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Find the step response of the circuit shown in the Figure,

Find the step response of the circuit shown in the Figure,

enter image description here

1 Answer
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Solution:

Applying KVL to the circuit shown in Fig,

x(t)=Ri(t)+Ldi(t)dt

Applying Laplace transform,

X(S)=RI(S)+LSI(S)X(S)=[R+LS]I(S)

I(S)=X(S)[R+LS]Y(S)=LSX(S)[R+LS]

 For Step response x(t)=u(t)X(S)=1S

Y(S)=LS1SR+LS=LLS+R=1S+RL

Applying Inverse Laplace transform,

y(t)=eRLtu(t)

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