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.