Question

(a) Determine the current flowing through an element if the charge flow is given by q(t) = 10e^-4t cos 20t uC? ​

Answer 1

Answer:

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Answer 2

Given: q(t)=  $10$ $e^{-4t}$$cos20t$

To Find: Current

Solution: we know that current is charge flowing per unit time

$I$ = $\frac{d}{dt} q(t)= \frac{d}{dt} (10e^{-4t} cos20t)$$=10\frac{d}{dt} (e^{-4t}cos20t )$

using chain rule, $\frac{d}{dt} ab=a\frac{d}{dt} b+b\frac{d}{dt} a$

$I=10[e^{-4t}\frac{d}{dt} cos20t+cos20t\frac{d}{dt} e^{-4t} ]$

$I=10[e^{-4t}(-20sin20t)+cos20t(-4e^{-4t} ) ]$

$I= -40e^{-4t} [5sin20t-cos20t]$