RC Circuits Question: 1. A 3.00 Mo. resistor and a 1.00 ,IF capacitor are connected in series with an ideal battery of V = 4.00 V. At 1.0 seconds after the connection is made what are the rates at which (a) charge on the capacitor is increasing? (0.955 microA) t1 _ ()-&) = •. cE.. "C-\.,"f/O ')<1 (_b/a..c.) L :::<-(if -(. l~ .:L~I, l - 3YfO (-3 1,,)(1 I , ?ltoS') ~~~q.-S5-Y.-/O-1' .4-' (,"--- __J (b) energy is being stored in the capacitor? (1.08 mircoJ) \J l( =" V _ \}c~ - I _ b II --- 4(1 P '-(3.ss"c'D-'t-X(.r3) 11.O~)</O-(oJ] ~ (,) <h,,~1 ~"gy ;,.liP"';'" ;. <h, W'"'"" (274J<1 J) 0 L, c.., V ?r" L, 1(2 '" - t/~c.) e. + I ~ 5) I.l;~ ti ,5SlIO - 1-)[6 x/O"') ::- p:1-4 y: JO- (d) energy is being delivered by the battery? (3.82~ r~V 'L :; ~.55'J/O-1-.xy) J (f~/t/D (0 ( J r S1 35 .' AI' Advanced Physics RC Circuit Problems I.vnglh 0.02 2012 11I~ ~I Paper Su ir #2 A physics slUdent wishes to measure the resistivity of slightly conductive paper that has a thickness of 1.0 x I O-'m. The student cuts a sheet of the conductive paper into strips of width 0.02 m and varying lengths. making five resistors labeled Rita R5. Using an ohmmeter, the student measures the resistance of each strip, as shown ab"",e. The dala are recorded below. Resistor RI R2 R2 R4 R5 Length (m) 0.020 0.040 0.060 0.080 0.100 80.000 180,000 260.000 370.000 440.000 Resistance (a) (n) Use the grid below to plot a linear graph of the data points from which the resistivity of the paper can be determined. labels and sC(lles for both axes. Draw the straight line that best represents the data. ~ \ +--- "--[-'i':- ---- C -..l\~f\-:::.h:::: --::.::-: ~=i:::'-=-i-- -=- _. _L; __ ... ~ __ i_-l_J __ . I' ! ; Include - -- -~-'.'.-..;-i- ;--_.-----:~- _ =-:::.:::." ~ == :::..:= _.,_1=:====.__ .~-~-~ __ - --- I ; , ; -u= _.-i-~~I V ~:T-:-~-(iJ-':~='~~~~~~; ~-I"O OOD':- -- - - -. -T.H- -1-- - --- - - ~ _;__ ~_1 __._ -- -- -;-t--- ~j-= .-~~ ~ ~ ~ j0~ ~ ~ ~ ~~; ~ ===j- ~f~i~l:::: .~=~=Lt 9-o D :.L~-=;= -= I ! I ! J~_j~~.r /' ..-~- -'- -- - - --I--1-_A'-::L -- 100": ; _l-_ 1_. I __ ._ Ii! -.1_1I --1-- • -- - .------- _.- _--i_L. -- ' ..'--1 , 1. ..J_ ~_. 2V - _ J--;- L_ =- -= -= =-~=- == _~ _ =_:= =~=.:-=-~._~ =- = -t=!= 1 ' I-.r~i-_._ .. _._-_.~ .--.-;-.j-------.,.-.-iI ;--- • j : Using the graph. calculate the resistivity /'V\-:. (S::l6-Ic"o) I I '2. - I 3 Xlo . • (.10) (.w) (.0'1) (b) _ _ .~- ... ~:t:\_l,-- - ---~~-+-- ------" ---"."--;-b"";l~------4-:-- -/---f-,:-l---L Y • ._._ of the parer. J- 0:'& ~ f &.2.CJ 'IIDa;)(:),O'lIt5~J ("') ~ ~ (.01 ~I 'l:IO~) ::- Slo~ . A ,I~ t -) -= LC6/o+ {l' fY\ =' f AP Advanced PhlSics RC Circnit Problems R5 I./</O,DOO /\.- ° The student uses resistors R4 and R5 to build a circuit using wire, a 1.5 V battery, an uncharged I ~F capacitor, and an open switch. as shown above. (e) Calculate the time constant of the circuit. .L )lDixi> r ~::.~/f«s3fl (d) At time t = 0, the student closes the switch. On the axes below, sketch the magnitude of the voltage ii, across the capacitor and the magnitudes of the voltage~-l and VR5 across each resistor as functio~s oftime t. Clearl)~ laGefeach curve according to the circuit element it represenis:-bn the axes. explicitly label any intercepts. asymptotes, maxima, or minima with values or expressions, as appropriate. t.<;v ° " time (t) .' J: R T E: 2007EJ. S:,\h ~5°i T c = 4000 pF A student sets up the circuit above in the lab. The values of the resistance and capacitance are as shown, but the constant voltage G delivered by the ideal battery is unknown. At time t = 0, the capacitor is uncharged and the student closes the switch. The current as a function of time is measured using a computer system, and the follo\\ing graph is obtained. _? .' .) - - -- -,.- -- -'--r - - -- -1'-- - - -"-1-I .~ Z.O .•..~. 1.5 1.0 "~ (l.S U +. j I I I 1_ •. _. I J I I I I I I I I I I I I I 1 I I I I I I f I I I .: - - ---...,. - - - ---f- - - - -• I I - ---I 1 '"__.L. __ . I 1 • < " -=E ! . _.l. I ! t-- - - - ----1-- - - --1 _.---.i ------:------+---- - ~----I. I +. • J • j ~ c- ::[SSD)( 4tifJ '1-/01.) -:: ;( ,'d-s -~ I I -----t_-~--~ ••~-.L:-----t-----~------1 1---1 •••• _, , I o , ! •••••• 4 2 10 6 'lime IS) (a) Using the data above, calculate t7:-battery voltage G. t><1o R :l? ~ ~SM frJl~50):o~ (b) Calculate the voltage across the capacitor at time t = 4.0 s. \/::\1,,0.>1 (l_it{l2C.j :: V \ ::=\.~J,_()_'-I__ ) ~ L;;;J4 (1_.i~/z;J .. (c) Calculate the cha?,e on the capacit~\' at t = 4.0 s. Q::C\l -:.\,:!ODONO-~ II \ ]l1.0'-\\ =[O.oott C_ (d) On the axes below, sketch a graph of the charge on the capacitor as a function of time. ,605 '- 10 'lilll~(~) (e) Calculate the power being dissipated as heat in the resistor at t = 4.0 s. . i P -:: r; l- f.... (\.. ~ ~ -5' - - L{~~2.lSEo) =- '6 ,~).IO tY (I) The capacitor is now discharged, its dielectric of constant K = 1 is replaced by a dielectric of constant K = 3, and the procedure is repeated. Is the amounJ_of charge on one plate of the capacitor at t = 4.0 s now greater than. less than, or the same as before? Justify your answer.- vi Grealer than . L -. Less thanT .he same ~ ,,--I' et;J:;;J:!:u Q~G-I.J Vs.U"~ $0 1't... ~ l'Q ww.. L4# 60 b!1 l?o.W I SJ -.......: 11 E-=- ) C L ..-' ___ r R1 ~ S2 R2 2006E2. The circuit above contains a capacitor of capacitance C, a power supply of emf E , two resistors of resistances R, and R,. and two switches. 5, and 5,. Initially, the capacitor is uncharged and both switches are open. Switch 5, then gets closed at time t ~ O. a. b. ~ a differential equation that can be solved to obtain the charge on the capacitor as a function of time t. E-U<,- %:~O L:: d~= £ - CfJ R (Jt G --.1- Clf>- C£) IZL Solve the differential equation in art a. to detennine the charge on the capacitor as a function of time t. (1u i{') \n (O-U: - D JAo Cb-Ct, )\% -:0 - o 5- ~ (2.c.. %-cs:i -c.~ b \umerical values for the components are given as follows: In j .:~~ :::-tiL ,j. -tk.c. t IlC 1;- Go:; 0 Cf.-C£.tJ tt-= Q£C'-e, E~12V tJ - /4, C= 0.060 F R, ~R,~4700n c. 1.\ \-,1.. Determine the time at wh~h thetapacitor has a voltage 4.0 V across it. Vc..~VlJqlf(f--i /rl") ~'" I '2. 1- e.:t-/ it "/IY 20'Z. . 5\ After switch 51has been closed for a long time, switch 5, gets closed at a new time t '" O. d. On the axes b~low, sketch graphs ofth~ current 11in R1 versus time and of the c;rrent J.:. in R2 versus time, beginning when switch 5, is closed at new time t ~ O. Clearly label which gniph is I, and which is I, . Current TlIIle ) R2 S R, 20V= :-l I ~ 12 / 8 / ~ ~ E 6 'w~ 4 ""- U I ....-- ~10 .'! 20~F 15 Jill I I 14 / I 1/ 2 0 o 5 15 10 Time (5) 2004E2. In the circuit shown above left. the switch S is initially in the open position and the capacitor C is initially uncharged. A voltage probe and a computer (not shown) are used to measure the potential difference across the ~apacitor as a function-of...time.after the switch is closed. The graph produced by the computer is shown above right. The battery has an emf 0.QQ..Y and negligible internal resistance. Resistor .Kt.has a resistance of Jil91 and the capacitor C has a capacitance of~F. a. Determine the voltage across resistor R2 immediately after the switch is closed. 'dfJ V '0 Ie I Cap ~ tJiJJ ukfe (JJJ b. Determine the voltage across resistor R2 a l?ng time after the switch is closed. 20 '6Y -{L-;; c. Calculate the value of the resistor R,. '6 V -= ~ 12'L q;/'?,'f./Ti<{ .;; ~2- "'" d. Calculate the energy stored in the capacitor a long time after the switch is closed. , lh= \( c V 'I... -::.. ~I e. 20 y< F( J 0, 601Y'/ 12-)1.: On the axes below, graph the current rn R, as a function of time from 0 to 15 s. Label the vertical axis with appropriate values. 'J. "'--'-_ L __ J. __ _ 20 T" '-1'-' J. __ J__ ,,'-'-'T"" -1'-' _ _ -1 L. __ L __ l.__ I~ __ • 1 __ •1 __ ~I I 1 ~1 1 1 __ ~ 1 __ + 1 ~ I 1 I ',' -,_. r '-1'-' __ J __ J 1 L __ I' 1~ __ 4__ ~ __ ~1 I •• I 1 -- --r--T--'-- --,---r--r--T-- --~--,--"'T---~-- --r- IO,XO ••• _J 1.--t--,---~---t--r--+---1--1--~---r-.L.._I._. _•. _1_ . .L.._1._ .. ..J.._I_ .•.. __I._. 1 I 1 1 I I 1 1 1 I 1 I 1 1 I 1 1 I 1 I I --r--~--T -,-- --"'T---r--~--T----'--~--"'T---r-1 --r--r--T--' __ L.__ L __ J. __ - ---l---r--r--r-J__ _~ ~ __ ~ __ L --'--'---I---r-J __ ~ L __L.__ --r--~--+--~-----r--~--T--__~--~--~--r--,'_'-'T"'-l'-',-. --1'-' ','-l-'r-'-I--' Current I I I 1 I 1 I I 1 1 __ L __ l. __ J. __ in{~~\ J 1 ~ I 1 1 1 I I 1 1 1 1 I I __J __ J __~ __L. __ L __ ~__ 1 1 1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • I 1 1 I I 1 1 I I • 1 1 I -~--+--+--~----~---~--~--~----~---r--r--T--'-- --,---r--~--T-- --,--~---r--r--.•.-f-- _._ - t- -.•.. +--,----:---:--r-- t-- --1-~---:---:_-_1._. . ...•._1_ ..•... _1._. ...J.. _1_ .•.. _1._. --r--r--T--'-- --"'T---r--~--T-- --,--~---r--r-- -__-}---tt-- --4---1-- -:---r-L __ L __-4--4 ~ __ -- - --:---tL.__-~-~ __ L r __~--+--+--~--__~---~--~ __ --~--~--~---r-J 1 I • 1 1 1 1 1 o ~ J __ ~__ ~ 1 1 1 1 1 1 T-1 1 1 I' ~ __ I 1 1 1 15 10 5 Time (s) Resistor R2 is removed and replaced \vith another resistor of lesser resistance. Switch S remains closed for a long time. (f) Indicate below whether the energy stored in the capacit~eater than, less than, or the same as it was with resistor R1 in the circuit; "'y"'Greater -I than __ Less than __ The same as An. v~ 1\.1 \') I .." ~ v-ou IJ (MV{W:Ji ~ Explain your reasoning. ~ IS ~D.-:C'J1 ~1J.i \~, A vc,'\ 2003E2. In the laboratory, you connect a resistor and a capacitor ,,;th unkno"n values in series with a battery of emfE ~ 12 V . You include a switch in the circuit. \\'hen the switch is closed at time t = 0, the circuit is completed, and you measure the current tTiroli'gh the resistor as a function of time as plotted beloVo'. i(A) 0.010 t (5) 8 4 16 12 A data-fitting program finds that the current decays according to the equation i(l) = E: e -1/4 R a. Using common symbols for the battery, the resistor, the capacitor, and the switch, draw the circuit that you constructed. Show the circuit before the s\\"itch is closed and include whatever other devices need to measure the current through the resistor to obtain the above plot. label each component in your diagram. \ . you CO e:. b. Having obtained the curve shown above, determine the value of the resistor that you placed in this circuit. -8. 12- (( c. I 2..00 J\- ,01 What capacitance did you insert in the circuit to give the result above? Vc(V) Switch at A Charging y::;:.,e. c. Switch at B Discharging I ---------------------~---------------------~ \2.00 G I t (,) 4 8 J2 16 20 24 28 32 You are now asked to reconnect the circuit with a new switch in such a way as to charge and discharge the capacitor. When the switch in the circuit is in position A, the capacitor is charging; and when the switch is in position B. the capacitor is discharging, as represented by the graph below of voltage V c across the capacitor as a function of time. d. Draw a schematic diagram of the RC circuit that you constructed that would produce the graph above. Clearly indicate switch positions A and B on your circuit diagram and include whatever other devices you need to measure the voltage across the capacitor to obtain the above plot. Label each component in your diagram. .. vI" o 1 T R~::;'ill c 1 Q L <: 10 /y ~~~ 2002E2. Your engineering firm has built the RC circuit shown abov~e currentis measmedu:r'the time t after the switch is closed at t ~ 0 and the best-fit curve is represented by the equation I(t) ~ 5.20 .-"10, where I is in milliamperes and t is in seconds. ·D.~;"'."~:C;'''~:~.~(';;;;:;5)"e V l (PO b. Determine the value of the capacitance C predicted by the equation. c. The charging voltage is measured in the laboratory and .fu!!.l!d.Jobe greater than predicted in part a. i. Give one possible expl~nation for this finding. _L.. ' • ~ _' k ii. Op.e..",ed-t''Jed a-v. ~. (h,a..O 0- .J\.LA-.L~1>\ l,.l) ,{ -&? '9(~(( \/l 10 ~ (f'-I¥f' _ ~ V\A . ~~ • U(e.u-d Explain the implications that your answer to part i has for the predicted value of the capacitance. -~ c..0J'7IU_dO~ \..0Z)\"J d ~ ~ d. Your laboratory supervisor tells you that the charging time must be decreased. You may add resistors or capacitors to the original components and reconnect the RC circuit. In parts i and ii below, show how to reconnect the circuit, using either an additional resistor or a capacitor to decrease the charging time. i. Indicate how a resistor may be added to gecrease the charging time. Add the necessary resistor and connections to the following diagram. •• II. Instead of a resistor, use a capacitor. Indicate how the capacitor may be added to decrease the charging time. Add the necessary capacitor and connections to the following diagram. l' WV ~ \__ - __ 3 '\1 ~ > ~ " ~ ~ ~ " /~ ij "5 I 8 I 1 ! I" '\. 6 1 1 1 1 1"'- I I" 4 I I ! 2 0.. o I I 1 , \. 1 "- I - •..••• 1 o 20 40 60 1 1 80 •.•.• 100 ••••• 1 1 120 140 160 180 200 Time (min) 2001E2. You have been hired to detennine the internal resistance of8.0 "F capacitors for an electronic component manufacturer. (Ideal capacitors have an infinite internal resistance - that IS, the matenaroetween their plates is a perfect insulator. In practice, however, the material has a very small, but nonzero. conductivity.) You cannot simply connect the capacitors to an ohmmeter, because their resistance is too large for an ohmmeter to measure. Therefore you charge the capacitor to a potential difference of 10 V with a battery, disconnect it from the battery and measure the potential difference across the capacitor every 20,mmutes with an ideal voltmeter, obtaining the graph shown above. - -- ~a:--I5efennine the internal resistance of the capacitor. {} r I, l- VJ oJ ~i%Vo :: 1-0 ()\Ir- ~.1, 1"" l..Q /..f\ '>c'(vu 1f/ 1lLIl 'YJ0 .s ----- . 'f, ) ~ 'f./O-11J rhe capacitor can be approximated as a parallel-plate capacitor separated by a 0.10 mm thick dielectric with K ~ 5.6. b. Determine the approximate surface area of one of the capacitor "plates." "" (?c'o)(~.gSYlo-ll) 4 .1 x/0-3 d. Determine the magnitude of the charge leaving the positive plate of the capacitor in the first 1;-C£ LI_e--t1u.. ) (f)xIi);Il)( {- ~~) _ - Q _ _)". ~X ID "- ( I - e.. ~ \,I.i~\ C. (,/11S) ) J GOmin. • AP Advanced Physics Circuits ~<t Cir.l;1'il? ~ Name: _ 1. When lighted. a 100-watt light bulb operating on a 110-volt household circuit has a resistance closest to A. 10" 0 B. 10.10 f C. 10 D. 100 E. 1000 2. The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which has the greatest resistance? ( BI f--1-J (AI A (Al IC)!-1-j f------ 21-----1 \..1) (Al 10) II 7. Two resistors of the same length, both made of the same material, are connected in a series to a battery as shown above. Resistor II has a greater cross. sectional area than resistor I. Which of the following quantities has the same value for each resistor? A. Potential difference between the two ends B. Electric field strength within the resistor C. Resistance D. Current per unit area E. Current f--- 21----j H {~1 GA) lA B X IA 10 V -: 10 v 10 y 8. The batteries in each of the circuits shown above are identical and the wires have negligible resistance. 3. In which circuit is the current furnished by the battery the greatest? (A) (B) (C) (D) (E) 4. In which circuit is the equivalent resistance connected to the battery the greatest? (A) (B) (C) (D) (E) 5. Which circuit dissipates the least power? (A) . (B) (C) (D) (E) In the circuit shown above, the emfs of the batteries are given, as well as the currents in the outside branches and the resistance in the middle branch. What is the magnitude of the potential difference between X and Y? A. 4 V B. 8 V C. 10 V D. 12 V E. 16 V R 2A fA 40 60 R 6. 9. ,~ 24 v In the circuit shown above, what is the resistance R ? A. 30 B. 40 C. 60 D. 120 E. 180 In the circuit shown above, the capacitor C is first charged by throwing switch S to the left, then discharged by throwing S to the right. The time constant for discharge could be increased by which of the following? A. Placing another capacitor in parallel with C B. Placing another capacitor in series with C C. Placing another resistor in parallel with the resistor R D. Increasing battery emf E E. Decreasing battery emf E 2010 AP Advanced Physics Circuits Test Questions 10- 12 refer to the circuit shown below. Assume the capacitor C is initially uncharged. The following graphs may represent different quantities related to the circuit as functions of time t after the switch S is closed 10. Which graph best represents the voltage versus time across the resistor R ? (A) (B) (C) (D) (E) 11. Which graph best represents the current versus time in the circuit? (A) (B) (C) (D) (E) 12. Which graph best represents the voltage across the capacitor versus time? (A) (B) (C) (D) (E) \ Name: _ Av0lA.,~ ~ KL Uy~ P(O~)e-n'\O .?bl1-tf.2 u..)S\F"Y?~ o!' Q l)<IO')J) v ~ L-LW\\ C, 'Y~;},o\s :lCDlof:l --- Q)\. ;:).'-1 vb") ).0'-1 V d) ~ q,o fL''', (j:; 2-) (2C- r:, t, , v'~'i~ iIi's- C) D. 0 ali 2- (. 'PI G'V~ a.') J.~ ~ _ {(1- z c) J1 Lf+P) d)\~'J\~.VC. ~ c:tD'1 b' 1::;) '\ .• J) IL b}~o.tc (I-e . -s .eo) 7-.J..? 'IIi) --%G) \'1/ c)t-;./N.35

© Copyright 2018