Question

Find formulas for the current in and the voltage vc for the circuit described by the equation below, assuming R1 = 0.4 ohm, R2 = 3 ohms, C = 0.25 farad, and L = 0.5 henry. The initial current is o amp, and the initial voltage is 12 volts. R2 IL Cafe 1 VC (RC) |_(t) = and vc(t);

Answer 1

Criven, R=0.4 ohm 20125 found R2 = 3 ohm L = 0.5 henry ů, 10) = 0 amp V. Col = 12 volts. •Ra L --- 4 E M. - (RIC) Ve Putting value, in 151 N Vo Composing with x = Ar -6 A = [ For eigenvalue of A, And Il=0 -6-2-2 3 --- 20 UJU (-6-2) (-1-2) +8 = 0 6+60+ A++8=0 22+72+1= 0 -7 tug-56 - 7tJ7

Now eigenveetor orrsponding to eigenvalue, -7+371 -7+570 E 103 -7+hi а -6a-2b na-b 2 -74571 b 2 sta i a +2b =0 b= 1s+578 la 4 2 let a=-I then b = strti 4 9 eigen vector coresponding to d= -7+S4 is 2 -1 stoti 2 Since we know that know that for conjugate eigenvalue eigen vectors are also conjugate. s el govectoy coresponding to do -7-J71 is 2 5-76

Then solution is, 1 같 33 e sturi of t) + Sin() ( (V) General solution is, 2 크t [1] [동시] e 들비플티 플50플티 플 t도 똘비플바들 1플티 Since. L10) = V, 100 = 12 1 0 +뇌 월 } C 월 키 G=0 2 뜰 어플도 = 12 Taco & z = 24 ㅋ 플티 (t)+ St) ① Ans,