Question

Q3. (1) Initial energy stored in the circuit is zero. Use Laplace transform to find Thevenin equivalent voltage (Vth) and Thevenin equivalent impedance (Zth) in the s domain with respect to terminals 'a' and 'b'. (12 points) 22 M 20u(t) (2) Find the time-domain solution for current iz(t). (8 points)

Answer 1

solution: given time dossain cirurt ato is calsverted into s domain by using Laplace transform. 0-2 enda CircuTE TD s-domain Apply KC2 at Node vai 8 & tarvy - VH & Vinh where vx=4 + V + 2Y - Vyhts Step (14+6.55) Vi - 670.55) Vy = 4 0 Applag kez at rode Vest VA - 02rx- & - o VH-E24 - Ask-sho o - (-2+0.55) 4+ [1+0.55) Y - + 256) VCA V = U+0.55) Dag

substitute V pean (1.4 +0.55) (+0.55) - (1+0.55) KH = 4 1oES (1-4 7.13S+ 0-253 Vast - (10:55) [1-340.55 Hygge = 4(1.240.655) (1.44 125+6258²) KX-1:2 +11S+ 8.255 47=48+25 tolstar) VH = 4.8725 Slalsto2) | reveren armpedana is tatwlated by shost. croit the voltage source. short circuit current Isc is calculated by shost circuit the asb terminals. 2 its Affly ka at Nodern -20 & Vitoarxo & ho 5 Where x = v.

V + ,40-211 M 265 0.55+14) = 4 = 40.5 Apply kat at hode ovu - 0.28x1 & orvo Isco (055+1.4) Isc = 18.5St124 =410.55+1.2) (6. 1884 sloosstly) Theresin impedance Zara opers circuit voltage short circuit current open ecruit voltage Voc & There is voltage Yap Zrt = 248 +25) 6.55+. Slous+0.29 oilsto.2 4 10.55 +1.27 slo.5stry ZH = 557141, k-205748 St2 sis+2) cirwit is shown below 2) Theresin equivalent SA - 25448 sloys+02) = 200+ 48 ZIA 205tus VH S1542) Sista)

уу? К то та tе. 5St14 ILS) + (2 ts) It's) = V - Sosthus [5544+ (543 ) I+13) = 285446 (3²+ 9+ 18) ILIS) = 4(58712) (st) (5+3) IL'S =4185712) Ins) - 20s+48 S1543) (ST6) Foortial fraction agestod to IL'S). Apply 205+48 = A + B 56 Als+3)(56) + BS(+6) + CSS3) 2o5+48 S(5+3) (ST6) 205+48 = A(3298+18) 431576) 4 c1335) 205 +48 = (A+B+C) +(94+68+30)5+ 18A compare as power coefficients of both sides of a book of A+B+C =0, 9A+GB+30=20, 180=48, A=2.67 BAC= -2.67 GBtsC=-4 sove the above erns and an ihen B= 1.3867, ceny Piis) 2-64 + 13967 - 4 Apply Is verge Laplace Transtoon to the ILSS. (Lt) = (2-67+ 1.33618 est just