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

Solution:

Applying KVL to the circuit shown in Fig,

$$ x(t)=R i(t)+L \frac{d i(t)}{d t} $$

Applying Laplace transform,

$ \begin{gathered} X(S)=R I(S)+L S I(S) \\\\ X(S)=[R+L S] I(S)\\ \end{gathered} $

$ \begin{gathered} I(S)=\frac{X(S)}{[R+L S]} \\\\ Y(S)=L S \frac{X(S)}{[R+L S]}\\ \end{gathered} $

$ \text { For Step response } x(t)=u(t) …