Question

In the given circuit, identify (0) and i(t) for t> 0. Assume 10) = 0 V and 1(O) = 2.50 A. + 5u(t) A 222 v+0.5 F ell 1 H [3.780 e-t2cos(1.3229t - 90°)]u(1) V [5 + 2.67252 e-t2cos(1.3229t - 200.79] A [0 – 2.67252e-t2cos(1.3229t – 200.7°)] A [5 – 2.67252e-t/2 cos(1.3229t+ 200.79] A [2.673e-t2cos(1.3229t – 90°)]u(0) V [1.336e-t2 cos(1.3229t+ 90°)]/(t) v

Answer 1

For the given problem,

The values of V(t) and i(t) are Option 1 and 2 respectively

Given! Hi VI OV 16) -2.50A 2012 0.5F low 11 1 5uct) A Vit) - ? i(t) = ? for to sol: Wo= =r2 =1.414 ric Ixo.5 da 2Rc =0.5 2X2X 0.5 since, a < wo under damped Response Wd (2)*(0.5) = 1-3229 : wodad? ilt) = 1s + ces ust +B sin het) e e] Is - 5 A. Wol = 1.3229,0=0.5 -0.5% ilt - 5+ A Cos 1.32291 +Bsin 1.3224t) e 5+CA Cos 0 + B sin co] i(a)=5+ A 5+A=2.5 [:7(0) = 2.54 (Given) A=2.5-5 A=-2.5 V= Ve=VL = L. dioro at di dt [132296-A 3in l. 328€ + 3, C09 1.924) 05]+ [-0.5(A los 1374€ + 2 sin 1.3944)e 056 dio dt 20= 1.3229 B -0.5 A Apply the A value, 1.32298 -0.5(-25)= 0 1.322982 -1.25

21:25 B2 41.3220 B=-0.9449 i(t) = 25+ [[2.5 los 2.5 Los 1.32296+0.9449 sin 1-3220 -2.5 Cos 1.32296 -6.9449 Sin 1.32297 A B A los wt + B sinot =c cos (wt-o) c = O=tan (4) A²+B² 62.574760. -0-946972 -2.67252 c=2.6726 * *.9449 o = tant 72-5 0 = 20.70 (-2.5 cos 1.3229€ + 0-9449 Sin 1-32296 2.6726 cos (1.3229t- 20.70) finally -t/2 tilt = 5+ 2.67262 Cos 1.3229t- 20.70 14 10.707A ficts

To find Vlt) we use, - N16) = Vilt)= L. dilt) at from above, -0.50 X di It [1.3224 (-Asta 1.3129+ Bees 1:324) * [-0.5 (Acos l: 3234€ + Bain 132432 * ] 1 . V (t) = L. di dt -0.5t + = 1 1.3924 (- Asinl.3396 +8 cos (13224+) e [-0.5 (A cos 1.322q + Esin 1.3290)20.st] -0.5 e It (1.3224 (-629 2.5) Sin 1-32297 – 0.9449 Cos 1.3225 60.5)(-2.5) AOS 1:37 760.5)(-0.74ks)cas 1:324)? *e] 2.5 in 1:3226 -0.9449 Cos 1. 322942e05€ + (t) = [1.32263 -0.50 1.25 Cs 1.3226 +0.47245 65 1. 32246) e " -0.50 (3. . 30125 Sin 1.32294 -1.25 COS 1.32295) e + -0.55 (1-25 cos 1-32297 +0.47245 cos 1.32297)ėdos -0.5t (3 3.7797 Sin 1.32296 -0) sino = cos 0-9009 - 9.5t sin 1.32295 v (t) = 3. TTTe YUG) V(t) = 3.78 et 2 cos (1.322qt-98) ult)