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Electrostatic Potential And Capacitance

Question
CBSEENPH12040111

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

  • Increases by a factor of 4

  • Decreases by a factor of 2

  • Increases by a factor of 2

  • Remains the same

Solution

B.

Decreases by a factor of 2


Charge on capacitor
q = CV
when it is connected with another uncharged capacitor.

straight V subscript straight c space equals space fraction numerator straight q subscript 1 plus straight q subscript 2 over denominator straight C subscript 1 plus straight C subscript 2 end fraction space equals space fraction numerator straight q plus 0 over denominator straight C plus straight C end fraction
straight V subscript straight c space equals space straight V over 2
Initial space energy
straight U subscript straight i space equals space 1 half CV squared
Final space energy
straight U subscript straight f space equals 1 half straight C open parentheses straight V over 2 close parentheses squared plus 1 half straight C open parentheses straight V over 2 close parentheses squared
space equals open parentheses space CV squared over 4 close parentheses
Loss space of space energy space equals straight U subscript straight i space minus straight U subscript straight f
space equals space CV squared over 4

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