Question

PAST FINAL SIGNA... BENT 3373 Signals Tutorial 4 LAPLACE... 3 / 4 © 9. Assuming there is no initial energy stored in the circuit, find i, and iz using Laplace transform technique for t > 0. 8.4 H 10 H 1 = 0 + 1 336 V 34212 48 12 10. For the circuit shown in figure below, find the transfer function of the system V/V:(s). 2 Ω 0.2 F

Answer 1

Energy Assuming there is no Initial stored in the circuit, find i, & iz using Laplace transferm technique for too. 8-4H 10H 02 t = 3422 3482 رية دا < 336 V Solutions Apply Laplace transform to the above circuit. Hence the circuit becanes, 8045 los a M 33+ + 5 I 42.2 | I2) 482 Apply Kul at Loop © -336 s + 8.45. I, +42 (I, -12) -0 336 S + (42+ 8.45) I 4212 -0 >0 Apply KVL at Loop 1OS-Iz + 48I2 +42 CIZ-I)) = 0 (105 +42+48)I2 - 421 So

(105 +90) 12 42 1 = 0 +421 = + cios +90) 12 .. I (los +90) Iz 42 fubstituting Equation ② In Equation ③ - 336 + 4a + 8.45) (105 +90) I2 -421, 30 S 42 336 + 42] [(42+8.45) Clos +90) -42]12 - 336 (42 +84 s) Clos +90) 42 - 42 | I2 = 0 42 → 336 X 42 Iz (s) s[242 +8.45) (10s +90) -423] 1336 Xu2 vs s[4 4205 +3780 +848+7565-1764] 336 XU2 s[845+11765 +2016] 168 336 x y z 84 [s? +1482 +245 Iz (S) 168 3 53 +1482 +245 2

3 Substitute Equation Equation ③ In Equation lie I1(s) = (108 +90) 83 Hys? +245 168 4 [ 405 + 360 Iics) s3 +145² +245