Ch App. A A-1 A-4 Ch Ch 6.1,.3,.4,.8,.10,.11 Quiz , Lab 1: HW1 Ch : Lab 1 Notebook

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1 Fri. / Mon. /6 Wed. /8 Thur. /9 Fri. / Ch.9-. ntermedite DC Ciruit & App. A pg. A--A-4 Ch.-. & lightly Ch 6.,.,.4,.8,.,. Quiz Ch & 6, L : DC Ciruit More of the me Ch.-.: Cpitor HW: Ch Pr 4, ; Ch 6 Pr 9*, L Noteook Tody Struture Quetion out previou reding oltge Divider o Derive reltion, o Speifi emple with potentiometer qulittive tereo peker. o Conider with lod Meh Loop rule o ntrodutory remrk nightful v Sytemti o Coneptul / proedurl differene from wht you re fmilir with o do n emple jut etting up eqution o They do n emple jut etting up eqution o Mtri method trnlte mine into mtri form nd hve Eel olve They trnlte their into mtri form nd hve Eel olve For the ke of prtie getting to oure weite, they get it from there. equet from lt reding:. Ground. Sfety hzrd to not hve the rd prong? i. Generlly, if the devie i not ple of produing high enough urrent, then we don t need to worry out the zpp. ii. Note: ome devie hve rd prong for their fety rther thn our very enitive devie need well etlih ground o tht the kind of tti eletri zpp tht we n deliver doen t hrm it; or try eletri/mgneti field ould hve notiele effet on the ignl o the ground line i onneted to the e to hield it innrd.. Work & Chrge motion. Chrge moving through potentil differene, work i done where doe thi ome from, when doe it pply? When it in reitor, wht effet doe tht hve? i. Let tep wy from iruitry for moment nd riefly refreh our memory of hrge, field, nd potentil. Chrge (one nhored, one free to move) intert nd the kineti energy of the free one hnge; there hnge in potentil energy oited with tht; we define voltge differene in term of tht hnge in potentil energy. Conider

2 hrge etween hrged pitor plte. So we n ee tht energy i trnferred to the free hrge / work i done on it. ii. eitor role without reitne, the hrge would peed up nd peed up; with reitne, the hrged prtile ollide lot nd thu energy i trnferred eond time to the tom of the reitor whih then jiggle more violently nd o the reitor i wrmed. Of oure, the reitor itelf trnfer wy tht newly quired energy rdite nd ir ondut. More Generl Quetion. Alterntor. How doe n lterntor keep r ttery from running down? i. Of the t, m not ure where the nme ome from, ut in very rod troke, the lterntor i n eletri genertor. Thnk to the r motor, hft pin, it proly h wire wrpped round it nd tht pinning hft i ened in doughnut of mgnet. The eletron tht nturlly inhit tht wire, the wire move in the preene of the mgnet, feel fore tht puhe them long the wire, thu urrent i driven long the wire. The wire re onneted to the ttery to drive eletron k in the oppoite diretion from tht whih the tterie hemil proee would drive them. Thi undoe the hemil proee nd thu rehrge the ttery. 4. Why AC v. DC?. When do you hooe whih? i. Eletriity get ued for two thing imply trnmitting energy, nd trnmitting/mnipulting informtion. AC h n dvntge for the former.. Energy trnmiion. Mot devie run on DC; however, there n dvntge to trnmitting energy eletrilly in AC inted. When urrent flow long wire, reitive heting our. So energy i ontinully getting hed, thu, to keep the urrent flowing, omeody (the power plnt) h got to keep epending energy. The rte of tht lo goe like P lo =. So, the greter the urrent, the more energy i lot. On the other hnd, the rte t whih you n get thi eletriity to do work for you wherever you deliver it i P ue =, where tht i the differene etween the voltge t whih the eletriity i eing trnmitted nd tht to whih you ll ultimtely ink it (y, through lightul with one end onneted to the power line nd the other to the ground.) So you n trnmit the me mount of energy ut with muh le reitive lo long the wy if you trnmit it t high voltge nd low urrent. Now, here where AC eome ueful. Ultimtly, mot devie we ue wnt firly lower voltge. So, we wnt to trnmit from

3 the power plnt to the ity & houe t high voltge, ut ue t low voltge. n lter hpter you ll lern out trnformer whih re devie tht n tep up or tep down ignl voltge (nd ompentingly tep down or up it urrent) without wting lot of it energy, ut tht work y mgneti indution whih only our with vrying urrent. So, we ue AC urrent o we n eily trnform the voltge from trnmiion to ueful level.. oltge Divider. Ue, prtil emple peker volume.. Deriving the eqution (.7) 6. Meh Loop. Emple. Whettone Bridge 7. Mtri tuff. efreher, plee lo go over the eqution form A- onwrd. - oltge Divider, Potentiometer, nd Current Divider -. oltge Divider The ook doen t epliitly y thi, ut the voltge re reltive to the voltge t C, i.e., the voltge of the negtive terminl of the ttery. n iruit, thi i ommon referene point, one tht often grounded. B X C + - ( ) ( Sutituting in the reltion for give )

4 ( ) So, the voltge t point X (reltive to the - terminl) i et frtoin of the whole voltge ro the oure. -.. Emple.4 Uing two reitor, one whih h k reitne nd ttery, deing iruit from whih n 8 potentil (reltive to the negtive terminl) n e derived So, the rel quetion i, wht the pproprite vlue of the eond reitor? We hve our hoie of whether the k i or. X Let y tht i the k, then, we wnt to olve for the tht give u the deired 8 drop ro. k k With Lod o A voltge divider i very ommon hunk of iruitry, though in the ontet of divie, it uully jut one mll piee. Mye + i otined not from ttery 4

5 ut from trnduer, perhp preure enor, nd it vlue i proportionl to the preure you re meuring. Perhp you need to divide the ignl y efore you n input it to your omputer interfe, o you elet nd o tht = + /. Then i ped to the interfe. o o But you ve got to e reful. The interfe i ompoed of iruitry too, o, it h ome reitne etween the two led tht onnet to your divider, we ll jut ll tht L, L for lod. So, when the divider driving lod, the ompoite iruit look like L L o So, dding tht new pth for urrent to tke hnge the voltge. How? Well, L nd re in prllel, o thi new iruit i equivlent to the voltge divider with repled y the equivlent reitor,. p L o Then hnge to L o A you might imgine, if the lod reitne i muh lrger thn, it h little effet on the iruit ine / L << /. o Tht why the internl reitne of mot voltge meuring devie i quite lrge. -. Potentiometer rile reitor / voltge divider

6 o mgine you hd long ron r tht you wnted to ue reitor in your iruit. Now, you ould lip the wire onto the two fr end, nd tht would give you one reitne, or you ould lip one wire on one end, nd the other omewhere ner the middle, tht would give you mller reitne. Tht n emple of very rude potentiometer you n hooe where long the length of the reitive element to mke your onnetion, nd thu through how muh of tht mteril the urrent mut flow / how muh reitne it ontriute to the iruit. For tht mtter, you n ue the potentiometer like two reitor in erie one onnetion t one end, one t the other, nd one omewhere in the middle then you ve got voltge divider rrngement, jut like in the digrm on the previou pge. -. Current Divider while So u u or flipping it round up - The Meh Loop Method nightful v. Sytemti 6

7 The Meh Loop Method oneptulize the iruit ompoed of djoining loop. Eh loop h it own urrent, nd omponent hred y more thn one loop hve onurrent urrent flowing through them. o Note tht ene of irultion need not gree, o the voltge drop ro hred element my e evluted in oppoite diretion. o The ook doe thi one, o ll only reprodue the et up Loop ) Loop ). Thee two eqution n e omined to olve for the two unknown of the urrent nd the urrent through reitor n e found ( - ). By the onvention of loop, if thi i poitive, the urrent goe down the pge.. (. ( ) ) ephre in Mtri Form ( ) We ll get to in moment. Now, how do we tkle thi one? They Do jut the etup: =6 = + A =9 = - = B =. 7

8 We hould nlyze eh loop in the irultion we ve repreented nd e reful out whether eh voltge tep i up (poitive) or down (negtive) following tht pth. Eel -. Whettone Bridge Thi i n emple where it muh eier to jump in with the Meh Loop pproh thn pplying the independent node nd loop rule ine we need only, rther thn ditint urrent to onider. 4 4 Three eqution, three unknown it dole. Now, the lger mightn t e pretty, ut you n log through it. Alterntively, mtri mth i gret for hndling oupled liner eqution. errnging Appendi A: The Method of Determinnt Thi informtion ould e rephred in mtri form 4 Appendi A give reipe for olving for the urrent. t little tediou. The good new i tht Eel good t tediou thing. ve poted on the oure weite doument tht eplin how to ue Eel to del with mtri reltion like thi. Here the i ide. The i point i tht the mthemtil opertion of multiplying y mtri h n invere, jut like multiplying nd dividing, or oine nd r-oine. f you multiply oth ide of n eqution y mtri invere, the mtri i removed from one ide, nd it invere i left on the other. Writing the ove eqution ˆ where ˆ i the reitne mtri. Then, it invere would e repreented ˆ (whih doen t literlly men tht the mtri i upide-down). So, 4 8

9 ˆ ˆ ˆ our urrent rry. ˆ. The i the identity mtri ˆ whih i trivil to multiply y A id, Eel will hndle thi for you, o hek out the weite nd look t tody entry on the hedule. -.. Wht the Whettone Bridge good for nywy? Hitorilly, thi peulir onfigurtion h een ued very enitive Ohm meter, i.e., to meure reitne. f 4 i unknown, ut the other reitne re known, nd one of the other reitor, y, i preiion potentiometer (o it reitne n e vried), then tht reitne n e vried until + = + 4, t whih point the urrent through =. So would e vried until urrent i, then + = + 4 mut e true nd, knowing the other three reitne, 4 n e olved for. 9