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Linear Circuit Analysis I

by: Cassidy Casper

Linear Circuit Analysis I ECE 20100

Cassidy Casper
GPA 3.59


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This 9 page Class Notes was uploaded by Cassidy Casper on Saturday September 19, 2015. The Class Notes belongs to ECE 20100 at Purdue University taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/207904/ece-20100-purdue-university in Electrical Engineering & Computer Science at Purdue University.

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Date Created: 09/19/15
H H to 03 EP 01 a 1 00 to ECE 201H POTENTIALLY USEFUL FORMULAS A Electrostatics Force felt by a charge q inside a static electric eld Gauss s law in free space Electric eld 7 voltage relationships E7 V V27V17El P 1 Voltage produced by a single static charge q in free space V Ci a 4m R 7 Pa Equivalent polarization charge densities pm 13 pps13 in Electric Displacement D 60E P If a material is linear7 isotropic and homogeneous7 13 soxgE and D 63er 6E Ohm s law J 0E 11 Continuity of charge 13 Total power dissipated in a volume V electrostatics PEfdv V Some Useful Vector Identities ABXCBCxACAXB AxBxCBAC CA39B VipV1VV Vth V A39 VAAV Vx A VxAV xA VAxBBVxA AVXB VVVV2V 39VxVxAVVA VZA VxVV0 VVXAO VV A do i A 39 ds Divergence theorem L V x A ds 9QCA d6 Stokes s theorem Gradient Divergence Curl and Laplacian Operations Cartesian Coordinates x y z 0V 6V 6V VV a ay az ax 0y 6z 64 8412 lt22 6x 6y az VA ax 3y az A a 6 6 6y 6z 39 6A aAz 39 aAy aAI az a 6x 6x 6y IGI 645L OJegp644 I eq 5 Witxiq fiV 660 644 Reqigt sn quzows M4 Mrer 52 vnxi svaeq i erh M sr Xli jvsxxtekiSRP 2 62 Wls 511p syv svo jsvxli jsgs mck tvsfpiq wws Xlex tempgihmc ger fi ewukrih2 Gvsvm syxgplevg er svo lngl nwxs fi hmzikevhih2 F i gi39xmem Xlexxli em ivnwhmmrkyrmlefp jvsq Xli SD2Y rwyttsvxih em ivw Imvrsx fi knzir gvihnx yrplvm sxliv nwi mchnge h2 72 Q eoi syvem ivggevojsvieq tp390ft1Egnfkmmf e fs2 82 I xve tetivnwezengafp39 nj riihih2 F i wyvi xs pafipxli tvsfpiq ryq fivjsviegl teki sj syv SVOZ 92 Ywi yrmM livi viuynvih2 2 F i wyvi Xlex syv SVOO erh hnwgywmsrw erh i tpErexnsrw lir viuyimdhOevi gpevOgsrgmvio erh svkermih2 7 Useful vector identities differential elements and constants and physical relations are given exxli feg ijli I eq2 lt2 Xli tsrctthmmfyxmsr sr Xlnwieq nweszgs wgt Tvsfpiq EFIX swgsqi Tsmrxu Wgsvi 5 m 74 64 54 54 LOGO 59 33333 59 IEFIXI Wgsvi Viwypcl m 3544 iw3 rs 52 74 tmlz Jsviegl ijli jsgs ruck uyiwmrwotpewi erw ivm 516 pcriwmhcrk xs fi eweggyve erh gsrgnwi m syv i tparexnsrw erh gegypamsrw ew t swmprZ a 5 pts A capacitor has 10 p0 stored charge and 10 ml stored energy Please nd its geteguergiZ C 1 L WL V1 Qza u gi E Lf103p 2 2C 2W 1NDquot b 5 pts Please make a two dimensional sketch of the electric eld lines and equipotential Wjegiw sj er ipigmng hntsp392 syvvobigl wlsypn fi eweggy39ve ewtswmfp g 9 tmlz Ng39xli ipigmng tsxinmpnwivs exe tsrctxm vtegiOhsiwmcjng Xlexxli ipngrg eld is also zero at this point as well Please explain Ne 11 u VicI Me E39s 3v on mm m M4 V lquot 7quotquot l39 0 r wl 39 smaiw39 4wecmah mu bc m a tun539wa by HM cmwa cl d 5 pts Please de ne mobility of the electrons in a conductor 3911 he 371m r Hquot 444m My 1 H wk Hp Hw quotwhen Wed am new 39m HM onclm fw w A meme 04 ivm39cle n w 42m Hem 4 me e 5 pts Please state Kirchhoff s voltage law in words The alfelavait mm 0 all Vallave Jar 611 an equal bahtw j 9 tmE lex hs i q ier f weka Xlexe hnipgmrgq e vvepnwmsmstrgc Krrzi leii ieq tp39w sj hnipigwrgnl exger fi ywyegj gsmmivjh msth ls olrcfic 7 i q rain and la l39 a mulag 2 0quot 5 Cang PK qn By Mary 97 641 RAWFLA H l 39 mad 62 64tm12 Gsrwfnive tevemptpzm39 getegusv nxl tpaxi evie E Otpaxi Mtevexmr h erh jvii space between the plates Ignoring fringing eld please prove that the capacitance of the getegmltsvan A amp4EAh Note if you know the eld produced by an in nite charged plate sy ger ywi nxm syv svo mdsyxtvszmck m2 SOQULHDV in HM no k4 72 54tm12 G srwmive q ihnyq nxl gsrwexxgsrhygmmc a2 Tvszi XlexV X MA 4 iziv livi m Xli q ihnyq 2 J 4 We mow ko a Vx5o Since 366 w M 9 quot l and 539 ch r is uni914 Vvlt a a J 6x3 9 9 V 0 b 82 54 tmlz E zsgq i glevki hmmmfymsr pz A 9 rGAq 7 exists in the region de ned as 4 S S 60 5 S S 704 S S 82Tpewi gegypaxi Xli xsxepglevki m X1ivikm3r2 L 3 1 lsSPan SJXaigJy 1j2JE V o O ithlt9 3 391quot 5 15 pts In a dielectric material the relationship between the ux density Pf and electric eld 1 nwkrrzir fgt Ff A 6amp41 My livi p erh F evi e gsrwxexx vgepev erh zigxsvvivtigmiQZ Jmch Xli tspevmemsr sj Xlnw hriggmng ewe jyrgmsr sj MOI39OM erh 172 w L quot E E quot 39 quot v o nanJ DEn l qEOEpzaEFB 39 o D is E P 3 since AE 1 p of Pamp 2 59 tmlz Gsrxmhiv X 5 mg tpi hniggxmgwE erh F2Xli igngng Witxfmnx sj q egtdwepE is three tirn larger than the electric susceptibility of material B If the electric ux density is the same in both materials nd the relationship between the polarizations in materials A erh F m sxliv sxmmitviquE ewe jyrgxmsr sj F 2 7k 37 s 9 6A93 EOEA 9 v 4 quot 1 oEB39Puu7 F39m 4 a quot39 v a LEA 53 EA EEg 2ng r w r t4 quot Q f39Xu E3 a E4 B 53 1amp V 39 Thu 39PA azk5k 50 37 23 5 323 3l PB 53911 773L753E 393Zu


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