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A capacitor of capacity C(0) is charged ...

A capacitor of capacity `C_(0)` is charged to certain potential and enrgy stored in it is `U_(0)`. Now this capacitor is connected in parrallel to uncharged capacitor of capacitance. `C`. Find the loss of energy.

Text Solution

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`U_(0)=(1)/(2)C_(0)V_(0)^(2) C_(0)V_(0)^(2)`
`DeltaU=(1)/(2)(C_(1)C_(2))/(C_(1)+C_(2))(VG_(1)-V_(2))^(2)`
`=(1)/(2)(C-(0)C)/((C_(0)+C))(V_(0)-0)^(2)=((c)/(C_(0)+C))((1)/(2)C_(0)V_(0)^(2))`
`=(CU_(0))/(C_(0)+C)`
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Knowledge Check

  • A capacitor of capacitance C_(1) is kept charged to a potential V. If this capacitor is then connected in parallel to an uncharged capacitor of capacitance C_(2) then fin the final potential difference across the combination.

    A
    `(C_(1)V)/(C_(1)+C_(2))`
    B
    `(C_(2)V)/(C_(1)+C_(2))`
    C
    `1+(C_(2))/(C_(1))`
    D
    `1-(C_(2))/(C_(1))`

  • A capacitor or capacitance C_(1) is charge to a potential V and then connected in parallel to an uncharged capacitor of capacitance C_(2) . The fianl potential difference across each capacitor will be

    A
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    B
    `(C_(2)V)/(C_(1)+C_(2))`
    C
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  • A capacitor C_1 of capacitance C is charged to a potential difference V_0 . The terminal of the charged capacitor are then connected to an uncharged capacitor C_2 of capacitance C//2. Match the entries of Column I with the entries of Column II and choose the correct option from the codes given below.

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