Laplace Transform Models of Circuit Elements

Time domain

Laplace domain

Rendered by

    \begin{equation*}v_R(t) = i_R(t) R\end{equation}

Rendered by

    \begin{equation*}V_R(s) &= I_R(s) R \end{equation}

Rendered by

    \begin{equation*}i_C(t) = C ~ {d \over dt}\left(v_C(t)\right)\end{equation}

    \begin{equation*}v_C(t) = {1 \over C} \int_o^t i_C dt + {v_C(0^-)}\end{equation}

Rendered by

    \begin{equation*}v_L(t) = L ~ {d \over dt}\left(i_L(t)\right)\end{equation}

    \begin{equation*}i_L(t) = {1 \over L} \int_o^t v_L dt + i_L(0^-)\end{equation}


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