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.

Refs & Notes


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