Question

An RLC series circuit has a voltage source given by E(t)= 20 V, a resistor of 245 Q, an inductor of 7 H, and a capacitor of 0.05 F. If the initial current is zero and the initial charge on the capacitor is 9 C, determine the current in the circuit for t> 0. |(t) = (Type an exact answer, using radicals as needed.)

Answer 1

Given ECU) - QOV Qu557 H Ect) or sims 10.05F given ico) = 0 and 200)=90 Q-CV 201-C VOO) 9 = 0.05* VCO) - VCO) = 180 Wits, I dio) -ve at t-o* ckt is, dt 24532 ve 180 V gov © V = 160V Ldio).-160 => dic) --180 --22854. de dt

for serias RLC 20x2.857 35 dict) +9.857iCt) = . dk dt Homogeneous Soln. (0+358+2-854] ict) = 0 02+350 +8.857 -0 D.,2= -34.918, -0.081 .: iG): 46-34.9184, 28-0.081t Paticula soin ect)lec ict) = +2+350 +2.857 Put D=0 ict) - dor2-857 -20 2857 total sol ict) = 20 + - 34.918+ - 0.081t AC tBe

Put to - A+B A+B=0 -0. 16-34.9184 +88-08816x -0.081 a) = -34.918 AC dt di) -20-854 dt put t=0 , -34.918 A -0.081 B dico o A @a85= -34.918 A -0.081B on soluing oluina og & 1.10 -☺ V A=0.656 B: -O -0.081 3419487 ,-34.918+ - 0.6566 .: ict)- 20+ 0.656 €