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Capacitor question

2022 · 24 Jun · Shift 2 · Q59
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  5. /2022 · 24 Jun · Shift 2 · Q59

Capacitor question

2022 · 24 Jun · Shift 2 · Q59

JEE MainPhysicsCapacitorMCQ+4 / −1
If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)
  1. A
    10
  2. B
    20
  3. C
    30
  4. D
    40
View written solutionFree

Correct answer: A

  1. Use the energy formula for a capacitor

    For a capacitor of fixed capacitance CCC, the energy stored is U=Q22CU = \frac{Q^2}{2C}U=2CQ2​

  2. Let the original charge be QQQ

    After increasing the charge by 2 C2\,\text{C}2C, the new charge becomes (Q+2)(Q+2)(Q+2)

    So the new energy is U′=(Q+2)22CU' = \frac{(Q+2)^2}{2C}U′=2C(Q+2)2​

  3. Use the given percentage increase in energy

    The energy increases by 44%44\%44%, so U′=1.44UU' = 1.44UU′=1.44U

    Therefore, (Q+2)22C=1.44⋅Q22C\frac{(Q+2)^2}{2C} = 1.44\cdot \frac{Q^2}{2C}2C(Q+2)2​=1.44⋅2CQ2​

  4. Simplify

    Cancel 12C\frac{1}{2C}2C1​ from both sides: (Q+2)2=1.44Q2(Q+2)^2 = 1.44Q^2(Q+2)2=1.44Q2

    Taking square root: Q+2=1.2QQ+2 = 1.2QQ+2=1.2Q

    since charge is positive.

  5. Solve for QQQ

    2=1.2Q−Q=0.2Q2 = 1.2Q - Q = 0.2Q2=1.2Q−Q=0.2Q Q=20.2=10Q = \frac{2}{0.2} = 10Q=0.22​=10

  6. Check with options

    The original charge is 10 C\boxed{10\,\text{C}}10C​

    So the correct option is A.

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