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NEET Sample Paper NEET Sample Test Paper-49

  • question_answer
    Consider a capacitor charging circuit. Let \[{{Q}_{1}}\]) be the charge given to the capacitor in a time interval of 10 ms and \[{{Q}_{2}}\] be the charge given in the next time interval of 10 ms. Let 10 \[\mu C\] charge be deposited in time interval \[{{t}_{1}}\] and the next \[10\,\,\mu C\] charge deposited in next time interval \[{{t}_{2}}\], then-

    A) \[{{Q}_{1}}>{{Q}_{2}},\text{ }{{t}_{1}}>{{t}_{2}}\]           

    B) \[{{Q}_{1}}>{{Q}_{2}}.\text{ }{{t}_{1}}<\text{ }{{t}_{2}}\]

    C) \[{{Q}_{1}}<{{Q}_{2}},{{t}_{1}}>{{t}_{2}}\]          

    D) \[{{Q}_{1}}<{{Q}_{2}},{{t}_{1}}<{{t}_{2}}\]

    Correct Answer: B

    Solution :

    during charging \[q={{q}_{0}}\left( 1-{{e}^{-}}^{t/RC} \right)\] \[\frac{dq}{dt}=\frac{{{q}_{0}}}{RC}\,{{e}^{-t/RC}}\] i.e., rate of charging \[\downarrow \] with time for same time interval \[{{Q}_{1}}>{{Q}_{2}}\] Also for depositing same charge time taken by later will be more i.e. \[{{t}_{1}}<{{t}_{2}}\]


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