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Capacitor and Inductor

Through out these notes, we use upper-case letters $I$ and $V$ to represent DC (direct current) current and voltage that are constants in time, and lower-case letters $i(t)$ and $v(t)$ (sometimes simply $i$ and $v$) to represent time-varying such as AC (alternating current) current and voltage.

Capacitor

Conceptually a capacitor is composed of a pair of plates of conductor which can be charged by a voltage source. The voltage between the two plates is proportional to the charge $Q$, but inversely proportional to the capacity $C$ of the capacitor:

\begin{displaymath}V=\frac{Q}{C},\;\;\;\;\;\;\;Q=VC,\;\;\;\;\;\;\;C=\frac{Q}{V},...
...ad]=\frac{[Coulomb]}{[Volt]}
=\frac{[Ampere][second]}{[Volt]} \end{displaymath}

capacitor.gif

capacitoranalogy1.gif

capacitoranalogy2.gif

The current through C is:


\begin{displaymath}i(t)=\frac{dq(t)}{dt}=\frac{C dv(t)}{dt}=C\frac{dv(t)}{dt} \end{displaymath}

If the voltage is DC which does not change over time, then $dv/dt=0$ and the current $i(t)$ through C is zero. If the voltage is AC which changes polarity over time, then $dv/dt\ne 0$ and the current $i(t)$ through C is not zero.

Inductor


next up previous
Next: Linear Elements Up: Chapter 1: Basic Quantities Previous: Basic Quantities
Ruye Wang 2012-07-02