Question

3. The switch is in position a for a long time. At t= 0, switch changes to position b. Find: a) V.(0") b) dv.(0*)/dt c) Vo(t)fort 20 24 k12 4k12 to 122 02H 20 V 28 V 8 nF V.lt)

Answer 1

03> 2017 b 24ku 4 kv. 0.24 m2 12 kn + 28 8nE Volt) 20v at tro switch is at position a 4kn len 0-2H TLV) + 2.tv Volt) anF Ne10 20v at +=0 circuit is in steady sterte has frequene to source fo Xo = eiffe a capacitor open circuit RIFL 0 incluctor as 4kn short cirinit 12km into) + 28v Duo Nolo) 20 apply kul in the loop. -20 t leil16) + (4K) i Lion)

16kn) illon) 48 v Velo) 4 AV 48T 16 ku H6X103 3 x 103 A 140-) 11163 3mA Noitge a leness Capuitor Nelor) -28+ (4km) illos -28 + 4x10?x 3X163 Velo) - 28 +1% = 16V Velo -16V Voltage acewels Capacitor Cannot change instaning Velo) ve 10+) throng irchetor Commort change corrend tunzo instantly illo) inlot) 3mA t>o switch is at Let's moved to positions ciruit 04 +0+ Droo the 24kn 0.24 sm inlot) + 12kn t &nf Velot) Volot) 20 V

3 12 kn and 24 KV so their core in parallel aquaral and resistance 12+24 14x2 = 8kur 128 84 8 км 365 inot) + om + enf Nelor) Nolot) Dlhop apply peut in loop -volot) +(8kn) iclot) Vclot) = 0 Vol 6+) Velor). +8HM) (40+) -16 + 3x103 x 3 x 10-? -16 + 24 = 8 v VOLO+) Vo 10+) SV - final duolot) 140*2 Kelts the Dron 2 kn cruit tro ILI) 0.24 + Velt Volt)

apply kut in the roop - 20 + (0.2) dilles +(3 km) 1414) + Velt) = 0 dot gia dilim + fakub i 2199 + V114) = 20$ dt we and lopp can write by applying kut in smaller -Volt) + (8 km) ILIt) twelt) - 1114) ILU) Vo (1) -V1) 8 km Volt and Velt) Veit) t TO I dalt det ILIA) Volt) Ź l'illot. 8kn differatul ILLA with respeed tot dium dvoldo old Ź illo o kn 9.4 tot dillot) d vol 10t) £illot) 97 8ku

from eam alt toot 0? diilot) dt +(8km) IL10t) + ve 10t)120 0.2 dinot) dt LoVelot) (8km) i 40+) = 3m A illot) Velot) = 6V dillot) बम -20 -(416) - 8X1023X10-3 0.2 20 +16 -24 0.2 dillot = 12. 120 clillot) cat Goals ora om Eq? dillots dt drolot) X (81er) X 3X183 88109 3x10 8X10 X 60 a dvolet) da 8 duocot) 5 d1 = 4.8X10 + 3.75 X 105 8.55 X.105 ys

dvolts dt 8.55X105 vs 07 Volt) = ? for tro at +70 11149 mm 0.24 + ant Volt) 200 > up from ean 0.2 diela 0+ +(8kr) illt) + V (+) = 20 and apply Kul in loop -20 0.2 dillt) + . + vo14) = 0 0.2 dilih :- Vol) +20 dt Velt: 는 In Hidt pur Vc!) in ga 0.2 din at + (Bleve) i414) of & filles

Differentiate 7 bn both side. Doe die daa +(8ku) dicily tieto बन 0.2 dilt) da2 illes 88109 50 devitt) d42 + 8x10? dicles ata 4 + 8X102 • dicit) dta *10 +19,5x1071214)=0 dielts d42 it 4x104 dictus dt + 1253106 1119= 0 Characteristic egn 48104 D + 1858106 24 noot's of this characteristica tegn > 1 E-36583.123 De :.3416. 87. So general soln of in ILH2 DIH) Ае Det of Be at to illo) - smo AdB AAB 3X163 ()

from En chelot) Differentiate Equi diem de dielot) Dit Adie Det + Boqe 60 at Aur + B De 60 2-36583 · 113 A -3416,87B 36 563.123 A 3416.87 B = 60 ti) multiply Ear (V) 36583.123 by & add in Eqn (ris 286583/123 A 3416.8713 36583.123 A + 36583.123B + = 109.741 + 2016 6.250 p =169.749 B - 5-11 8 X10-3 ATB = 3x10-3 A. - 3x100 B - 2.115 X103

1114) -2.118X1013 - 36573.199ť e + 5.118x13'e -3-3416.14 from Eq? li Volt) 20- 0. dilla at. Vo14 _ 20 -6.2 -3 -36563-1981 2.118X10*xl-36583•113) e -3916. 37 ) x +5.116 Xin é 3416.87 €) Volt) = 20 + 3.497 e -3416.87 € - 36583.821 -15.496e - 3416.87 € -36583.17 Volf) = 20+ 8.497 e 15.496 e to or