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## Homework Statement

R=50Ω

L=5H

C=1/125F

v

_{s}=200.[1+u(t)] V

Find i(t)

## Homework Equations

## The Attempt at a Solution

Write the KCL equation

-v

_{s}+Ri+L.i'+1/C.∫idt=0

Do the derivation to get rid of the integral, replace all possibly values, we got:

i''+10i'+25i=1/5.v

_{s}' (*)

solve A(s)=s

^{2}+10s+25=0, we got the natural response i

_{n}(t)=A1+A2.e

^{-5t}

Replace the inductor with a short circuit, the capacitor with open circuit, so I have i

_{p}=0

and the initial condition i(0

^{+})=i(0

^{-})=0. (**)

So the solution should be i(t)=i

_{n}+i

_{p}

I thought I was wrong at (**) and maybe at (*) cause the vs' would be zero and the solution would be zero as well.