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JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Question Bank Critical Thinking

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    The current in a conductor varies with time t as \[I=2t+3{{t}^{2}}\] where I is in ampere and t in seconds.  Electric charge flowing through a section of the conductor during t = 2 sec to t = 3 sec is                                                [Orissa JEE 2003]

    A)            10 C                                          

    B)            24 C

    C)            33 C                                          

    D)            44 C

    Correct Answer: B

    Solution :

                       dQ = \[Idt\]Þ \[Q=\int_{t=2}^{t=3}{\,Idt}=\]\[\left[ 2\int\limits_{2}^{3}{tdt}+3\int\limits_{2}^{3}{{{t}^{2}}dt} \right]\]  = \[\left[ {{t}^{2}} \right]_{2}^{3}+\left[ {{t}^{3}} \right]_{2}^{3}\]= (9 ? 4) + (27 ? 8) = 5 + 19 = 24C.


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