled 'COM'.. Set the selectin dial f the DMM t the highest vltage measurement setting. Cnnect the tw wires frm the DMM t the tw pints between which yu want t measure the vltage, as shwn belw. T measure vltage, the DMM must be placed in the circuit s that the ptential difference acrss the circuit element yu want t measure is the same as the ne acrss the DMM.

3 3. If n number appears, try a different measurement scale. Start at the highest vltage scale and wrk yur way dwn the scales until yu get a satisfactry reading. Measuring Current: 1. Set the selectin dial f the DMM t the highest current measurement setting (10 r 0 amps). Insert ne wire int the scket labeled '10A' and a secnd wire int the scket labeled 'COM'.. Attach the DMM int the circuit as shwn belw: T measure current, the DMM must be placed in the circuit s that all the current yu want t measure ges thrugh the DMM. 3. If n number appears while the DMM is at the 10A (r 0A) setting, mve the wire frm the 10A scket t the 00mA scket and then turn the selectin dial t the largest setting. If there is still n reading, change the dial t a smaller setting, etc. 4. When yu have taken yur measurement, return the DMM selectin dial t the highest current setting (10 amps) and mve the wire back t the 10A scket..3 Oscillscpe. An scillscpe (shwn in figure ) is used t bserve circuit behavir graphically by displaying wavefrms n a screen. It is a basic tl used in the study f time varying phenmenn f vltage and current in electric circuits, such as measurements f frequency and perid f wavefrms. After cnnecting the scillscpe t the electric pwer supply and switch it n, it is necessary t becme familiar with the frnt panel. Seek the advice f the instructr..3.1 General cmments. Generally, all scillscpes have three basic sectrs, Vertical, Hrizntal and Trigger (time), f BNC cnnectrs, which cnnect the measurement prbes, and the input channels, typically labeled as I and II (r A and B). The existence f tw channels allws us t make the cmparisn between signals in a mre simple way. Recmmended steps in the basic setting f the analg scillscpe: 3

4 Cnnect the signal t be measured at the scillscpe channel I (this will be set as the trigger channel I). Adjusting t a psitin r scale intermediate vlts / divisin f the channel I (fr example 1V/div). Place in calibrated psitin r cntrl variable vlts / divisin (central pt, maximum pssible t the right). Discnnect any hrizntal and vertical multipliers. Put the shting mde (trigger) t autmatic. Lwer the cntrl f intensity t the minimum necessary t see the signal n the screen, and fcus fr a display as crisp as pssible Measuring and Estimating Prcess Perfrmance - Measure frequency and amplitude f a peridic signal. A peridic sinusidal vltage signal, will appear in the scillscpe screen similar t the next figure. The vltage can be described by the fllwing equatin: V(t) = V0sen ωt Where V 0 is the amplitude f the signal and ω is its frequency. V 0 V 0 V(t) V PP T -V 0 0 π/ π 3π/ π t (s) V PP is the peak t peak vltage: π T =. ω Where: V π ω = πf =, T and f is the frequency f the signal. V = PP 0, and T is the signal perid. 4

5 - Study f infrmatin. vlt div ms div 6.5 div 7.3 div - Measure vltage. Figure. Analgical scillscpe where [ V ± V ] V =14.6 ± 0. V PP PP vlt div V PP = = 0. V div vlt V PP = 7.3( div) = 14.6 V, div ( 5) And a div crrespnds t a picture, which is divided int five parts in bth the vertical and the hrizntal axis respectively. /5 =0.4 vlt vlt Measure the perid Where: T = 6.5( div) = 13 ms, 3 [ T ± T] s = ( 13.0 ± 0.) ms = ( 13.0 ± 0.) 10 s ms div ms div T = = 0.ms div ( 5) V PP and T are the precisin uncertainties f the scillscpe n the vertical and the 5

6 hrizntal axis respectively. This is half f the smallest divisin that is being measured. - Phase shift measurement. Usually, the hrizntal sectin cntrls the time base r sweep f the instrument. The primary cntrl is the Secnds-per-Divisin (Sec/Div) selectr switch. But it is als included a hrizntal input fr pltting dual X-Y axis signals. The hrizntal beam psitin knb is generally lcated in this sectin. Mst mdern scillscpes have several inputs fr vltages, and thus can be used t plt ne varying vltage versus anther. This is especially useful fr graphing I-V curves (current versus vltage characteristics) fr cmpnents such as dides, as well as Lissajus patterns. The perid f a signal crrespnds t a phase f 360 º (π). The phase shift indicates the angle f delay r advancement which has a signal with respect t anther (taken as reference). One methd t measure the phase shift is t use the XY mde. This invlves placing a signal in the vertical channel (usually channel I) and the ther in the hrizntal channel (II) (this methd nly wrks crrectly if bth signals are sinusidal). The resulting wavefrm n the screen is called Lissajus figure in hnr f the French mathematician Jules Antine Lissajus ). Lissajus figures are an example f hw an scillscpe can be used t track phase differences between multiple input signals. This is very frequently used in bradcast engineering t plt the left and right sterephnic channels, t ensure that the stere generatr is calibrated prperly. Histrically, stable Lissajus figures were used t shw that tw sine waves had a relatively simple frequency relatinship, a numerically-small rati. They als indicated phase difference between tw sine waves f the same frequency. 6

7 Tables 1. Lissajus figures.4 Relatinship between the quantities measured with the scillscpe (instantaneus values) and measured with a multimeter (RMS). RMS value (Irms) in a time-varying current, I (t) is the mean square value f this magnitude (rms: rt mean square.) I ef ( I( t) ) i1 = t t dt 1 7

8 In the event that the time dependence is sinusidal is btained a relatinship between Irms and I given by the frm: I I ef = = I PP In the case f a vltage signal with a sinusidal dependence can als write equivalent expressins: V V ef = = V PP 3 Learn mre... TIPLER, PA & MOSCA, G. Physics Vlume. 6 th editin Ed. W.H. Freeman/Wrth Publishers 007 Cap. 5 Pags KEITHELY, Lw Level Measurements, 5ª editin, Sectin (.1-.5). Pags -3 a In internet

9 4. Equipment. 1. Digital multimeter.. Analgical scillscpe. 3. Pwer supply. 4. Transfrmer V battery. 6. Breadbard (Prtbard). 7. Cnnectrs Figura 3. Figure Puest 3. de Experimental trabaj e instrumentación setup 5. Experimental prcedure. 5.1 Use f multimeter as a vltmeter and hmmeter Measure, using the multimeter as a vltmeter, the DC vltage at the terminals f the battery. Cmpare the results indicated by the manufacturer Measure, using the multimeter as an hmmeter, the value f the tw resistrs, R 1 and R. Cmpare these results with the value reprted by the manufacturer using the clr cde. 5. Using the multimeter as an ammeter and vltmeter Assemble, using the breadbard, the circuit shwn belw: 9

10 V A 4.5V Figure 4. Measure current and vltage drp resistance. 5.. Indirect measurement f resistance: measure the vltage drp acrss the resistance R 1 and the current flwing thrugh the circuit. Calculate using Ohm's law, the resistance value R 1 and cmpare with paragraph Indirect measurement f Current: measure the vltage drp acrss the resistr R and the current flwing thrugh the circuit. Knwing the value f R btained in 5.1., calculate the current value using Ohm's law, and cmpare it with that btained frm direct measurement n the ammeter. 10

11 5.3 Using the scillscpe t measure amplitude and perid f time-varying signals. Figure 5. Measure amplitude and perid f a signal V(t) Measure, using the scillscpe, the vltage value n the battery and cmpare this result with that btained in paragraph Using the different transfrmer utputs, measure the amplitude and frequency fr each ne f them. Check that the utput signals f the secndary are described by the equatin V(t) = V0sen ωt (Remember V 0 is calculated frm V PP vltage peak t peak and ω frm T.) Discuss the frequency values btained and give a value fr the frequency f the netwrk. Is it expected? Why? Measure, using the multimeter as a vltmeter, the vltage at AC in at least three f the utputs f the transfrmer. Cmpare RMS vltage with the amplitude value fr these utputs V 0 btained in the previus sectin. 11

12 5.4 Obtain Lissajus patterns Cnnect the frequency pwer supply utput t channel I f the scillscpe and set it t bserve a sinudidal signal n the scillscpe with a frequency f 50 Hz. Cnnect the scillscpe channel II f the transfrmer secndary utputs. Using the XY buttn, bserve the Lissajus figures n the screen (if necessary, fine adjust the generatr frequency arund 50 Hz). Figure 6. Lissajus figure 5.4. Increase the generatr frequency t 100 and 150 Hz and bserve the crrespnding Lissajus patterns cmpared with 1: and 1:3. 1

13 Figure 7. Relatin between frequency 1:1; phase tag = π/ Figure 8. Relatin between frequency 1:; phase tag = π/4 Figure 9. Relatin between frequency 1:4; phase tag = π/ 13