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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Grouping of Capacitors

  • question_answer
    100 capacitors each having a capacity of \[10\mu F\]are connected in parallel and are charged by a potential difference of \[100\,kV\]. The energy stored in the capacitors and the cost of charging them, if electrical energy costs \[108\ paise\ per\ kWh\], will be                  [MP PET 1996; DPMT 2001]

    A)                    \[{{10}^{7}}\ joule\] and \[300\ paise\]

    B)                    \[5\times {{10}^{6}}joule\] and\[300\ paise\]

    C)                    \[5\times {{10}^{6}}joule\] and\[150\ paise\]

    D)                    \[{{10}^{7}}\,joule\]and \[150\ paise\]

    Correct Answer: C

    Solution :

               Energy stored in the capacitor \[=\frac{1}{2}C{{V}^{2}}\times 100\] \[=\frac{1}{2}\times 10\times {{10}^{^{-6}}}\times {{(100\times {{10}^{3}})}^{2}}\times 100=5\times {{10}^{6}}J\] Electric energy costs \[=108\,Paise\,per\,kWH\]\[=\frac{108\,Paise}{3.6\times {{10}^{6}}J}\] \Total cost of charging \[=\frac{5\times {{10}^{6}}\times 108}{3.6\times {{10}^{6}}}\,=150\,Paise\]


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