Solve the following electronics applications using any method you choose. Find t

Question

Solve the following electronics applications using any method you choose. Find the current l as a function of time t (in seconds), given that I satisfies the differential equation I' + R/L I = sin(2t). Where R = 550 Ohms, L = 4 Henrys, l(0) = 0. q" + R/L q' + 1/LC q = 1/L E(t) where R is resistance (in Ohms), C is capacitance (in Farads), L is the L LC L inductance (in Henrys), E(t) is the electromotive force (in Volts), and q is the charge on the capacitor (in Coulombs). Find the charge q as a function of time for the electrical circuit described. Assume that q(0) = 0 and q'(0)= 0 R = 20, C = 0.02, L = 2, E(t)=35

Explanation / Answer

taking laplace transform, s*I+137.5*I=0.25*2/(s^2+4) I*(s+137.5)=0.5/(s^2+4) I=0.5/((s^2+4)*(s+137.5)) so i(t)=2/(75641*exp((275*t)/2)) - (2*cos(2*t))/75641 + (275*sin(2*t))/151282 b) taking laplace transform, s^2*q+10*s*q+25*q=17.5/s q(s^2+10*s+25)=17.5/s q=17.5/(s*(s^2+10*s+25)) q(t)=7/10 - (7*t)/(2*exp(5*t)) - 7/(10*exp(5*t))

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