Capacitors

Voltage-Current Relationship

i = C \frac{d u}{d t} ⟹ u (t) = u (t_{0}) + \frac{1}{C} \int_{t_{0}}^{t} i d τ

W_{C} (t) = \frac{1}{2} C u^{2} (t)

C_{S} = \frac{C _{1} C _{2}}{C _{1} + C _{2}}, C_{P} = C_{1} + C_{2}

u (t) = L \frac{d i}{d t} (or E = - L \frac{d i}{d t}) ⟹ i (t) = i (t_{0}) + \frac{1}{L} \int_{t_{0}}^{t} u d τ

W_{L} = \frac{1}{2} L i^{2} (t)

L_{S} = L_{1} + L_{2}, L_{P} = \frac{L _{1} L _{2}}{L _{1} + L _{2}}