Question

Problem 10.6-19 4 H 2 4 m 3 15 2 vy(t) 27 1 = v(t) 3 vit) $ 20 mF + v.(t) The input to this circuit the voltage source voltage is vs(t) = 8 cos(2 t) V. First, represent the circuit in the frequency domain using phasors and impedances. next, Apply KCL at nodes 2 and 4 and arrange the results in matrix form to to obtain the node equations: Tatjo 0 T 13-1-ja VO [, 1-ja][M]-[:) Determine the values of the constants a, b and d: a = 1/2,6 = 1/2 and d = 1/2.

Answer 1

@ 1 © 15 Sin Volt) = 0 Coot 12 t) volt , wag youll see Vs (t) = 0 Loi volt A t Jose JAL - jisse * The induetive Reactanee r XL = jw L=jx ax 4 =jor Volt) 6 2743 vit) Agust) The capacitive Regatance, atance. Leto jasa - hall) E Ốc - Nga - Mega Twe, = x 3 =]]2 54 obrovis3 = -3252 VLt) - Velt) vit) - 30lt) -0 => s vlt) 97 y Vit jo -J125 197000T 4490° Applying kel at, mod et 2, 7 View] + Vet) vocet) vit) - 30Lt) = 0 '3) vlt) [ 37 * 36 * fiosta ja → Vlt) 1 3375+j1000 + 439 7 = 0209. - 12-90º = -1) =) (0-037-30-141) vlt) = -3; - 0. Applying KCL at nodes ③ Volt), suce) u li = 0 ) -3 VLt)+(5-), 6) = 0 =) - 3 vit) +(1-5) W14) = o ;) -3 V (+) + ( 125-15) Wolt) = 0 = 3 Vlt) +( 15.-.)25) volt) = 0 5' 3VCt) +(-30-6-1) Vlt) = 0 = 3 Vlt) + (-1-jo:6) Bolt) = 0 10.037-30.14% 0 Trul- j 1 3 -1-3016 a = 0.037 21, b = -0.141127, d = 0.6 .5 15