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
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a
60 coulomb
b
24 coulomb
c
48 coulomb
d
30 coulomb
answer is C.
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Detailed Solution
Let dq be the charge which has passed in a small interval of time dt, then dq = idt = (4 + 2t)dtHence total charge passed between interval t = 2 sec and t = 6 sec q =∫26(4+2t)dt =∫264dt + ∫262tdt=46-2 +62-22 =48 C