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NEET Sample Paper NEET Sample Test Paper-24

  • question_answer
    A series combination of\[{{n}_{1}}\]capacitors, each of value \[{{C}_{1}},\]is charged by a source of potential difference 4 V. When another parallel combination of\[{{n}_{2}}\]capacitors, each of value\[{{C}_{2}}\] is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of \[{{C}_{2}},\]in terms of \[{{C}_{1}},\]is then

    A)  \[\frac{2{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}}\]             

    B)  \[16\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]

    C)  \[2\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\]               

    D)  \[\frac{16\,{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}}\]

    Correct Answer: D

    Solution :

     Case I. When the capacitors are connected in series \[{{U}_{series}}=\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}\] Case II. When the capacitors are connected in parallel \[{{U}_{parallel}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}\] According to question, \[{{U}_{series}}={{U}_{parallel}}\] or         \[=\frac{1}{2}\frac{{{C}_{1}}}{{{n}_{1}}}{{(4V)}^{2}}=\frac{1}{2}({{n}_{2}}{{C}_{2}}){{V}^{2}}\] \[\Rightarrow \]   \[{{C}_{2}}=\frac{16{{C}_{1}}}{{{n}_{2}}{{n}_{1}}}\]


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