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NEET Sample Paper NEET Sample Test Paper-59

  • question_answer
    The current flowing through a wire depends on time as\[I=3{{t}^{2}}+2t+5\]. The charge flowing  through the cross-section of the wire in time from t = 0 to t = 2s is:

    A) 22C                             

    B) 20C   

    C) 18C                             

    D) 5C

    Correct Answer: A

    Solution :

    [a] \[I=3{{t}^{2}}+2t+5\] \[\frac{dq}{dt}=3{{t}^{2}}+2t+5\] \[dq=(3{{t}^{2}}+2t+5)dt\] \[\int{dq=\int\limits_{0}^{2}{3{{t}^{2}}dt+\int\limits_{0}^{2}{2t\,dt+\int\limits_{0}^{2}{4dt}}}}\] \[q=\left[ \frac{3\times {{t}^{2}}}{3} \right]_{0}^{2}+\left[ \frac{2{{t}^{2}}}{2} \right]_{0}^{2}+5\,[t]_{0}^{2}\] \[=(4-0)+(4-0)+5(2-0)=22C\]


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