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J & K CET Medical J & K - CET Medical Solved Paper-2004

  • question_answer
    A source of emf E = 15 V and having negligible internal resistance, is connected to a variable resistance, so that the current in the circuit increases with time as 1 = 1.2t + 3. Then, the total charge that will flow in first 5 s will be:

    A)  10C                                       

    B)  20 C

    C)  30 C                                      

    D)  40 C

    Correct Answer: C

    Solution :

                    Charge (q) is given by \[q=\int{Idt}\] Given,     \[I=1.2t+3\] Integrating the expression using                 \[\int{{{x}^{n}}}dx=\frac{{{x}^{n+1}}}{n+1},\] we have                 \[q=\int{Idt}=1.2\int{t\,dt}+3\int{dt}\]                 \[q=1.2\left[ \frac{{{t}^{2}}}{2} \right]_{0}^{5}+3[t]_{0}^{5}\]                 \[q=\frac{1.2}{2}\times 25+3\times 5\]                 \[q=15+15=30\,C\]


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