Voltage Source Network - Physics for Scientist and Engineers - Solved Past Paper, Exams of Engineering Physics

Download Voltage Source Network - Physics for Scientist and Engineers - Solved Past Paper and more Exams Engineering Physics in PDF only on Docsity! Department of Physics, University of California, Berkeley Final Examination Physics 7B, Lecture 1, Prof. Smoot § AM - 11 AM, 12 May 2006 Discussion Section; Name of TA: Problem i Problem 2 Problem 3 Problem 4 There Problem 4 roblem 3 no 5t Problem 6 | Problem 7 Problem 8 Score: 2. (25 points] Resistor and Voltage Source Network - Is: I,rIu | We will (arbitrarily) cheese the ‘4° direchong 6S the currents as shown R 2 -— ¢c Figure 2: Resistor and Voltage Source Network. (a) [5 points] Write down the ap 1, through points P, (2) Ih resistor Rg. propriate equations to determine the four currents: (1) through resistor Rs, (3) Ig though point Q and (4) J; through Junction Rules : A: I= Latte Bi I, = Z+ty Cc Is+1,? Le @- Utte, senate Ts € I] Net all of thee are indepeadeats We will elininde D6 Ty, Sine they ae net labeled sn te problem! > [r,: Leds Ty | > 1 geeten L op Rules : We need three in dependent loops So we cm have Sow equa fivas Se Sow un kaown y ri €,- TR, + &- TRs- RI, 70 L2: - (1, DIR, - ER, e &; + TLR 7° Ve _ SO geny agent convent > signs Flo is: “LR~ & + TsRs *0 yy Gi) T- l- lie ~(Re RT, - RT . Ra La ~ (er )T, — Rede > Aes + Ry Tz - &etar & (i) bie) Pecblen 3 “user to the pede Qa. how Ouwheut Rahs \zoon Yoooo 20 Yoroe 1400 {0d 400 240 10 Yor ito 2. i pe! b. Phau = Dime * Var = SOA* ROV = CkW Bes = T?R= CAN eal loss K = ‘ /Aq)'R = oe a) 0482 = 16 v4 \N i oe (cee) so = V5 W “Average USA fosses ~ % “ : part > Was prvblew. 1S nd grate’ C, Trainstoriar ansmaor on ually pots 5 sng, — tors N= 200 t= 200 winds Tinduclance - G crlonond of ‘o L, N fern Naweler D+ “2 = B= N<@~ 7(2)’ Keogh -poUt wD? Uae pe a “LT DIL - ee eae Gir core) <=> Lo Dir « in? N/a = Qo)" x “O25 4-0 4w L= 3.9 mit Ferro woop atic Core: jr= 4000. > Y= Sool Lie is. 34H ————SSSS Zy = ®L= SFI rei x. sAwt = LAT kL a Bie = “oon, C. Continued 1 ew cutrent = Vpeb Q400V =" kN) > CSA. L c > R27 > “ere plows load” f just G rear ser Zz = Cs i Cal- z= j pre v _ ~{ coh~ ax AV-dTs & GE = AZ Te cold. > c. - 7 © cot. C= 7 = \B mF if Git core [2x x60 ex 3.Ietl \ Cz = o.A4 BE f Rerena = Qe vlLO = 277 col  We Cth nee ahat someting MAME) ot =TeRs for P Bf must be snto page Oy oUt SG PHAR ‘ Bal =~ Aho Lene for y> (2 Bc2wr ) = wer “a B= Ao A ® => BE vine He 4 = Bank 5 th nontd Ae pads fred eo eunment GUi~cG Pa%e, constant uf Aotonl (O 2 wis make cee Eis mh HAL > Wrecttun . Yu would ye QO Aime - vou) B owt He page, inside radius R So Bed& = WR*BO) anol at (% ae rie at Wo aE = Ecztr) = TR? A Ber) E = R? pay OE “ \S Oe RQ den) : 2 Gt fF Zao GFK ¢ c = TMS Omnfiquraton should penaiind «2 Oj A Soluncid uf GMsrant B inside nd B=O outsides We Cunent ward gust be AAW our inty C) If we Wad oly a vane dong Yd disttibviti¢n , VXE=O - lets check: fo; Krak | Ee Crd> G§ Eo i VxE= LL PEz > Ep A ray gt + Ober _ a€e A L at oe [P + LL 3 _ A vr L & br Ee) 2G S ~O +0 + 45. (r@L) z Le e = =D or nw _£ om re 2 I 40 frlso , coukd Around a logo Cmservative (ie. db we - Ge" oy Lo 3c Gringy) tin éltofro stot fretd Must te Cngervanhic. | gwrs js NOt . 6. [25 points] Microwave Oven (a) [3 points} The operating wavelength of a microwave oven is \ = 12.24 cm. What is its operating frequency? Save BIS 2 THES Hy = 245 Ahn, A DVUL I (b) [5 points] If the power of the microwave is about 1000 watts and the microwaves are generated in a device called a klystron and transmitted to the microwave cooking area through a wave guide which is one half wavelength wide and one quarter wavelength high. What is the average Poynting vector < [S| > or Intensity I, and rms Electric Egys and Magnetic Brass field values in the waveguide, when it is operating? We A au te A y ~ Cs = Teceg™, Ee suena 62 5.5400 Wh — 7 (gts we _—_ 2 ec ome < Se > an € oe TO a Wee Vas? & = tty (c) [5 points] The volume of the microwave cooking area is 1.4 cubic feet (3.9644 x 107m’), what is the energy density, and rms Electric and Magnetic field values in the microwave cooking area when it is gperating? Assume that the Quality factor of the circuit - microwave cavity (an LC) and food (R) is such that there is about 10 times the energy stored than is being drawn out per cycle. - We & 2 See _ One eB kak VEE 70 a y= efee+ & ote (et es > Ex fe+ a= ee oe 2 pe Zz v => EF = > {4 (d) [2 points] Why is the microwave oven enclosed in a metal container? Note that even the window in the door is covered by a metal screen and the rest of the inside is fully enclosed by metal. bys. alec’ to fetedih. Conn ie fervabrats Roun a t bea A jour wide, So the we Bing tent meertte pes on Kaa, oe es ‘ coe Bing LO eS Ney soe We & Ot Smadox Ron Bo longa G Oe waned car Se ar wee Wo . * Dee oved wer 7p ore (20nd Ir tyrng Hee Ss ond Wes oki cen 94 rr tee. oeterrwusaese Soe iw aie “s pacadeanars (e) [3 points} Why is it a bad idea to put a cup with a gold rim (e.g. 10 cm diameter circle) é in the microwave? How about food wrapped in tin foil? What about other metal utensils or Chinese food boxes with wire handles? How much power could be coupled into the circuit produced by Xa metal? pa wknd in 9 6 Foore uy llailen dored loop» wrQick ae, vdeo EYP wr) Oo Insp fos Coda Sing 2a carssse antl diss: pda Ral prtforvane Bar, (f) [5 points] One warning buried in the microwave manual is that a clean smooth cup full of water can be superheated so that it has sufficient internal energy to boil but not yet started boiling because nothing has yet triggered the formation of steam bubbles. When picked up or disturbed, it will then errupt in a geyser of hot boiling water. For how long would one have to heat a container containing 100 grams of water starting at 20 C so that it was overheated and ready to errupt into boiling? Assume that the water’s internal energy is distributed uniformly. haat mp od iey yee Bre \ oO ote (ats an Ss » Won Ges if Gproernd Yon 20'S be Oc ve aor BOONE Lo pes €099 Shiels = 23QHOT 209 o 22 C008" = Sh Seconda (Omaus Che latex baat (post 15537 GW Aen = SSF 00Cab re => 2126085 2226085. 22-2e6 Socal) ago Ww 21 sD SRG = 2. Obs 7. [25 points] A coaxial cable has an inner conductor with radius 7) = 1 mm and an outer conductor with inside radius r2 = 2 mm and they are concentric. They are separated by an insulating dielectric with x = 5. r@__} Figure 5: sketch of coaxial cable with dimensions labeled for problem 5. ‘Treat as two concentric cylinders. (a) [5 points] What is the capacitance per unit length of the coaxial cable? Te find the cap aortance ' Fanngint pees a chaege deuwnty rH pe nel Gupht, On the tamer and tader conducts. Te elechc field can be found using Gaus¢ haw! €> Et, =e eg - Wb oylabe ¥ , A radina ty A at hive ss & L —> Ee: Aw. Hl debchic, Ee We _ = 3 ~ “Pre pokuctinl ius is AVE fe-a ~ Se oA. de > pace . % - Af cH > FEE uh) & = UEek = zx _(eapcee) F = extol? 2 : kn ve, Kz : (b) [5 points] What is the energy stored per unit length of coaxial cable, when it contains a charge q?? iF enc — wut tough, baw cherge a1 then . 2 _ qh %, L Tr. OY wy, = 2 ME SE = fm ARG Fr tol’? 22 8. [85 points] Tethered Satellite for electrodynamic power generated from orbit consists of a major satellite and a secondary satellite lowered on a conducting cable. This concept was tested on a Shuttle flight in # near equitorial orbit around the Earth. The smaller satellite was lowered 20 km below the Shuttle. (a) [5 points] If the orbital speed is 7 km/s and the mean Earth's magnetic ficld is 0.5 x 1074 T, what is the voltage difference gencrated between the Shuttle and secondary satellite? © “The general formula for Eu is $ = a 1Okm €,P> J oats id) Assomins PLR, we AAW C= BLv = OFklo% Tt. 20003 mx 2k/0% mls = J0ee V (b) {5 points] What charge must be on the secondary (lower) satellite for this voltage. Ap- proximate the satellite as a conducting sphere of radius r = 2m with the Shuttle very (nearly infinitely) far away? First calculate its capacitance. Then calculate the charge. a= Qik CD ys eb the ano TWisV Qa Va xPeSk/a-r x FOGOX Dun 4 4 = [56xX/0°C 25 (c) [5 points] Approximase both the Shuttle and secondary satellite as two conducting spheres of radii 3m and 2 m respectively connected by an electrical cable 20 km long and supporting the voltage difference you found in (a). Sketch the field lines for this configuration and label. Explain what is different than one would have naively thought for the electrostatic case. La the electestetic case, the two ae Comached by a Mine {lat would tend +g Cischangs th Spheres, Hew, the Chara Litera ix 1 + “ al » ) malwtoned by te VxB force in te / \ oh, (d) [5 points] Power was taken from the system by letting a current flow and power experi- ments on the Shuttle and tethered spacecraft. Ifthe current is T and the voltage is V, what is the electrical power provided? How much force is exerted on the cable? Evaluate for a cur- rent of | ampere. Does it speed up or slow down the Shuttle-cable-satellite system’? (Hint: Docs it change the altitude? Which way is the force?) What makes the circuit or closed path? The basically stationary Karth’s upper atmosphere, the ionosphere, is conductive and completes the circuit. f= TV = Joeoed, Fe TGR = flor « Skits ty, ad a is perpordivuler to fle win. By lenz's lay, tle Pores mW @ drag ores , ad Shaul cocreat the altitude . “The ionasplure act as a Lispersion fekl ton te electrons, 26 (e) [5 points: Could you run the experiment backwards’? That is could the Space Station use solar cells or fuel cells to produce electrical power and run current down a tether cable to a secondary satellite and produce a force to match or overcome the residual atmospheric drag at its altitude and keep its orbit stable? How much electrical power would be required to keep the Space Station of mass 183,283 ke in its orbit, if its altitude is 353 km and loses about 2 km per year. If the tether cable is 5 km long, what is the required current and voltage? Th orbits Ws fmt and fle yinal theorem sags < KE >= -F CPE ? CB( You Can heck this L cipculer orks by suty mV Cw Me ) % td Usd Bm Me re ln losug only Vem, te Shotle lors crergy of aol x) f { fre =o or Pr . Wh Aus Udrtsed-ucr)= Au ddr 4. 24/0? aly r Th rate of power Oss Uo Re sod (3.000 49,6 x 287 nly TROP BL y m = Set this equah equal @ Five Te8y to get Sid, S47 aBee Store § xo Tx? f «6800 10? m 27