RC Circuits In this lab you will be working with a variety of voltage sources each driving an RC circuit.

Transcription

1 RC Circuis In his lab you will be working wih a variey of volage sources each driving an RC circui. RC Circuis Exponenial decay by discharge In his aciviy you will use he following circui o quickly charge and hen slowly discharge he capacior hrough he resisor. You will measure he volage across he capacior a fixed ime inervals as i discharges. b C R Single pole double hrow swich (SPDT) Circui #1 b =6, C=0.47F, and R=R1=100Ω. When he swich is hrown o he up posiion, he baery is aached o he capacior. The capacior charges unil he volage across i equals ha of he source (his happens nearly insananeous). When he swich is hrown o he down posiion he baery is disconneced and he resisor is conneced across he capacior. This gives a pah for he capacior o discharge. Since he rae a which he charge leaves he capacior is proporional o he amoun of charge on he capacior, his discharge is exponenial. As discussed in class and chaper 28, he ime consan for he decay is τ=rc. Firs observaions of he phenomenon: Firs charge and discharge he capacior while waching he volage across he capacior, c wih one of he mulimeers you used las week. To do his assemble he circui and connec a mulimeer across he capacior. Flip he swich o he power supply and observe he charging of he capacior. Now ha he capacior is charged, flip he swich o he resisor and wach c decay. Recording your daa: You may record your daa ( c every 5s unil he capacior has compleely discharged) by hand from he mulimeer, or if you find his edious, you may use your compuer o record he informaion using he Daa Sudio sofware. To use he compuer o record your daa: a. Turn on he inerface box. b. Connec he leads of he volage probe across he capacior. (Leave he mulimeer aached, oo.) c. Sar Daa Sudio. (I is on he deskop) d. Selec Creae Experimen. e. The volage probe is plugged ino he inerface box bu you mus ell he compuer ha his is so. Click on por A and selec olage probe. f. To creae a graph of your daa drag a graph from he Displays window up o he volage probe in he Daa window.

2 Page 2 of 7 g. Click on START and observe he volage reading in he digial display on he screen as you flip he swich firs o he power supply and hen o he resisor and a graph of he volage as a funcion of ime. STOP aking daa when he capacior is discharged. The values on he screen should be abou he same as hose shown on he mulimeer. h. Repea if necessary. Analyzing your daa: If you have no already done so graph your daa. a. Fi he daa o a Naural Exponenial Fi. The fi equaion is y=a*exp( x*c)+b where A, B, and C are fi parameers. Noe ha he fi parameer C is no capaciance. b. No all of your daa corresponds o exponenial decay. You will need o selec only he daa ha corresponds o he ime during which he volage is decaying exponenially. Do his by high lighing he relevan daa. c. Wrie he fi equaion below in erms of your physical variables, and : d. How do you inerpre he fi parameers A and C physically? Use he resuls of your fi o deermine he ime consan τ. e. Graphing your daa so ha i looks like a sraigh line is useful. We expec ha he daa should be an exponenial curve, bu as a final check graph he naural log of your daa. To do his click he Calculae buon near he sar buon. In he definiion box ener y=ln(x) and define he x variable as Daa Measuremen. Graph he resuls of his calculaion and fi i wih a sraigh line (over he same period of ime as in he las fi). How do you inerpre he slope and wha is he value you find? f. Prin boh of your graphs.

3 Page 3 of 7 RC Circuis volage during charging In circui #1 he capacior charged quickly because of he very low resisance of he wires, baery, and capacior iself. We analyzed in class he charging of a capacior in series wih a resisor. Rearrange your circui elemens o make circui #2, a circui wih a single loop ha conains he capacior, resisor, baery and swich (you will only use one of he hrows). Predicion: Based on he resuls we found in class, wha equaion do you expec o describe he volage across he capacior as a funcion of ime, c (), as i is charging? Wha is he value you expec heoreically for he ime consan given he nominal values of he capacior and resisor? Recording your daa: Using he same mehod as above, record he value of c every 5s (or more frequenly if your daa collecion is auomaed). Analyzing your daa: Graph c vs ime. Fi he daa using an Inverse Exponen Fi. Double click on he window wih he fi parameer values o see heir role in he fi he equaion. Use he resuls of your fi o deermine he ime consan based on your charging experimen. Commen on he level of similariy beween he values of he ime consan based on he discharge experimen, charging experimen, and heoreical predicions Prin your graph.

4 Page 4 of 7 RC Circuis sinusoidal volage source In addiion o soring energy from a seady power source (DC) hey can be used in a circui powered by an alernaing curren power source (AC). To creae and observe such a circui you will need o use a funcion generaor (a conrollable AC power source) o power your circui and an oscilloscope o measure i. You will need o spend some ime geing accusom o hese pieces of equipmen before you can use hem in he circui we are ineresed in. MEASUREMENTS OF ARYING OLTAGES INTERLUDE Measuremens of varying volages are commonly done wih an oscilloscope. The oscilloscope displays a plo (graph) of volage versus imes. This is done by deflecing a sream of elecrons (which has been acceleraed from he back of he insrumen o he fron) boh horizonally and verically before i srikes a fluorescen screen. The amoun of verical deflecion is deermined by he volage under sudy; he horizonal deflecion is proporional o he ime elapsed since he sweep began. The oscilloscope always responds o volage, bu hese volages are ofen characerisic of oher phenomena. For example, a microphone changes he variaions in air pressure associaed wih he sound o changes in volage ha can hen be observed wih he oscilloscope. The oscilloscopes you will use in his lab all have common feaures. Each is a riggered dualrace D.C. coupled scope. Dual race means ha wo races, or beams, can be viewed simulaneously. Each inpu volage goes ino is own amplifier and is displayed on he screen independenly of he oher. Triggered means ha he elecrons sweeping across he screen begin heir journey from he lef side only when "old o" or "riggered." There are several ways o rigger he beam. For many, bu no all, of our uses, he beam will be riggered by he inpu volage. If he riggering adjusmen is no se correcly, he paern will drif across he screen and will no be "locked in." (You will probably find his adjusmen a bi of a mysery. Don' worry ask your insrucor if adjusmens are needed.) D.C. coupled means ha any inpu volage, including a consan volage, causes a deflecion. (In A.C. coupling, only variaions cause a deflecion; he average of he display is zero). Abou he only hing you can do o hur a scope is o leave a brigh do a one place on he screen for a long ime. Also, avoid puing a sharp pencil or pen on he screen as his scraches he surface. 1. Spend some ime sudying he fron panel of he scope. There is a myriad of swiches and knobs. Locae he following imporan ones: a) On Off (or A.C. on) b) Inensiy or brighness c) Focus d) erical Gain, in vols/div (one for each channel) e) Horizonal Sweep rae, in ime/div f) D.C. A.C. inpu swich Be sure you undersand he marking on he verical and horizonal conrols. Each mus be se o he CAL posiion before he marked values will be accurae. 2. Turn on he scope. Afer a minue or so, you should have a focused line cenered on he screen. Turn he sweep rae o is slowes value. Wach he do move across he screen. Now sep bysep, increase he speed of he elecron beam's ravel across he screen. The spo will develop a come like ail which finally seems o urn ino a coninuous line. Remember ha his line is an illusion caused by he persisen glowing of he phosphor afer being hi by he elecrons. There is sill a do of elecrons moving across, now very rapidly. Coninue o increase he sweep rae.

5 Page 5 of 7 The line will ge very dim a he highes raes because he ime spen a any place on he screen decreases. 3. Se he verical gain o.5/div and he inpu o D.C. Read he volage of a 1.5 vol baery on he oscilloscope. Try i wih he opposie polariy of he baery by reversing he leads. Wha would happen if he gain were changed o 1/Div? Try i and find ou if wha you expec indeed happens. Now se he INPUT o AC and ry o measure he baery. Wha happens? 4. A funcion generaor (AKA signal generaor) produces a volage which varies wih ime. The ype of variaion is characerized by a plo of he volage versus imes. The plo may look like a sine wave a square wave a riangular wave or some oher form. The frequency of he signal is he repeiion rae of he regular paern (frequency is he inverse of he period, which is he ime beween adjacen peaks). The ampliude of he signal is he maximum volage of he signal (half he peak o peak value). (See he figure below). period ampliude peak o peak a) Turn on he signal generaor. Make sure i is se for sine oupu. Se he scope inpu o

6 Page 6 of 7 A.C. Connec he oscilloscope cable o he oupu of he generaor. You may have o vary he sweep speed (horizonal on he scope) o spread he paern enough o make a frequency measuremen and you may need o vary he verical gain on he scope o make i fi nicely verically on he screen. If you have rouble geing a sable paern, see your insrucor. As you are making hese changes in gain and sweep speed, he paern will change; are he characerisics of he inpu signal changing? Based on your measuremens wih he scope, wha are he period, frequency, ampliude and p p volage of he signal you have? b) Now connec a small speaker o he oupu of he signal generaor and leave he scope also conneced o he oupu. Now he same signal ha he oscilloscope looks a is driving he speaker, convering i o sound waves of he same frequency. Do you hear he one? c) Find he conrols on he signal generaor which would change he frequency of he signal. You should be able o observe on he oscilloscope when you have found he righ conrol. Now find he conrol on he signal generaor which would vary he ampliude of he signal. Again, you should be able o observe on he scope when you have he righ conrol. Adjus hese unil you can hear a one; large enough ampliude (loud enough) and a frequency you are sensiive o. Change he signal frequency and noice he effec i has on he display and he pich of he one. Make sure you undersand how he display changes as you go from low o high frequency and vice versa. In going over he range of audible frequencies, you may have o change he sweep rae of he oscilloscope. When you do, make sure you undersand ha he display looks differen because of a scale change and no necessarily a change in frequency of he signal. Find he highes and lowes frequencies you can hear. d) Now ry o use your speaker as a microphone. In (b) and (c) you supplied a varying volage o he speaker and ha caused he speaker o vibrae. Suppose you cause he speaker o vibrae (by apping i or "hiing" i wih sound waves). Would i oupu a volage? Disconnec he speaker from he signal generaor so ha only he speaker is now conneced o he inpu of he oscilloscope. See if you can deec any volage oupu from he speaker as you ap i or alk ino i. (You may need o increase he sensiive by changing he verical gain of he scope.) You can now make circui #3 by placing he 220nF capacior in series wih he 100Ω resisor and he signal generaor. Recording your daa: Use he oscilloscope o measure he ampliude of he volage across he capacior as a funcion of frequency. Make your measuremens a 10Hz, 30Hz, 100Hz, 300Hz, 1kHz, 3kHz, 10kHz, 30kHz, 100kHz, and 300kHz. Use he oscilloscope o measure he ampliude of he volage across he resisor as a funcion of frequency. Make your measuremens a 10Hz, 30Hz, 100Hz, 300Hz, 1kHz, 3kHz, 10kHz, 30kHz, 100kHz, and 300kHz. Noe: he capacior and resisor measuremen canno be made a he same ime because of he common ground on he oscilloscope and he funcion generaor (he black connecors from boh machines mus be aached o he circui in he same spo).

7 Page 7 of 7 Analyzing your daa: Graph C and R vs ime on he same graph. Prin ou your graph. To see how his circui is useful you could replace he power supply wih a music source and hook your speaker up across he resisor and hen across he capacior and noe he difference in sound qualiy. Advanced: for hose wih he ime, abiliy, and ineres. The funcion generaor is creaing a volage ha obeys S = So Cos(ω ). And he volage across he resisor you have seen has he same funcional form R = Ro Cos(ω ) Which according o Ohm s law ells us ha he curren flowing hrough he resisor is given by i R = R /R=( Ro /R) Cos(ω ). Bu he curren flowing hrough he resisor is he same curren flowing hrough he funcion generaor, is he same curren flowing hrough he capacior. Use his informaion o find a heoreical expression for he volage across he capacior and hence explain he behavior found in he graph above.