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Capacitor question

2019 · 9 Apr · Shift 1 · Q57
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  5. /2019 · 9 Apr · Shift 1 · Q57

Capacitor question

2019 · 9 Apr · Shift 1 · Q57

JEE MainPhysicsCapacitorMCQ+4 / −1
A capacitor with capacitance 5μF is charged to 5μC. If the plates are pulled apart to reduce the capacitance to 2μF, how much work is done ?
  1. A
    2.16 × 10–6 J
  2. B
    2.55 × 10–6 J
  3. C
    3.75 × 10–6 J
  4. D
    6.25 × 10–6 J
View written solutionFree

Correct answer: C

  1. Given data
  • Initial capacitance: C1=5 μF=5×10−6 FC_1 = 5\,\mu F = 5 \times 10^{-6}\,FC1​=5μF=5×10−6F
  • Final capacitance: C2=2 μF=2×10−6 FC_2 = 2\,\mu F = 2 \times 10^{-6}\,FC2​=2μF=2×10−6F
  • Charge on capacitor: Q=5 μC=5×10−6 CQ = 5\,\mu C = 5 \times 10^{-6}\,CQ=5μC=5×10−6C

Since the capacitor is isolated while the plates are pulled apart, the charge remains constant.

  1. Energy stored in a capacitor when charge is constant

The electrostatic energy is

U=Q22CU = \frac{Q^2}{2C}U=2CQ2​

So,

Initial energy

U1=Q22C1U_1 = \frac{Q^2}{2C_1}U1​=2C1​Q2​

Substitute values:

U1=(5×10−6)22×5×10−6U_1 = \frac{(5 \times 10^{-6})^2}{2 \times 5 \times 10^{-6}}U1​=2×5×10−6(5×10−6)2​

U1=25×10−1210×10−6=2.5×10−6 JU_1 = \frac{25 \times 10^{-12}}{10 \times 10^{-6}} = 2.5 \times 10^{-6}\,JU1​=10×10−625×10−12​=2.5×10−6J

Final energy

U2=Q22C2U_2 = \frac{Q^2}{2C_2}U2​=2C2​Q2​

U2=(5×10−6)22×2×10−6U_2 = \frac{(5 \times 10^{-6})^2}{2 \times 2 \times 10^{-6}}U2​=2×2×10−6(5×10−6)2​

U2=25×10−124×10−6=6.25×10−6 JU_2 = \frac{25 \times 10^{-12}}{4 \times 10^{-6}} = 6.25 \times 10^{-6}\,JU2​=4×10−625×10−12​=6.25×10−6J

  1. Work done in pulling the plates apart

The work done by the external agent equals the increase in electrostatic energy:

W=U2−U1W = U_2 - U_1W=U2​−U1​

W=6.25×10−6−2.5×10−6W = 6.25 \times 10^{-6} - 2.5 \times 10^{-6}W=6.25×10−6−2.5×10−6

W=3.75×10−6 JW = 3.75 \times 10^{-6}\,JW=3.75×10−6J

  1. Option check
  • A: 2.16×10−6 J2.16 \times 10^{-6}\,J2.16×10−6J ❌
  • B: 2.55×10−6 J2.55 \times 10^{-6}\,J2.55×10−6J ❌
  • C: 3.75×10−6 J3.75 \times 10^{-6}\,J3.75×10−6J ✅
  • D: 6.25×10−6 J6.25 \times 10^{-6}\,J6.25×10−6J ❌

Therefore, the correct answer is Option C.

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