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Capacitor question

2000 · Q126
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Capacitor question

2000 · Q126

NEETPhysicsCapacitorMCQ+4 / −1
A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is
  1. A
    U/2U/2U/2
  2. B
    U/4
  3. C
    4U
  4. D
    2U
View written solutionFree

Correct answer: B

Let q be the charge on each capacitor.

∴\therefore∴ Energy stored, U=12CV2=12q2CU = {1 \over 2}C{V^2} = {1 \over 2}{{{q^2}} \over C}U=21​CV2=21​Cq2​

Now, when battery is disconnected and another capacitor of same capacity is connected in parallel to the first capacitor, then voltage across each capacitor, V=q2CV = {q \over {2C}}V=2Cq​

∴\therefore∴ Energy stored = 12C(q2C)2=14.12q2C=14U.{1 \over 2}C{\left( {{q \over {2C}}} \right)^2} = {1 \over 4}.{1 \over 2}{{{q^2}} \over C} = {1 \over 4}U.21​C(2Cq​)2=41​.21​Cq2​=41​U.

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