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Capacitor question

2002 · Shift 0 · Q162
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Capacitor question

2002 · Shift 0 · Q162

JEE MainPhysicsCapacitorMCQ+4 / −1
If there are nnn capacitors in parallel connected to VVV volt source, then the energy stored is equal to
  1. A
    CVCVCV
  2. B
    12nCV2{1 \over 2}nC{V^2}21​nCV2
  3. C
    CV2C{V^2}CV2
  4. D
    12nCV2{1 \over {2n}}C{V^2}2n1​CV2
View written solutionFree

Correct answer: B

  1. Capacitors in parallel

    If there are nnn identical capacitors, each of capacitance CCC, connected in parallel, then the equivalent capacitance is

    Ceq=nCC_{\text{eq}} = nCCeq​=nC

  2. Energy stored in a capacitor combination

    The energy stored in a capacitor is given by

    U=12CV2U = \frac{1}{2} C V^2U=21​CV2

    So for the equivalent capacitance Ceq=nCC_{\text{eq}} = nCCeq​=nC connected across a voltage VVV,

    U=12CeqV2U = \frac{1}{2} C_{\text{eq}} V^2U=21​Ceq​V2

  3. Substitute Ceq=nCC_{\text{eq}} = nCCeq​=nC

    U=12(nC)V2=12nCV2U = \frac{1}{2}(nC)V^2 = \frac{1}{2} n C V^2U=21​(nC)V2=21​nCV2

  4. Match with the options

    • A: CVCVCV — incorrect, wrong formula and wrong dimensions
    • B: 12nCV2\frac{1}{2}nCV^221​nCV2 — correct
    • C: CV2CV^2CV2 — missing factor 12\frac{1}{2}21​ and nnn
    • D: 12nCV2\frac{1}{2n}CV^22n1​CV2 — incorrect

Therefore, the correct answer is B.

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