KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    A circuit is arranged as shown. At time \[\operatorname{t}=0 s,\] switch S is placed in position 1. At  t= 5 s, contact is changed from 1 to 2. The voltage across the capacitor is measured at t = 5 s, and at t = 6 s. Let these voltages be \[{{\operatorname{V}}_{1}}\] and \[{{\operatorname{V}}_{2}}\] respectively. Then \[{{\operatorname{V}}_{1}}\] and \[{{\operatorname{V}}_{2}}\] respectively are

    A) 10 volt and 0 volt

    B) 9.18 volt and 3.67 volt

    C) 9.18 volt and 3.37 volt

    D) 10 volt and 3.67 volt

    Correct Answer: C

    Solution :

    (i) \[V={{V}_{0}}\left( 1-{{e}^{-\frac{t}{2RC}}} \right);\]
    \[V={{V}_{0}}\left( 1-{{e}^{-\frac{5}{2}}} \right)=9.18volt\]
    \[V={{V}_{0}}\left( {{e}^{-\frac{t}{RC}}} \right)=9.18{{e}^{-1/1}}\]

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