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12th Class Physics Electrostatics & Capacitance Question Bank Case Based (MCQs) - Electric Potential and Capacitance

  • question_answer
    A capacitor with capacitance \[5\,\mu F\] is charged to \[5\,\mu C\]. If the plates are pulled apart to reduce the capacitance to \[2\mu F\], how much work is done?

    A) \[6\centerdot 25\times {{10}^{-6}}J\]

    B) \[3\centerdot 75\times {{10}^{-6}}J\]

    C) \[2\centerdot 16\times {{10}^{-6}}J\]

    D) \[2\centerdot 55\times {{10}^{-6}}J\]

    Correct Answer: B

    Solution :

    Work done \[{{U}_{f}}-{{U}_{i}}=\frac{1}{2}\,\frac{{{q}^{2}}}{{{C}_{f}}}-\frac{1}{2}\frac{{{q}^{2}}}{{{C}_{i}}}\] \[=\frac{{{q}^{2}}}{2}\left[ \frac{1}{{{C}_{f}}}-\frac{1}{{{C}_{i}}} \right]\] \[=\frac{{{\left( 5\times {{10}^{-6}} \right)}^{2}}}{2}\left[ \frac{1}{2\times {{10}^{-6}}}-\frac{1}{5\times {{10}^{-6}}} \right]\] \[=3\,.\,75\,\times {{10}^{-6}}\,J\].


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