Question

the 14 In the following RC exponential, RC circuit; 20 tkt Loizut 20 -0.2uF I loov. a) Find Velot the capacitor voltage at the instant I after the switch changes position. b) Find Ve(s), the capacitor voltage as t ox c) Find the time constant, i, for tyo d) Write the expression for Velts for tzo e) sketch Velt) for tzo, 2 Find the to, the witch chances age at the in

Answer 1

secution - In dhe giren cinset diagram for txo! The swich es kept in open postision the refore the network is only energized by the presence of 100V Die findependens energy source enu

such that the giren networks u operating at tready state condition therefore, capacitor acts as an open circuit at this case - un ner 100 V As current flowing in the network is zero due to open circuit path therefore = [vatos = 100 Voet] At t=0t in the switch is in closed position as the voltage acrous capacitor cannot change instantly - there for, V-16 = V VO Floovalt. y At t=0 in the switch is closed now, any count is opeonting Under bready state therefore ! (ko HM M The current powing in cionit - 1100) = 200 - 100 Ampere 5000 T 1800) = 0.02 Ampere (o) [ico) = 20mA]

Vaing kul 200 - bilm) - 100) =0 Velou) = 200 -(4x20] Cycl) = ipo Vect] (c) finding the time conferant for txot: Calculation of Requin Replace all the independent energy Louree present in the circuit by their internal resistances - ie; Die independent voltage acts as short circuit Now, Equera lent resistance looking from the terminal of Capacitor in Akr Ikr Reg = 462 like = 481 kr 4+1 As, Req = 0.8 K2 Time connant for the cirant is given by T= Requc sec

C = (0-8x102)x(0.2x106) C = 1.6x109 sec (t = 0.16 millisecond] now, writing differential equ for tzo Using ke at node'c' 402 C IK2 wki Music X 7 200-VC + 100-Vc = id 4000 1000 As ie = cdue Ampere - - cele mai ( 1 + +) = to takto do . at (0.2x70) du cou en vect dv.64 +6250 Vekt) = 75x104 5 het of d =D .: (+6250) [= 75X10“ _ ®

solving for Homogeneous post of Velits by making A His=0 (D+ 6250) Wit =0 Farming characteristic equation: Replace 'D' by Is' We get- CHE = S + 6250 =0 Roots of Charaderistic equation - S=-6250 AS Rools are real therefore voltage Vacht a ciest (CF) response takes form of Ego - solving the particular secution - ) - fra flag 70 fio . If f(a) =0 then en if f'(a) & up pras to thon ese it fra# f"(a) and so.ma

• ,th = 1 (5x10 xe°C (pon) (+6250) Replace is by '0' we get - WCH = 75X10% = 120 RID 6250 -- Create = 120] Now total responde a 2 = VGH + V.CH RO VlH = -6250t Ge +120 eft t=0 in Veld) = cieº +120 As V. 10) = 100V of 100 = 6 +120 → C= 100-120 = 612-20) substitute the value of 'C' in equ ③ we get- UCH = (120-20 082507) volt valid for t>ot | es Sketch of Velt u geren an zy varying the value of time and tabulate the data for Velha At teoir V, 10) = 120-20 V, 10) = 100 V At t = 0.1 msec z VOCO.ID =120-200mm Verol) = 109:20 U

-(6280 X 0.5X103) At troismsec : - Vcl0.57 = 120 - 20 € At t +0 - VLOO) = 120 - 2020 = 120volt. skerching the past Velt A 120V 119.12V 109.29v Tod vº s time 0.1 msec 0.5 msec Variation of velti vs time Answer