# The current in a wire varies with time according to the equation I = 4 + 2t, where I is in ampere and t is in sec. The quantity of charge which has passed through a cross-section of the wire during the time t = 2 sec to t = 6 sec will be

Total charge flowing -

$dQ=Idt\Rightarrow \int dQ=\int Idt$

$Q=\int Idt$

- wherein

$Q\rightarrow$ Total charge

Let dq be the charge which has passed in a small interval of time dt,

then dq = idt = (4 + 2t)dt
Hence total charge passed between interval t = 2 sec and t = 6 sec
q = $\int\limits_2^6 {(4 + 2t)dt}$ = 48 coulomb

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