User:Foxjwill/Physics

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

 * $$Q(t)=I_0\sqrt{LC} \sin{\frac{t}{\sqrt{LC}}} + C\mathcal{E} = I_0\sqrt{LC} \sin{\frac{t}{\sqrt{LC}}} + Q_0$$
 * $$I(t)=I_0\cos{\frac{t}{\sqrt{LC}}}$$