# Circuits¶

## Capacitor¶

Capacitance is defined as

$C = \frac{dQ}{dV}.$

Since current is defined as $$I = \frac{dQ}{dt}$$, we derive the current and potential relation for capacitor

$\begin{split}&C dV = dQ \\ \Rightarrow &C \frac{dV}{dt} = \frac{dQ}{dt} \\ \Rightarrow & C \frac{dV}{dt} = I.\end{split}$

## Inductor¶

Inductor is defined as

$L = \frac{d\Phi}{dI},$

where $$\Phi$$ is the magnetic flux of the inductor and $$I$$ is the current going through the inductor.