next up previous
Next: Examples: Mechanical and Electrical Up: Chapter 1: Basic Quantities Previous: Linear Elements

Energy Dissipation/Storage in Linear Elements

By definition, $v=dw/dq$, $i=dq/dt$, therefore the electric power associated with an element is

\begin{displaymath}p(t)=v(t) i(t)=\frac{dw}{dq}\;\frac{dq}{dt}=\frac{dw}{dt} \end{displaymath}

where $i(t)$ is the current going through it and $v(t)$ the voltage across it. Energy is power integrated over time:

\begin{displaymath}w=\int_0^T p(t)\; dt=\int_0^T v(t)\; i(t) dt \end{displaymath}

Comparison with mechanical systems:

The work of a mechanical system does is $w=\int_0^X f(x)\; dx$ where $f(x)$ is force and $X$ is displacement.


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