Question

1. (20 points) Determine the differential equations for the given electrical circuit shown below. Equa- tions should be purely in the form of in, and in and their derivatives (no integral terms). Simplify to the simplest form. Assume: E(t) = 2sin(t)Volts, R1 = 112, R2 = 52, L1 = 2H, L2 = 4H, C1 = 0.5F, C2 = 0.25F R1 C1 L2 E(t) :C2 } R2

Answer 1

From the leve in loop ☺ 4 Idi, at diz dict +(116)-iz L4) B. 1,145.27 + < fi,Lt) edt + Elt): 'Diffueultate both sides with respect to de d Elt) را تلك + Tilt) ) - Lid'ely + R2 dict) + df dt dt - R₂ dilt) det رها ,لى .2 d in Lt) 2 + dilt) (6) - 5. diel) dt + 21,61) - 2. Cost d? dit dt dilt) dizla) + 3. dict) Cost dt2 2.5 dizlt) ti, (e)s det dut? dut 0 - do 5 dize) č. (13.4.df - + Rz (izla)-'(t) + 4, dient at Differentiation both sidei with respect to dt' O=L₂ diz Lt) dt? 1217) C₂ + Ry dizut) dt R2 dict) thid I2 (+] _ u dily dt dt2 dt² O 4. dielt) dt? 2 diz Lt) 2 d'Tilt) dit +5 dictty -5 dilt) + 4.72 (+) du dt dut

dut otp Qз (+) d XP 7 (Т. Р 5. (74P 5 7)" РТ diz(t)

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