Question

6.60 Using Multisim, draw a series RLC circuit with Vs = 24 V, R= 12 S2, L = 300 mH, and C = 10 mF. Use the Transient Analysis tool to obtain a plot of vc(t) for 0 < t < 0.2 s. 1) Provide the analytic solution. (10 points) 2) Provide the plot of vc(t) (Tips: refer the schematic below for your simulation,) (10 points) XSC1 Ext Trig J1 R1 2 L1 300mH 120 V1 Omsec 1msec - 24 V 61 10mF 두 HU

Answer 1

6.GO t. Analytical solution : whew, OX E Ims : 4 300mH WWW RI mm 니 24V F Ri= 12-2 C = 10mF 24 ast I 24 I So, Vels) = Analyzing is s-domain, 3:R, + 418+ so, Vels) : I las) = SCRI+15+4) 615) 8x103 <Replacing ,CRI 5 (324405 + 333.3) Taking inverse laplace transform Velt) = (2400) - 24.0 Cosh (8.16 +) +0.21 Simh(8:16) Sans) .-0 24 152 + 405 + 333.3) -zot And I So, 14+) = 0.232 e - 20th Sinh (8.1656) 11657)} 2.

Whew, Ims t 0.25 Ij m Li Ri C, I So, I, R, +37415 -I,4, I(ti) + Illets) + Veilti) = 0 As, by putting ti= 0.001 s in eque and Ilti) 1.855mA Veiltu) = 0.435 V T,211.87 100 S - 0:435 013 St } (-01435) (11.87 1095 11.87 +0.35 + 10015 so, Ver ts) = (1969 Taxing Laplace inverses - 19.78t Veilt) = 0.525 é +{ sinh (7.61 t)} Ans)

2.

Simulation Circuit:

0.001 R1 L1 2. 1 U1 12. 300m 2. V1 24 U2 AH C1 10m 0.001 0

Plot of Vc:

160mV. 120mV - 80mV. 40mV OVH OS o V(C1:2) 20ms 40ms 60ms 80ms 100ms 120ms 140ms 160ms 180ms 200ms Time