tearstreakdl

2022-01-10

Determine the current flowing through a circuit element if the charge flow is given by:
$q\left(t\right)=10{e}^{-4t}\mathrm{cos}50t$

Jenny Sheppard

$q\left(t\right)=10{e}^{-4t}\mathrm{cos}50t\phantom{\rule{0ex}{0ex}}i=\frac{d}{dt}10{e}^{-4t}\mathrm{cos}50t$
$=10\left[{e}^{-4t}\left(-4\right)\mathrm{cos}50t+{e}^{-4t}\left(\mathrm{sin}50t×50\right)\right]$
$=10\left[-4{e}^{-4t}\mathrm{cos}50t-50{e}^{-4t}\mathrm{sin}50t\right]$
$=-40{e}^{-4t}\left[\mathrm{cos}50t+12.5\mathrm{sin}50t\right]$

Do you have a similar question?