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  4. A current in a wire is given by the equation, I = 2t2 - 3t + 1, the charge through cross section of wire in time interval t = 3 s to t = 5 s is

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Q. A current in a wire is given by the equation, $I = 2t^2 - 3t + 1$, the charge through cross section of wire in time interval $t = 3\, s$ to $t = 5\,s$ is

Current Electricity

Solution:

As $I=\frac{dQ}{dt}$ ;
$dQ-Idt$ ;
$dQ=\left(2t^{2}-3t+1\right)dt$
$\int \,dQ=\int \limits ^{t=5}_{t=3}\,\left(2t^{2}-3t+1\right)dt$ ;
$Q=\left[\frac{2t^{3}}{3}-\frac{3t^{2}}{2}+t\right]^{5}_{3}$
$=\left[\frac{2}{5}\left(125-27\right)-\frac{3}{2}\left(25-9\right)+2\right]$
$=43.34\,C $