KVPY Sample Paper KVPY Stream-SX Model Paper-28

  • question_answer
    A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of \[10V\] between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:

    A) \[692\text{ }pJ\]

    B) \[508\text{ }pJ\]

    C) \[560\text{ }pJ\]

    D) None of these

    Correct Answer: D

    Solution :

    \[W=\frac{{{Q}^{2}}}{2c}-\frac{{{Q}^{2}}}{2ck}\]
    \[=\frac{{{Q}^{2}}}{2c}\left[ 1-\frac{1}{k} \right]\]
    \[=\frac{1}{2}\times 12\times 100pJ\left( 1-\frac{1}{6.5} \right)\]
    \[=\frac{12\times 100\times 11}{2\times 13}pJ\]
    \[=507.69pJ.\]


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