The rate at which the capacitor in a series RC circuit charges or discharges depends on the capacitance C of the capacitor and resistance R in the circuit. We define a time constant, T, as the time taken for the current in the circuit to drop to 37% of its initial value in either the charging or discharging situation boxa nortelmicairs gridelgros To I can also be defined as the time taken for the voltage across the capacitor to increase to 6076 of the battery voltage when the capacitor is being charged or to drop to 37% of its initial maximum value when the capacitor is being discharged. vo ard esvisna If we analyze the dynamics of the discharging process (quantitatively done using the methods of calculus), we find the following results At t = 0, when the switch is closed on node b, o the current in the circuit is maximum and has a value of Io = (c)/ R o the capacitor voltage is at a maximum value of (AVc). = 2/ clairw epivab isshoals ne al lolpages . Att > 0, o the current in the circuit decreases at a rate given by 1 (t) = loe-ton neswied noise o the capacitor voltage decreases at a rate given by AV. (t) = (AVc)oe- naswted , VA ageilov ardi of a As we analyze the behavior of a series RC circuit, we will continue to use the laws we have studied in previous experiments. Recall that for a resistor that obeys Ohm's Law, the voltage across it and the current through it are related bo ofireworks woled sib by AV = IR. For a capacitor, the voltage across it is related to the charge on it by AV = /C. We use Kirchhoff's Laws to explain the behavior of circuits in an the following manner: i Jenuo ers elidwingsM . visited off 10 ageilov and) alsups 10156963 93 220198 mus esaubong fluorias jogos o pripuboval aunt .diss of mixam Suppose we consider the circuit shown above. Kirchhoff's 2nd Law, KVL, tells us that AVswitch + AVA + AVB = AV Batt. Since the switch is open there is no current flowing, therefore the voltage difference across cock butt must be zero. Since the sum of the voltage differences must equal the voltage across the battery, AV switch = AV Batt. Once the switch is closed, AVswitch = 0 so we must have AVA + AVB = AVBatt. If the two bulbs have the same resistance, then AVA = AVB and the voltage difference across each bulb must be half that across the battery. If the two bulbs ramon paristango than the and with the greater resistance will have the greater AV and will be pull brighter. What happens if we add another bulb in parallel to bulb B? We know that the current through the 16 battery will increase and the current through bulb A will increase. Hence the voltage across bulb A will increase. Since the battery voltage stays the same, then the voltage across bulb B must decrease. Bulb B becomes dimmer.IV: Start with the same circuit from Part III above, except add a second bulb in series with bulb A and the capacitor. 1. (2 points) Take a screenshot of your circuit and paste it in the space provided below. You may need to reduce the size of your image to fit this page. we boy isjam lov ano ying al eyed sonia mnemsis iboss nohis Have 19196 bogtarbell PASTE YOUR IMAGE HERE 11/2 xGM beniupstabspijoy hed wespin. SAVA evolveng ent movAVA lot sulov way ban wol amiO s20 aniH .oml anol sets bris ,nago al SA ratings high 1531A emIT anoJ senA vistsibernal 2. (1 point) Predict how the brightness of the two bulbs will compare to each other and to the single bulb from Part III above after switch #1 is closed and keeping switch #2 open. al Th rbsiwe ishis wistsibomami rotiosso sell ons olud on dguould gniesq Ingmun sidi mussaM (ziniog s) 8 erdi bas dlud ends dguovil anizesq ineno andi guessm of smit anel shafts brisknegg el Studiwe bris bezola dlud bag jolipops off rhiw ashee ni aslamme ant tonnes 10158950 19HA smiT good youTA vistelbamm! 3. (1 point) Start with an uncharged capacitor. Charge the capacitor and test your prediction by closing switch #1 and keeping switch #2 open. Describe the result here. non beansfan ns most of of Totiesqa eris not belupa) smil er squabsM :miH . been woy li eaniffee art ni babivong dotswqofearly sau vem uoY .so Sit lative anigga 31 9sa (10a boy 20 701 2p ,priwole al dlud erdt raidwoldied gnlysel start nworda 4. (2 points) Take a screenshot of your circuit and paste it in the space provided below. You may need to reduce the size of your image to fit this page. PASTE YOUR IMAGE HERE noa = $ sonstaleof diva soubar of been yom uoY .woled bobivong soage ordi ni fi siasq bris tivolio woy to forlaneswa s ousT (ainlog s) .[ 4. Disconnect the capacitor and bulb from the circuit. To do this, right click on each of the two nodes on either side of the element and select "Split Junction". i. (1 point) Predict the voltage differences across the lamp and the capacitor when they are disconnected. Bulb: AVA = Capacitor: AVC = (2 points) Measure the voltage differences across the lamp and the capacitor when they are disconnected by placing the voltmeter probes across the element. Explain why these values are reasonable based on your understanding of resistors and capacitors. nolive Bulb: 206 zi # AVA = 15716 visisibemimi 1010695 9 Capacitor: AVc = flovent jaibail (laiog !) S smit snol s ists bos nago al SH 5. (2 points) Describe how you would modify the circuit in Activity 1 Part I to discharge the capacitor, that is, to reduce AVc to zero. Your modified circuit must include a light bulb. You do not need to build the circuit. 79JA smit anoJ =VA SAVAActivity 1: Understanding RC Circuits To answer the questions in this activity, you will have to use the PhET simulation Circuit Construction Kit (AC+DC). The URL for the simulation is https://phet.colorado.edu/en/simulation/legacy/circuit-construction-kit-ac. Click on the picture to download the simulator file. You will be prompted to download Java in order to open it. The Java and Flash simulations will run on most PC, Mac, and Linux systems. More details about this can be found here: https://phet.colorado.edu/en/help-center/running-sims. Several internet browsers, including Google Chrome and Safari, block Flash by default. You may have to install or enable Flash in your browser to make the simulation work. Instructions for doing so for Windows, Mac and Linux can be found here: https://helpx.adobe.com/flash-player.html 1: In this question, you will first predict the behavior of the RC circuit shown 4 alongside, without building any circuits. Suppose we have a bulb, a capacitor, a closed switch and battery that have been connected together for a long time, say several minutes. 1. (1 point) Predict how the brightness of bulb A would compare to an identical circuit without the capacitor. Explain your reasoning. ne wesom bris slidw s to1 bezels dofive sill evesl ,evods tiumla arts qu 192 (23nlog s) , nedamilov ord szu bnis agniise alooT ers ni "islamlov" zyse Jeri xod edxperia , 1919milov erhi sau of a biomilov .zedong >bald bnis ber erdt riofive evitegen at anibsen assilov vos Itsasqathow moy ni quewords fail 2. (1 point) Predict how the voltages across the battery (AVs), bulb (AVA), and capacitor (AVc) compare. Explain your reasoning. analiwe = 2VA :VISHisa only SU .bagtoria al fi Jeri yea ew I noitzsup ni es vested 6 of batubrings allofbosque art nanw (etniog E) .S Invoms sni brit of tionis to ni sonsfiasqes end to sulev end bnis noloubount ends monl constipsuso to noifiniteb .ylisslo enoilslualso woy lis word . rollosgea shi no agusta to Il: Start the simulation. . Make sure to check the "Schematic" and "Show Values" options in the Visual settings on the right. If you wish, you can click on the Advanced settings and check the box to "Hide Electrons" Set up the circuit shown above by dragging components onto the workspace and connecting them together. Right click on the battery element in the simulation and change the value of the battery voltage to AV, = 10.0V. Right click on the bulb in the circuit and make sure the resistance is set to R = 500 I ) & Right click on the capacitor in the circuit and make sure the capacitance is set to C = 0.2F. Also, choose the option to "discharge the capacitor" in the same capacitor menu. Your circuit should look like the figure below. mCircuit Construction Kit (AC+DC) (3.20) Circuit For Orsons Het Save Visual- Quitelike scherast show Values Tools voltmeter 0.20 Fgrade Non-contad Stopwatch Current Chant Voltage Chart Size- Large O Medium 10.00 Volts advanced Hide ca Wire Resis Hide Electr Reset Dynamics Reset All no156960 erdt Juorillw thumil Isalinebi ne of sisqmoo blow A dlud to exsnighd ard) word blbord (Iniog D) 1. (2 points) Set up the circuit above, leave the switch closed for a while and measure the voltages using the voltmeter. To use the voltmeter, check the box that says "Voltmeter" in the Tools settings and use the voltmeter that shows up in your workspace. If any voltage reading is negative, switch the red and black probes. Bulb : AVA = Capacitor: AVc= nislexi sisqmoo (NA) rollosqso bris . (AVA) dlud .(2VA) visited and groups esgolov arti worl spiben9 (iniog 1) . Battery: AVs = .aningesen joy Switch: AV switch = 2. (3 points) When the capacitor is connected to a battery as in question 1, we say that it is charged. Use the definition of capacitance from the Introduction and the value of the capacitance in our circuit to find the amount of charge on the capacitor. Show all your calculations clearly. .notslumle ord nate voy il sigh and no zanijez lsuziV en ni anobigo "asuleV word?" one "olfamedse silobero of 912 976M "2nowbela abiH" of xod erb Aberdo bris agnilise beansvbA and no bib neo Dov deiw 15f/9goj mans gnilsennoo bas essqushow erdt ofno einsnogmos anisasib vo svods nworle fluorio and qu 193 3. (1 point) Does the capacitor have a net charge? Explain. has notslumie ers ni inemala yistied and no bils ingin woled swail ant exil lool bluorde twanis woY .unem 10156963 9m62 er1 ni "oflosgeo endi sgisselb" of nougo6. (3 points) Use the trendline feature in Excel and select the trendline that best fits the data. Display the equation and the R2 value on the graph that you pasted above. Paste your graph in the space below. 7. (3 points) The theoretical time constant for the circuit is given by t = RC. Using the values of R and C in your circuit, calculate the theoretical time constant for your circuit. Show your calculations clearly below. ansem aint NOV 93 8. (3 points) Compare your graph equation with the equation for the discharging current in an RC circuit, given in the Introduction as I(t) = loe . From this comparison, you should be able to extract an experimental value of t for your circuit. Show your calculations below. How do the two values compare? Explain. woled sidel sat ni eish mey thosell bee anActivity 2: Investigating RC Circuits Stopwatch Start Reset 0.00 1. Use the same circuit from Part III. Start with an 10.00 Amps uncharged capacitor. Place an ammeter in series with, .. the bulb and the capacitor. Place a stopwatch in the corner of the screen. Set up the circuit leaving both switches open. Your circuit should look like the figure shown here. Maintain the same values for the capacitance, bulb resistance and battery voltage as before: . Battery voltage AVs = 10.0V Bulb Resistance R = 500 Capacitance C = 0.2F 1. Charge the capacitor by closing switch #1 and keeping switch #2 open. How do you know the capacitor has bee fully charged? 2. Prepare the circuit to take measurements of the current flow during the discharging process: . Make sure that the Play button on the bottom of the workspace is as shown in the figure, . This mea that the circuit is paused and ready to "play" . Press the Start button on the stopwatch. The stopwatch will not run until the "Play" button is pressed. Be prepared to take current readings every 3-5 seconds once you begin. . Open switch #1 and close switch #2. ah popups stillw godsups lugg cy siegthoo frog olds ed bluons boy moshingmoo and more 3.(3 points) Press the "Play" to start the charging owl WOH t (s) ero blunts 1 (A) process, pausing every 3 seconds to take measurements of time and current. You may increase it to 5 seconds between measurements at the end. Record your data in the Table below. 4. Take at least 10 measurements, until the current in the circuit is close to zero. 5. (3 points) Using Microsoft Excel or other spreadsheet software, plot a graph of the current I (y-axis) versus the time t (x-axis). Use the scatter plot option in Excel when plotting your graph. Make sure your graph is properly titled and labeled, with proper Table 1: Current vs time in an RC Circuit SI units.offt bris A diud dinw ashee ni dlud briopos s bbe iqsaxe evode lil n89 mont thumbs amos ods ative here my 3. (2 points) Measure the voltage across the bulb and the capacitor immediately after switch #1 is closed and switch #2 is open, and after a long time. To measure the voltage across the bulb and the capacitor, connect the voltmeter across each element. Since there is only one voltmeter, you will have to repeat the experiment to measure both voltages required. Make sure the capacitor is completely discharged after each observation. Immediately After Bulb: AVA = Capacitor: AVc = Long Time After Bulb: AVA = Capacitor: AVc = 4. (1 point) Predict the current passing through the bulb and the capacitor immediately after switch #1 is closed and switch #2 is open, and after a long time. Hint: Use Ohm's Law and your value for AVA from the previous question to calculate the value of the current. Immediately After Long Time After 1= mont died signiz silt of bnis isto loss of sisqmoo lliw adjud owl ari to azantighd eds work isthere (inlog 1) .S .nego S# daliwe aniqead bris bezolo al LA rative fats avods lil $169 5. (2 points) Measure the current passing through the bulb and the capacitor immediately after switch #1 is closed and switch #2 is open, and after a long time. To measure the current passing through the bulb and the capacitor, connect the ammeter in series with the capacitor and bulb. Immediately After Long Time After 6. (2 points) Remove the ammeter and the voltmeter from the workspace. You can do this by right-clicking them and choosing the "Remove" option. Discharge the capacitor. Determine, as best as you can, how much time is required for the capacitor to go from an uncharged condition to a charged condition by closing switch #1 and keeping switch #2 open. You may use the stopwatch provided in the settings if you need. Hint: Measure the time for which the bulb is glowing, as far as you can see it. Time to Charge the Capacitor:Ill: Click the "Reset All" option at the bottom of the setting menu on the right of your workspace. Set up the circuit shown here, leaving both 4 switches open. Maintain the same values for the capacitance, bulb resistance and battery voltage as before: to fordenom 1 Battery voltage AVs = 10.0V . . Bulb Resistance R = 50 Capacitance C = 0.2F Start with an uncharged capacitor. To make sure the capacitor is discharged, right click on the capacitor and choose the option "Discharge the Capacitor". Change Capacitance Discharge Capacitor Snow Value Remove 1. (2 points) Take a screenshot of your circuit and paste it in the space provided below. You may need to reduce the size of your image to fit this page. PASTE YOUR IMAGE HERE veritis no esbon ow ers to ross no Mails tripit ,aids ob of Junio arti moni died bigholdsge, ers mennoazid A "nobanut silga" Joalee bnis memels gift to obia bolennoszib es ver nerw 101isgeo sidi bris qmal ardesoto esonewellib egsflovent bolbend (Iniog 1) AVA :dlu8 betosninosaib 916 ver nerw 1016q65 ends bris qmel er) 220106 2some19lib sgetlov or1 9quaseM (emlog s) no based eldsnozsen sis zoutay seerit yetw nisigel Insmais sill zoos zedong istemilov end aniasig vo 2. (1 point) Predict the voltage across the bulb and the capacitor immediately after switch #1 is closed and switch #2 is open, and after a long time. Immediately After Bulb : ogno ers sporoaib of 1 7169 4 vlivingA ni dium is ers vlibom blow boy word adinaasa (etiog $) .2 fluo AVA = blind of been Jon ob UoY died in Capacitor: Jaun Vc =13 baitibom 1QY o19s of .VA souber Long Time After Bulb: AVA = Capacitor: AVc =2. (1 point) Predict how the brightness of the two bulbs will compare to each other and to the single bulb from Part Ill above after switch #1 is closed and keeping switch #2 open. 3. (1 point) Start with an uncharged capacitor. Charge the capacitor and test your prediction by closing switch #1 and keeping switch #2 open. Describe the result here. 20105963 edfog153 of amir 4. (2 points) Determine, as best as you can, how much time is required for the capacitor to charge in the case of two bulbs in parallel, as you did in Part III Question 6 for the one-bulb case. How does it compare with the one- bulb case? oris A ding whiw fellers ni died brosse * bos spoke , svads Ill 1369 mont jubilo arse art fulw t sauli son divob add ni edind owt ed vino bluorde stand issol 1019sqes souber of been yam uoY . woled bebivong sarge of ni i sisq bus fluori woy to todaneeds a salsT (einlog Shit4. (3 points) Using your voltmeter, determine the final charge on the capacitor, as you did in Part II, Questions 1 and 2. Show your calculations. How does the final charge on the capacitor in the case of two bulbs in series would compare with the final charge on the capacitor in the one-bulb case? Explain. Remember the final charge is the charge after charging for a long time. 5. (2 points) Determine, as best as you can, how much time is required for the capacitor to charge in the case of two bulbs in series, as you did in Part III Question 6 for the one-bulb case. How does it compare with the one-bulb case? Time to Charge the Capacitor: ensgmoo #1 29ob well , 6265 dlud-eno erit to1 9 nonepub li hai ni hib yoy as.dallenso ni auind ows V: Start with the same circuit from Part III above, except add a second bulb in parallel with bulb A and the diud capacitor. Note: there should only be two bulbs in the circuit, not three. 1. (2 points) Take a screenshot of your circuit and paste it in the space provided below. You may need to reduce the size of your image to fit this page. PASTE YOUR IMAGE HERERemote Lab 6 - RC CIRCUITS is and ni i sonofalem ban jollapans Learning Goals: goldsuzie gnigysdozib to gnigisdo and) Tertia al sulev Isilini all 10 RVE of gob of Jivanjo After completing this simulation experiment, you should be able to . Understand the behavior of a series RC circuit . Test Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) for a series RC circuit . Analyze the dynamic behavior of the current and voltage in a series RC circuit beplodozlb Equipment Needed: orism or anled snob visvitallineup) eessoin ghiprodhalb only to esimanyb add ervisge ewil - Access to a computerto complete online simulations and a printer ( or DDE connor) to print out lab report Introduction & Theory: of to auley s est bris mumixam al diumto sidi ni insinua and A capacitor is an electrical device which consists of two metal objects, usually large, flat plates, separated by an insulator. When equal and opposite electric charges are placed on the plates, an electric field is developed in the region between the plates. Since an electric field is present, the plates are at different electrical potentials. There is an electrical potential difference, or voltage difference, AV, between the plates of a charged capacitor. We define the capacitance, C, of a capacitor as the ratio of the charge, Q, on a plate to the voltage, AV, between Movies, as given below. The capacitance is measured in Farads (F), where 1 Farad is 1 Coulomb per Volt. art peu of su ow dumbs 5/1 eshse s to voivaried erdt esvibra ow a/ Forty 10121291 CE "/ AV A athemhisqxe evolveng al baibule everd ew ews The figure below shows the circuit diagram for a series RC circuit. When an uncharged capacitor is connected in series with a resistor and a battery (switch S connected to node a), equal and opposite charges build up on the plates as charge is transferred along the circuit to each of the plates. This process continues until the voltage across the capacitor equals the voltage of the battery. Meanwhile the current in the circuit, which starts at a maximum, drops to zero. Thus, introducing a capacitor in the circuit produces current and voltage values that change over time. This contrasts with a circuit containing only a battery and resistors, where the current and voltage remain constant over time. sd orl) 220156 egsilov sdi Isups Jeum asoneoftil a so muz gru eonie .or Similarly, a fully charged capacitor connected in series with only a ever Jeum su 02 0 WW resistor R (switch S connected to node b), will discharge as current flows nge lib 95 lov ord bas aVA = AVA R through the resistor. In this case, the voltage across the capacitor starts at its maximum value and drops to zero. As in the charging case, the denio bb6 9 Hianequal IsriW .19/ current starts at a maximum and drops to zero. | sasani lliw A dlud dauout nj bris sessioni lliw yis ismimib somosed 8 dlud .9269noob Jeum & dlud 220106 agrilov andt norit ,sm