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JEE Main & Advanced AIEEE Paper (Held On 11 May 2011)

  • question_answer
    Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C - R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time needed for reducing the voltage of the fully charged series combination by half is :     AIEEE  Solved  Paper (Held On 11 May  2011)

    A)  10 second        

    B)  5 second         

    C)  2.5 second        

    D)  20 second

    Correct Answer: C

    Solution :

                                    Time constant for parallel combination = 2RC Time constant for series combination \[=\frac{RC}{2}\] In first case: \[V={{V}_{0}}{{e}^{\frac{{{t}_{1}}}{2RC}}}=\frac{{{V}_{0}}}{2}\]                                                                                                  ?..(i) In second case: \[V={{V}_{0}}{{e}^{-\frac{{{t}_{2}}}{(RC/2)}}}=\frac{{{V}_{0}}}{2}\]                                                                                                           ??(ii) From (i) & (ii), \[\frac{{{t}_{1}}}{2RC}=\frac{{{t}_{2}}}{(RC/2)}\]               \[\Rightarrow \]\[{{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{10}{4}=2.5\sec .\]


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