Question

Please write very clear

1. (20 points) Determine the differential equations for the given electrical circuit shown below. Equa- tions should be purely in the form of i1, and i2 and their derivatives (no integral terms). Simplify to the simplest form. Assume: E(t) = 2sin(t)Volts, R2 = 112, R2 = 512, L1 = 2H, L2 = 4H, C = 0.5F, C2 = 0.25F font E(t)

Answer 1

for Capacitor i=cdr => dt vehidh for Inductor V=L di i= 11 volt dt R. CI L2 Ect) 34 i in C2 R2 apply kue in lood @ - E(t) + Reit +16) flics + La (1.- + 4 d. i) Re (h. 12) = 0 li[ Ri+R] + á findt + li doneo - Lidia - Rz iz= Elt)

Take differentiation - (R+R) di + citli din Ziz - Rq diz -L2 d Elt) 042 dt de dut values 5 die 4 12 +2 Gdi. +2i, + 20° 42 2 Cost dt at 2 +6die +2i, - 4 +2i, – 4 dzie .5 diz 2 Cost a+2 at dt2 dt Now apply Avl in lood 6 — Ld (ig-i) Re (12-1) + L2 diz at + Ġ Si2d4 = 0 + apply differentiation — 22 (izli) & R al (12-21) + L2 iz=0 di d+2 Gut values as L, = 2H, P2=50, L2=4H, C2=0.256 2 ali 5 di (2+4) dig d+2 + 5 diz + 4iq- CH2 A+ dt

so the differential equation becomes 2 dlci d+2 +6 di, + 21,-4 džia dt 0442 -5 ولد و 2 Cost at Am and die + 5 die +4i2- 2 5 = 0 d+2 dt C+2 dt