Nodal and Loop Analysis, Exercises of Electronic Circuits Design

Download Nodal and Loop Analysis and more Exercises Electronic Circuits Design in PDF only on Docsity! Chapter Three: Nodal and Loop Analysis Techniques Chapter Three: Nodal and Loop Analysis Techniques 163 166 Irwin, Basic Engineering Circuit Analysis, 8/E 3.3 Use nodal analysis to find both V, and V, in the circuit in Fig, P3.3, PSV 2mA Vy Y> VV VAN oO 6kO 2ko + 12 mA Ct) 3kO 6 kQO 1kO Vo O Figure P3.3 SOLUTION: 3°30 Find Vy tV, by hodal. @\,: 43,-Ty, ev 4 Vee =o T, e aad ee oo \ ON, Ten 4 VaVey Vang YarMe o au “FT No BL Ry Ry - 7 ©r,: Vaste Ve = ok a bee Rye 2bie 2, OE Ree l\kn ays lama Dae2nd ~ = No? 241M V\= 224¥ Chapter Three: Nodal and Loop Analysis Techniques 167 SOLUTION: Continued on the next page. 168 Irwin, Basic Engineering Circuit Analysis, 8/E 3_4.txt MATLAB WORK Factor 1/24000 out of conductance matrix. EDU= g=(12,-6;-6,18] g = 12 -6 -6 18 EDU» i=[-0.002;0.006 i= -0.0020 0.0060 EDU» 24000*inw(g)*i ans = oo Chapter Three: Nodal and Loop Analysis Techniques 171 3.7 Find V, in the network in Fig. P3.7 using nodal analysis. cs 12V Figure P3.7 SOLUTION: 3.7 Finel Vo by nodal 172 Irwin, Basic Engineering Circuit Analysis, 8/E 3.8 Find V, in the circuit in Fig. P3.8 using nodal analysis. PSV 8mA Figure P3.8 SOLUTION: 3.3 Find Vo by nodah Mi Vi Me Fm Reber Ras 2k Res dhe Chapter Three: Nodal and Loop Analysis Techniques 173 3.9 Use nodal analysis to find V, in the circuit in Fig. P3.9. 4kO WA WA WY 2kO 7 VAT 8 ko 6V © 4ko 8k Ct) 2mA Figure P3.9 SOLUTION: 34 Find We by vigdal. v= 6V Va Yate ie vs V4 yi i -] Qo: Wey Va, Vals a ei yh Dens wtet Re | @ Va: VarVa WVU 2g (= Zea B= By dk, Ry Ry Ry Pye Pea Fin @ Vyr VarVs © 2x03 + and Voz Va “Ng Vs 5AV, Vy= Bay Ve= 3.6v | 176 Irwin, Basic Engineering Circuit Analysis, 8/E 3_1l.txt MATLAB WORK Factor out 1/12000 from the conductance matrix EDU» g=[12000,0,0;-3,7,-3;0,-3,4] g= 12000 0 0 -3 7 +3 0 -3 4 EDU» i=[6;-0.002;0] i= 6.0000 -0. 0020 EDU» v=12000*inv(g) *i ve 6.0000 -1.2632 -0.9474 Chapter Three: Nodal and Loop Analysis Techniques 177 3.12 Use nodal analysis to find V, in the circuit in Fig. P3.12. VW‘ VN O 2kQ, 6 kO + 3kO 5V oe) Vo 6 mA 6V O Figure P3.12 SOLUTION: 3.1Z Vo by hodal, Vi Py Vy te Wyes¥o a Vg2-bV A eA + @\;: Vo-\, p Vato _ bxuoteo = pg, e, a V. 5 Bonk INS @\g: VoN2 4 Ve-Ns og 6év _ ey 3 1___t—_i_. — Rezka Ri =bke B- 3kq [ Yer 0.27] 178 Irwin, Basic Engineering Circuit Analysis, 8/E 3.13 Use nodal analysis to find V, in the circuit in Fig. P3.13. VN VN 6 kO 4kO 8kO 12V G ©) 24V 4kO Vo Figure P3.13 SOLUTION: 3.1.3 Fina V, by Hoda. Vp = clay Vs =+z4v Vi Boy, be V5 ' : @Va: Var V0 V3 . VarVe ia ee R-s oy(E 2ay {2 @Ny: Vo-V2 . Yo ey ey he Chapter Three: Nodal and Loop Analysis Techniques 181 3.16 Find /, in the network in Fig. P3.16 1, VN 4kO, 3kO $6 KO 2mA 6V S2k0 Figure P3.16 SOLUTION: SMe Fina a) Vis -\2vV Na =6V Mi va Es 5 SS QV: Mooveve at en 5 ev Mev Ry __ 0 4 aud W,- Va-V3 ov Es fye bka Peed Bye 3k byezka EsiezmA 182 Irwin, Basic Engineering Circuit Analysis, 8/E 3.17 Use nodal analysis to find V, and Y, in the circuit in Fig. P3.17. R= 1320 Figure P3.17 SOLUTION: 3.10) Find Vy and Vy by ned al Qs za Bee Zeya hse Wn Ry = ee. Reston Qe Ie Chapter Three: Nodal and Loop Analysis Techniques 183 3.18 For the network in Fig P3.17, explain why the resistor R plays no role in determining V, and Y,. SOLUTION: 3.8 Os shew ih Ho Simple cireuwt here the A Currek sauree fixes Yo Carlet in ib branch, Vhdep ended of He Valu od Sine Va ey depend. onl (re Lee branch's eyerenhy Ho yeh of BR does nok impack Vy or Vy 186 Irwin, Basic Engineering Circuit Analysis, 8/E 3.21 Find 7, in the circuit in Fig. P3.21. VY VW 4kO 4kQ 2kO 24V CG) Io $ 2kO 6V Figure P3.21 SOLUTION: 3.21 Find a, Vi=Z24V YaoM Vac + 2 = Ry BB Py G > Va-6 Chapter Three: Nodal and Loop Analysis Techniques 187 3.22 Use nodal analysis to find J, and J; in the circuit in Fig, P3.22. I, WA Ws WA 3 kO 3 kO 2kO 1kO $ 6V 2mA $ 4kO Is Figure P3.22 SOLUTION: 3200 Find Do and T by bo dal Bis looa + 30a = 40en 0. tn bev bs S Da ae B= 2oooedo00 = GER - -\ -3 xr, -fv, - Ee = V Los = “0 Jha “= + 2x1o A. [z= [== =~ 0.u7mA ts= “MQ = Tse 0. 83rmA a Ry _ 188 Irwin, Basic Engineering Circuit Analysis, 8/E 3.23 Use nodal analysis to find V, in the network in Fig. P3.23. 3mA VY C) VV O Aka 2kO + 2kaS Vv 6 ko 1kO Vy O Figure P3.23 SOLUTION: 3.23 Find No by vo dal, Ts=Me LM Ey Pah ty + Ve vee vy (Bs \ ~ \ Be tity / Chapter Three: Nodal and Loop Analysis Techniques 191 3.26 Use nodal analysis to find /, in the network in Fig. P3.26. >) WW Wh 1kO 2kO 6V 2ka $ 2ka 4mA $ 2k T5 Figure P3.26 SOLUTION: Ni ioN2 = 6 Rs @,- Rye ky =2ka Raalken Is Alaa ‘ Vee ; @Ns aM Ne Ry Pas Be @ ref: My V2 4 M3 = 1. Ry h By tle s and Dy = Ve / Ry x, Se Bay) 192 Irwin, Basic Engineering Circuit Analysis, 8/E 3.27 Use nodal analysis to find V, in the network in Fig. P3.27. Then solve this problem using MATLAB and compare your answers. ©S Oo + Vo oO Figure P3.27 SOLUTION: 3.27 Find Vy by Wodeh ana MmrnTLMe Vq-V,2 12M at Vet Va-Na , VenMi L Ts Ry Re Orel Mi Ve Lats nn R= R= BR, <iq: \We vo [ye- 2 | Chapter Three: Nodal and Loop Analysis Techniques 193 3.28 Find V, in the circuit in Fig. P3.28 using nodal analysis. PSV 1ko 1kO $ VA VN O + 1kQ $ 12V 2kQ Vo O Figure P3.28 SOLUTION: 328 Find Vo ‘oy Vie dad Vo-Vy=6V Vas \2Nv 4 Vere 4 Ve Lg Bs Ry Vos | 0-3N Qek= Bg zien Ryan 196 Irwin, Basic Engineering Circuit Analysis, 8/E 3.31 Use nodal analysis to find V, in the circuit in Fig. P3.31. “@ Figure P3.31 SOLUTION: 3.31 Find Ve by ho deh, Viz 120 @Va Van Me + Va + Va “3 =0 EY coe es Vv. -V @ 3 Va oF an thta 3 No = V2-Vs Voz dav Chapter Three: Nodal and Loop Analysis Techniques 197 3.32 Find Y, in the network in Fig. P3.32 using nodal analysis. cs VV VV VV oO 4kO 4kO, 2 kD + 6V CG 2mA 4mA 2kO Vo O Figure P3.32 SOLUTION: 3.92, Fina Vy ly ho dal. Vi ebv @v wy ve ge Ry e, SA o @ Vy: Vy-\e + Va7Vo =Ty Ppa Br rsdken R= Ry = 2a Dsus armiy tye Ima R53 198 Irwin, Basic Engineering Circuit Analysis, 8/E 3.33 Use nodal analysis to find V, in the network in Fig. P3.33. 1kO O + Vo O Figure P3.33 SOLUTION: 3.33 Find V, by he dal Va =l2V ViNa pay Va-¥on 5 Ry Bs Vi: Tye VeV | VAN, ye V2 “Be Ry @ V+ Veh Vee Ves ig Chapter Three: Nodal and Loop Analysis Techniques 201 SOLUTION: Continued on the next page. 202 Irwin, Basic Engineering Circuit Analysis, 8/E MATLAB WORK Factor 1/1000 out of the conductance matrix. EDU» q=[0,1000,0,0;1.5,-1,0,-0.5;0,-1,1.5,0;-0.5,0,0,1.5] g= 1.0e+003 * Q 1.0000 0 o 0.0015 -0.0010 0 -0.0005 0 -0.0010 0.0015 0 -0.0005 QO 0 0.0015 EDU» i=[12;0.002;-0.006;0.004] is 12.0000 0.0020 -0.0060 0.0040 EDU» v=l000*inv(g) *i v= 11.5000 12.0000 4.0000 6.5000 Chapter Three: Nodal and Loop Analysis Techniques 203 3.37 Determine V, in the network in Fig. P3.37 using nodal analysis. 2kOD $ 1kQO 6V t (>) ° 2k Ss 1k Vo oO Figure P3.37 SOLUTION: 3.37 Fryd Vp oy nodal. Vi-Va = Gy vio-Nes bey BHR 2k Tsy= 4m Rs = Py kes tka 206 Irwin, Basic Engineering Circuit Analysis, 8/E 3.40 Use nodal analysis to find V, in the circuit in Fig. P3.40. 2kO s 6V 4mA 2ka 3 1ko Figure P3.40 SOLUTION: 240 Fra uy by vn oka Fis@, = 2k Ts Pee Roe e kh = lee Xe del Ay. = 2m Vos LS7V Chapter Three: Nodal and Loop Analysis Techniques 207 3.41 Determine V, in the network in Fig. P3.41. Figure P3.41 SOLUTION: B41 Find Vy KYL G12 42 ANAS EO V, = © axto®) (re) = -4y Vo: BY 208 Irwin, Basic Engineering Circuit Analysis, 8/E 3.42 Find V, in the circuit in Fig. P3.42. 4mA 1kO Figure P3.42 SOLUTION: 3.42, Fina Vv, Qi etelk (leat o\ Creed Nas no e fleck m Vol kve- 4-12+ Th, 47,282,506 To= 4m wee [a] Chapter Three: Nodal and Loop Analysis Techniques 211 3.45 Find V, in the circuit in Fig. P3.45 using nodal analysis. “4-8 1kO +4 12V Vv 2 1kO 2kO Vo O Figure P3.45 SOLUTION: 34S Find Vy by nodal. — Vi -Vy = 12V V2> Vo _ WL see arnete: Vive, Mig Ve co qe, te Ry 212 Irwin, Basic Engineering Circuit Analysis, 8/E 3.46 Find V, in the circuit in Fig. P3.46 using nodal analysis. Then solve the problem using MATLAB and compare your answers, ©S > ww O Y 1kO + 12V al <> 1kO 1kO 1kO V, Ky = O Figure P3.46 SOLUTION: a4 Find Vy by Kodeh £ wATLAB VieVg 212 @ Vy: Voi Veo = =o AU R= Ilha @ ref: 25+ Yo Me 26 Ry Ru Ry Ty = Vi fee [easy] Chapter Three: Nodal and Loop Analysis Techniques 213 3.47 Find J, in the network in Fig. P3.47, PSV Ww <> 2 kO 4000/, 2k S 4kO 12k qd) 12mA I, I, Figure P3.47 SOLUTION: 347 Find X. lara Moy 216 Irwin, Basic Engineering Circuit Analysis, 8/E 3.50 Find V, in the circuit in Fig. P3.50. PSV Figure P3.50 SOLUTION: 3.fa Find Vp Nodal Porakans 15! Zio 2 = VicNe t Vy _ : es Eytee, Ve Veaap. Dirowiar aN x a Vv oo‘ + Vo xe vif 4. | Loon Rs “Ey L Byrke < | Vue i /2 aa Chapter Three: Nodal and Loop Analysis Techniques 217 3.51 Use nodal analysis to find V, in the circuit in Fig. P3.51. In addition, find all branch currents and check your answers using KCL at every node. AAA aN AN Oo 12kO NZ 2ko + 2000/ , 6V G) 4ko 2mA 4kO Vo I. - O Figure P3.51 SOLUTION: 3.51 hse nodal Aalysis to find Vo dclech via KEL. Beek BL =4kan Ll, =2hk2 Ree AL Vy -GN Na -Ng = + Zo00T,, Ty = 2 Pe Va sNo . Vs Nai 4 V2 4 vy Ye 2 2xto™* Rs By & Re es T= Tt pk Fys O43. © = - 136th Tz 643,A @ V2 Tjtht+ -o? Wie+ L43 -|3S7=0 “ @v Tr + 2xip Aer ~1357 4 2000 = 643 3 3 v @ wef: E, +Ty +, = 2x0? TNL+INS 4443 -2000 -0 218 Irwin, Basic Engineering Circuit Analysis, 8/E 3.52 Find the power supplied by the 2-A current source in the network in Fig. P3.52 using nodal analysis. 10V 40 2l, 50 @ 2A Figure P3.52 SOLUTION: 352 Find an ‘oy Vodak Analysts. Vis tov Ty VMs 4 Poa (Q0(\2) => Sw Supp lice EK -Sodote absorbe SW Chapter Three: Nodal and Loop Analysis Techniques 221 3.55 Calculate V, in the circuit in Fig. P3.55 using nodal analysis. + 2k = Vy + oO + 12V eS Vo O Figure P3.55 SOLUTION: 3.35 Fina Ve by Vedat anaheysis. ey =R,= 2k2 Ce aky> Re = VED Vx eNig-No Ny = (2N ay Va = -2Vxe Ne, at Vy 3 =0 ad- Ng NarVo 4 2xlo = Vo Fa Es 222 Irwin, Basic Engineering Circuit Analysis, 8/E 3.56 Using nodal analysis, find V, in the network in Fig. P3.56. 1kOS 1kQ 4 VV o 1kO + 2V, o> 2kQ Vy oO Figure P3.56 SOLUTION: 3.5% FindWVe oy wadal analy sis. 4 Sopsrmeldl: Me gp Map VorNe 4 Vaowy 4 ate” Pe Ry Ry Es =6 Chapter Three: Nodal and Loop Analysis Techniques 223 3.57 Use nodal analysis to find V, in the circuit in Fig. P3.57. 1 Koa S 1kO 1kO 1 kO XK 12V <4 Oo ° NZ 4 2ko + amA Ch) 2k 2KN SV, 1kQ Vo O Figure P3.57 SOLUTION: 3.57 Find vy bom Ho dah ancy sis. Ms f= B= Py= Fy My =len Be = Rew kye2ee Vy-V3 = 1 V3 - Na= 2Ny Vinay Irwin, Basic Engineering Circuit Analysis, 8/E 226 Continued on the next page. SOLUTION: Chapter Three: Nodal and Loop Analysis Techniques 227 c) Ng, = Va Veg *¥g-Na Ma Me Mery | Maes = Bo Rs Bu Re 228 Irwin, Basic Engineering Circuit Analysis, 8/E 3.61 In the circuit in Fig. P3.61, use Gaussian elimination to determine V,,. (a) Would mesh or nodal analysis be the most efficient approach? Why? (b) If mesh analysis is used, are any supermeshes required? Write the mesh equations. If nodal analy- sis is used, are any supernodes required’? If so, how many? What is the best location for the reference node and why? Write the node equations. Figure P3.61 SOLUTION: Zt Eyad wy a) BY reskh m- nodal 4 wtoheo | 3 mon - ref Yodlta 2 uabkmnaye Sou cee = No pak Ne sepemeshts Argutud becane dere ae me cored Suu. Go Ne Seprrede au herded becaun He 2 welkage Sorrcee Comme att ty 3 dhe “odes » Aaaarivg doe Ath node free for epptrcatim wp kee. Book tocchm fer MH nad at bette od schemahe. Mt nahh Cc Chapter Three: Nodal and Loop Analysis Techniques 231 3.64 Use mesh analysis to find V, in the circuit in Fig. P3.64. 4kQ 4kO VN VAN O + 6 kO 2 Kas 2kO V, 12V O Figure P3.64 SOLUTION: 232 Irwin, Basic Engineering Circuit Analysis, 8/E BUG Uae mesh b fad Ve mt Qr4ba Pye zkk bye tk z = Ry an ‘, Rex 4kn Re-2kn Q, @rv Ty Ve = Take Tif, +2, 2 +0, aR, +lz-0 Ty by Dake + @-T)\ es aie T= ota mA Vo = 1 33V Chapter Three: Nodal and Loop Analysis Techniques 233 3.65 Use mesh analysis to find V, in the circuit in Fig. P3.65. 4kO 10 ko vA‘ WN Oo + 6 kO 8 Kas 2kQ Vo 6V O Figure P3.65 SOLUTION: R=ter Re= sham tg etl Rye deka gee Zk Vo > Fo bs- Tye +Tye, +O -TNRy eG Taeyt Tater .-Ty E,=-& Ty - 250.8 [Voz os] 236 Irwin, Basic Engineering Circuit Analysis, 8/E 3.68 Use loop analysis to find V, in the network in Fig. P3.68. PSV vw Ws S O 2kO 2kO + 12V $1 kO 2mA 1kO Vo O Figure P3.68 SOLUTION: 3.48 th v, voiny ang anlar ie ae Ria Pa= the Pann eka lev + g an. zmh Ax, ay Ne Vor Ty 4 T,-T, = 2m r,?, +t, 0 +2, 2, + Ty, @ = 12 T2= Ima Voz iv Chapter Three: Nodal and Loop Analysis Techniques 237 3.69 Find /, in the network in Fig. P3.69 using mesh analysis. cs I, WV 4kQ 2ko 2mA qd) 6k Cd) 4mA 12V Figure P3.69 SOLUTION: 3.64 Uae mech analunis to find anal Fa 2kn = 4k bye ck T+t2 2mh dim A Eye -2mA Ts -4mA (= GT +18, -)e3 + Ty= 2.7m A [x- 2-bImA Irwin, Basic Engineering Circuit Analysis, 8/E 238 3.70 Use both nodal analysis and mesh analysis to find /, in the circuit in Fig. P3.70. ® 3 > 0 2mA D> 2kQ f, oO S 4k Figure P3.70 SOLUTION: er nro dak frm & fio a 3.92 Gm Bie dian Tes f2-Ts Is = ZmA Ea = 2-67mA [Tos —o.n2ma Neb + Va, = 2x00 = 2k Rs adh No tat Vg-Ne = 12 3 -3 xo "4+ 2eto “4+ V2-M =O Fy 3 Chapter Three: Nodal and Loop Analysis Techniques 241 3.72 Find V, in the network in Fig. P3.72 using both mesh and nodal analysis. PSV O + 2mA > 2k 4kQ Vo 12V CG 2kQ oO Figure P3.72 SOLUTION: SIL Fink ye woing, Wooly fire dak. A Ry = Aber v No wav Mme No £ T,= 2m Vi = l2V \2= @,-T,) 2, + @,-)*ts Zutons Ven Ve | Ve Pe Pa o= @3-F) Par C-Tee rs hy + VMieve p ONR ag Ey es Mo = Eats Fas 1. 7l ma [Mv ~ a [ee] 242 Irwin, Basic Engineering Circuit Analysis, 8/E 3.73 Use loop analysis to find /, in the network in Fig. P3.73. cs 42V +) 1kO qd 2mA Figure P3.73 SOLUTION: 3.73 Use Lecy td fran Z. Que es = Vien Tn= 2@eA Ty-F3 = 4mA to Tye-Ty fas 2, e+ B27, -ry + 2g Ox, -r3\ oO Te? +R (o,-0,) + ty (4-H) RA Dy = 3.64mA | Fe I Ltmal Chapter Three: Nodal and Loop Analysis Techniques 243 3.74 Find J, in the circuit in Fig. P3.74. ©S Lo ev 2kO S 4k 2mA 2 kO > q ~ J 4 XY 6ka S 41mA S 2k Figure P3.74 SOLUTION: @\ Bo = Bye 2k Kardler B,sten Ey -Xy= 2m Ty-Ty=\mA Te, + ©, -Ty) Ay +(G-2) Qso Ge TLR, +Tqks + T5R3 Te= EF, -f a ee ie Tle oa Dye -tsmA 246 Irwin, Basic Engineering Circuit Analysis, 8/E 3.77 Solve Problem 3.35 using loop analysis. SOLUTION: 3.90 Find No Wong lowe wala sis, = 2B) = Ree Ve. BeeRe 2k LE, = GmAé Dy Pye Vo b=C, ~IYE, +& IPs AIL = (La-T)@, + Tee ta= Tye (Ly) Ry Ty = T.2mk& [Mer teev] Chapter Three: Nodal and Loop Analysis Techniques 247 3.78 Solve Problem 3.37 using loop analysis. SOLUTION: 3.78 Find V, by Aewe ard ley. ~e= Pg (OT, -Ty) + 2.0 5,) b= Des Tey ein \2= Tyts + y-T,)ey Ty = beh Vo= Nv | 2 248 Irwin, Basic Engineering Circuit Analysis, 8/E 3.79 Solve Problem 3.40 using loop analysis. SOLUTION: R= P= 2k Ry =¥y= Re = @.= iat Tys -2mA T,-T, = 4mA “b= g(t, -r)1+un4ze, bo = by (tye) + Oe (ty B+ 8 (44-T,) z= Pots + Bs bte-t,) x i Tse s = 7.5) mA [Vo= Sav Chapter Three: Nodal and Loop Analysis Techniques 251 MATLAB WORK reisv EDU» r=[=2000,0, 3000, -1000,0;0,-2000,-1000, 4000, -1000;-1000,5000,0,-2000,0;0,0,0, -1000,20 00;1,0,0,0,0) r= -2000 0 3000 -1000 Qo 0 -2000 -1000 4000 -1000 -1000 5000 9 -2000 0 0 9 0 -1000 2000 1 Qo 0 0 0 EDU» v=[6;0;-12;12;0.002] ve 6.0000 0 -12.0000 12.0000 0.0020 EDU» i=1000*inv(r) *v 2.0000 1.0986 4.0845 2.2535 7.1268 252 Irwin, Basic Engineering Circuit Analysis, 8/E 3.82 Write mesh equations for the circuit in Fig. P3.82 using the assigned currents. 2A (>) XY Is 42 ~ Ve + 42 WV vi VV 5Q 0.5Vy 12V *) Cay <p> Cn 7 (ay CG) 20v Figure P3.82 SOLUTION: Raz bid rete. tp rathions Ves (x, -E\s @ 3865, -1-25i,-06 ® eT, - 2 Ty-Ti)+-Z0 ® (S,-e34 + .-2,)S + 2ry =12 Chapter Three: Nodal and Loop Analysis Techniques 253 3.83 Use mesh analysis to find V, in the circuit in Fig. P3.83. PSV 4kO vy <> © + VA - \Z + 4V4 ev) 6 kO 2ka = Vo O Figure P3.83 SOLUTION: > Q: 4k Ree blert Bae take pathy oe 1 2 3 wD Me, f% Ax, Ne Ya= Ey@ Vo Tz By G= Tyr G-h) ey E,G+@,-n\)0,+ avys0 b= T (ree \- ty T, (Get) +5 (4, -B)=0 Tz = -0-25ma 256 Irwin, Basic Engineering Circuit Analysis, 8/E 3.86 Use loop analysis to find V, in the circuit in Fig. P3.86. 2kO 2kO VN VV O + 12V G) aa 1K OV O Figure P3.86 SOLUTION: 3.86 hind Vo wing bony amaloare a fe Bethe R-Zkr alle * ~ a ada of ve ve Boke a: ey. T, - Ty loco “IZ= ZR + Ts Tes Dae -1aymh | Vo =-n33V \ Chapter Three: Nodal and Loop Analysis Techniques 257 3.87 Use both nodal analysis and mesh analysis to find V, in the circuit in Fig. P3.87. 6 Vy t VA C) oO Te ? = 12k0 vy. 12 ko Vo 4kQO oO Figure P3.87 SOLUTION: 3.F7 ar bd nodah bom find Vo bvy = cna Qysiwzka Wrz eka 2s-4kn Cy Al2en Be ve CS yy poe ——C2)— . Be BA aE Ps ane No ov Muah. odak Ty -T = mA VarNe = 6 Vx GYx+ @yT, + Ri Tso Mx = 2 o= T2% + Gt e22+ G-B)ey Ye 4 Ye 4 Gxto? <0 2 5 Vy =f ©) es a oe Voz Ts lg 1 [a Ry Tes lta [ven | 258 Irwin, Basic Engineering Circuit Analysis, 8/E 3.88 Using mesh analysis, find V, in the circuit in Fig. P3.88. Oo + Ve Q } as t 2kO 4kQ Vo 6 mA aD 4ka, oO Figure P3.88 SOLUTION: 3. BB Fink Yo vowme, mtsh tnelapre ada b, Reha = dee Lee 2k Yk * + V2 Bs CTa-35 “ye a Ry Vo Vs = Ry ln LT, = bea iS Ne. ty 4toors o> Egh+ y-r, 0,4 G-T Db