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  4. The current flowing through a wire depends on time as I=3t2+2t +5. The charge flowing through the cross section of the wire in time from t = 0 to t = 2 sec. is

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Q. The current flowing through a wire depends on time as $I=3t^{2}+2t +5.$ The charge flowing through the cross section of the wire in time from $t = 0$ to $t = 2$ sec. is

WBJEEWBJEE 2009Current Electricity

Solution:

Charge $ Q =\int\limits_{0}^{2}\left(3 t^{2}+2 t+5\right) d t $
$=\left[t^{3}+t^{2}+5 t\right]_{0}^{2}$
$=8+4+10=22\, C $