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MGIMS WARDHA MGIMS WARDHA Solved Paper-2015

  • question_answer
    The current in a wire varies with time as \[I=5{{t}^{2}}+2t,\]where I is in ampere and t is in second. The quantity of charge which has to be passed through a cross-section of wire during the times\[t=4\]to\[t=6s\]is

    A)  220 C                   

    B)  340 C  

    C)  273.34 C                             

    D)  280 C

    Correct Answer: C

    Solution :

                    Let\[dq\]be the small amount of charge which is passed in small interval of time\[dt\]. Then, \[dq=tdt=(5{{t}^{2}}+2t)dt\] So, the total charge passing through the cross-section of the wire during the time\[t=4\text{ }s\] to \[t=6s\] \[q=\int_{4}^{6}{(5{{t}^{2}}+2t)}dt\] \[=\left[ 5\frac{{{t}^{3}}}{3}+2\frac{{{t}^{2}}}{2} \right]_{4}^{6}\] \[=\frac{5}{3}({{6}^{3}}-{{4}^{3}})+({{6}^{2}}-{{4}^{2}})\] \[=\frac{5}{3}(216-64)+(36-16)\] \[q=\frac{5}{3}\times 152+20=27334\,C\]


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