KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    In the circuit of following figure, the final voltage drop across the capacitor C is -

    A) \[\frac{V{{r}_{1}}}{{{r}_{1}}+{{r}_{2}}}\]                

    B) \[\frac{V{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\]

    C) \[\frac{V({{r}_{1}}+{{r}_{2}})}{{{r}_{2}}}\]              

    D) \[\frac{V({{r}_{2}}+{{r}_{1}})}{{{r}_{1}}+{{r}_{2}}+{{r}_{3}}}\]

    Correct Answer: B

    Solution :

    In steady state, the capacitor arm presents an infinite resistance.
    \[\therefore \]Current through that arm = 0
    So the potential difference across C is that across \[{{r}_{2}}\]
    Current through \[{{r}_{2}}=\frac{V}{{{r}_{1}}+{{r}_{2}}}\]
    P.D. across \[{{r}_{2}}=\frac{V{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\]
    P.D. across \[C=\frac{V{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\]

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