Capacitors

I-V

Current across the terminals of a capacitor is proportional to the time rate of change of the voltage in the capacitor

1. With constant voltage, current is zero, capacitor acts like an open
2. Voltage cannot change instantaneously in a capacitor

$$i(t)=C\frac{dv(t)}{dt}$$ $$v(t)=\frac{1}{C}{\int }_0^{t}id\tau +v(0)$$

Power

$$p=iv=Cv\frac{dv}{dt}=i\left[\frac{1}{C}{\int }_{t_0}^{t}i(\tau )d\tau +v(t_o)\right]$$

Energy