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Electrostatic Potential And Capacitance

Question
CBSEENPH12039996

A series combination of n1 capacitors, each of value of C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, 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 C2, in terms of C1, is then

  • fraction numerator 2 straight C subscript 1 over denominator straight n subscript 1 straight n subscript 2 end fraction
  • 16 straight n subscript 2 over straight n subscript 1 C subscript 1
  • 2 straight n subscript 2 over straight n subscript 1 straight C subscript 1
  • fraction numerator 16 space straight C subscript 1 over denominator straight n subscript 1 straight n subscript 2 end fraction

Solution

D.

fraction numerator 16 space straight C subscript 1 over denominator straight n subscript 1 straight n subscript 2 end fraction

Case I . When the capacitors are joined in series

straight U subscript series space equals space 1 half space straight C subscript 1 over straight n subscript 1 left parenthesis 4 straight V right parenthesis squared
Case II. When the capacitors are joined in parallel.
straight U subscript parallel space equals 1 half left parenthesis straight n subscript 2 straight C subscript 2 right parenthesis straight V squared
Given comma space straight U subscript series equals straight U subscript parallel
Or
1 half straight C subscript 1 over straight n subscript 1 left parenthesis 4 straight V right parenthesis squared space equals space 1 half left parenthesis straight n subscript 2 straight C subscript 2 right parenthesis straight V squared

straight C subscript 2 space equals space fraction numerator 16 space straight C subscript 1 over denominator straight n subscript 2 straight n subscript 1 end fraction

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