User:Foxjwill/Physics

Circuits

RC

$Q(t)=C{\mathcal {E}}\left(1-e^{{}^{-}{\frac {t}{RC}}}\right)=Q_{f}\left(1-e^{{}^{-}{\frac {t}{RC}}}\right)$

$I(t)={\frac {\mathcal {E}}{R}}e^{{}^{-}{\frac {t}{RC}}}=I_{0}e^{{}^{-}{\frac {t}{RC}}}$

RL

$I(t)={\frac {\mathcal {E}}{R}}\left(1-e^{{}^{-}{\frac {L}{R}}t}\right)=I_{f}\left(1-e^{{}^{-}{\frac {L}{R}}t}\right)$

LC

$Q(t)=I_{0}{\sqrt {LC}}\sin {\frac {t}{\sqrt {LC}}}+C{\mathcal {E}}=I_{0}{\sqrt {LC}}\sin {\frac {t}{\sqrt {LC}}}+Q_{0}$

$I(t)=I_{0}\cos {\frac {t}{\sqrt {LC}}}$