Ch 26 - Cpcitnce! Wht s Next! Cpcitnce" One week unit tht hs oth theoeticl n pcticl pplictions! Cuent & Resistnce" Moving chges, finlly!! Diect Cuent Cicuits! Pcticl pplictions of ll the stuff tht we ve een tlking out! "Electicl Btteyf Leyen js, meicn Philosophicl Society, Photo Ceit: Pete Hholt Review! 1.) 3.) L this week! q1q2 2 F E q0 Fk Electic Fiels " Exist in the pesence of chge pticles, pply foces to othe chges! q Guss s Lw!! # E in "0 Cn e use to etemine electic fiel in cetin situtions! U! " F! " qe Electic Enegy" Mesue of how much wok it tkes to q V!k move chges though electic fiels! Electic Potentil" V! " E s Mesue of how much enegy pe unit V chge it tkes to move though fiels! E! 2.) 4.)
Cpcitnce! Cpcitnce the ility to stoe chge.! C! Q "V [ Couloms] Volts [ ]! [ Fs] Cpcitnce is lwys positive, n is mesue of how much chge cn e stoe t given electic potentil.! 5.) Exmple 2! 2 conucting pltes hve chge of 1.2mC on ech, with 6.00-V potentil iffeence etween the two of them. Wht is the cpcitnce of this system?! +Q -Q 2.0x10!4 fs 7.) Exmple 1! Wht is the cpcitnce of this system, whee ech conucto hs chge of +/- 3 Couloms, n 9- Volt potentil exists etween the two conuctos?! Demo 1! Pllel Plte Cpcito! Physlet I. 26.1 1/3 F 6.) 8.)
Theoeticl Cpcitnce! Clculte the cpcitnce of n isolte conucto with chge Q n ius R. (ssume tht secon, concentic, hollow conucto exists with.)! if V k Q (fo this sphee) we cn wite: C Q V Q! k Q $ " # % & Exmple 3 - Pllel Plte Cpcito! Consie two pllel pltes, ech with e, septe y istnce n with equl n opposite chges on them. ssume tht pltes e close togethe compe to thei e so tht we cn neglect the ege effects n ssume tht E is constnt etween them. Clculte the cpcitnce of this system.! +Q -Q k 4'( o 9.) 11.) Sttegy! We cn clculte the cpcitnce of othe types of systems, using this sic sttegy:! 1. ssume chge of mgnitue Q! 2. Clculte V etween the pltes (using techniques fom lst chpte)! 3. Use CQ/ V to evlute the cpcitnce! +Q -Q l Exmple 3 - Pllel Plte Cpcito! Note tht V cp!"v pltes! E! (etween pllel pltes) n E cn e eive using Guss's Lw n E q in. Becuse # o ll of the chge is on the insie of the plte:! E q in # E $ # E $ Q We know tht % V cp &V % E!! ' Q * ( ) +, # C Q V cp Q ' Q * ( ) +, "$ ( ) +Q -Q 10.) 12.)
Demo 2! Pllel-Plte Cpcito! Physlet I.26.2 Exmple 4 - Cylinicl Cp.! cylinicl conucto of ius n chge Q is coxil with lge cylinicl shell of ius n chge -Q. Fin the cpcitnce of the system if its length is l.! l 13.) E 2k! (evelope using Guss's Lw) "V cp V " V " E $ V c # 2k! % $ V c 2k! ln ( & ' ) * $ C Q l V c 2k ln # ( ) 15.) Demo 3--Dielectic-Fille Cpcito! When you plce n insulting mteil etween the pltes of cpcito, the insulto expeiences Vn e Wl effect tht genetes n inuce chge on the insulto s sufce. This pouces n electic fiel in the iection opposite the iection of the fiel genete y the chge on the cpcito s pltes. This, in tun, iminishes the voltge coss the pltes n, s consequence, the tio Q/V (i.e., the cpcito s cpcitnce) goes UP. Dielectics o thee things:.) They incese the cpcitnce of cpcito vi the mechnism expline ove;.) They llow the pltes of the cpcito to e vey close (theey incesing the cpcitnce of the cpcito); c.) They llow pltes of vey lge e (hence lge cpcitnce) to e olle up into vey smll cylinicl elements Exmple 5 - Spheicl Cp.! Detemine the cpcitnce of spheicl cpcito, with n inne sphee of ius chge to +Q, n n oute sphee of ius chge to -Q.! E kq (evelope using Guss's Lw) 2 V cp V! V! E " # V c kq " 2 $ # V c kq! ' % & ( ) # C Q V c k(! ) 14.) 16.)
The Electic Bttey! 1780s - Glvni vs. Volt! Chging Cpcito! If 9V ttey is connecte to 300 µf cpcito, how much chge uils up on the pltes?! Cloth o ppe soke in slt o ci. g (silve) Zn (zinc) 17.) 19.) How It Woks! Two electoes (con n zinc) e immese in ilute ci (the electolyte).! Chging Cpcito! If 9V ttey is connecte to 300 µf cpcito, how much chge uils up on the pltes?! C Zn Becuse Q is ll locte on one sie of plte (why?): E! E! Q #V C $V # E!! % Q ( & ' ) * + C Q Q " o V C Q ( ) 18.) 20.)
C effective C 1 + C 2 21.) Cpcitos in Pllel! Cpcitos with oth of thei ens connecte s shown e si to e connecte in pllel.! C 2 C 1 Cpcitos stoe Enegy! cpcito cn stoe chge, n then ischge though evice, oing Wok.! But how much Wok?! V 23.) Cpcitos in Seies! Cpcitos connecte in ow s shown e si to e connecte in seies.! C 1 C 2 Enegy Deivtion! Wht is the iffeentil wok equie to move iffeentil chge q fom one plte to the othe?! W Vq W q C q V W Q! 0 q C q W Q2 2C 1 C effective 1 C 1 + 1 C 2 22.) 24.)
Othe enegy fomule! U 1 2 Q 2 C 1 2 CV 2 1 2 QV Exmple 6! Exmine the cicuit hee, whee C 1 > C 2 n oth hve een chge to the sme potentil V.!.) Wht is the potentil etween points n efoe the switches e close?! V Q 1 C 1 +Q 1 -Q 1 C 1 C 2 -Q 2 +Q 2.) Wht hppens to chges fte the switches e close?! Chge enges itself until the voltge coss ech cpcito is the sme. s Q1 is gete thn Q2, Q1 s excess flows to Q2 until V1V2.! 25.) 27.) Exmple 6! Exmine the cicuit hee, whee C 1 > C 2 n oth hve een chge to the sme potentil V.! +Q 1 -Q 1 C 1 C 2 -Q 2 +Q 2. Wht is the potentil etween points n efoe the switches e close?". Wht hppens to chges fte the switches e close?" c. Wht is the potentil fom to long time fte the switches hve een close?". Wht is the enegy stoe in the system efoe n fte the closing of the switches?! Dielectics! n insulto insete etween the pltes of n isolte pllel-plte cpcito cuses ecese in the potentil iffeence etween the two pltes, ecese of fcto 1!.! Why? Wht effect oes this hve on cpcitnce of the system?! C o Q o V o V V o! C Q o V Q o V o /!! Q o V o C!C o 26.) 30.)
Dielectic Vlues! Mteil!Dielectic!!Dielectic"!!Constnt (! )!!Stength (V/m)! Vcuum!1.00000!!------! i (y)!1.00059!!3e6! Ppe!!3.7!!!16e6! Wte!!80!!!------! C! o C! vntges to using ielectics in cpcitos inclue:! 1. incesing cpcitnce (!)! 2. incesing the mximum opeting voltge of the cpcito (most ielectics hve gete ekown stength thn i oes)! 3. the ielectic itself povies mechnicl suppot etween the pltes.! 31.) Exmple 7! pllel-plte cpcito hs pltes 2.0cm x 3.0 cm, septe only y 1.00mm thickness of ppe.!. Fin the evice s cpcitnce.!. Wht is the mximum chge tht cn e plce on the cpcito?! c. Wht is the mximum enegy tht cn e stoe in this cpcito?! 1. 19.7 pf 2. Dielectic stength16e6 V/m. VmxE16e6 0.001m)-16000V, so mx QCV(19.7pF)(16000V)0.315!C 3. UCV 2 /22.52e-3J 32.)