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JEE Main20198 Apr 2019Morning ShiftPhysicsCapacitanceActual

Voltage rating of a parallel plate capacitor is 500 V . Its dielectric can withstand a maximum electric field of 10 6 V / m . The plate area is 10 - 4 m 2 . What is the dielectric constant if the capacitance is 15 p F ? g i v e n   ϵ 0 = 8.86 × 10 - 12 C 2 / N m 2

Options

  1. A3.8
  2. B8.5
  3. C4.5
  4. D6.2

Correct answer

B. 8.5

Step-by-step solution

Electric field inside capacitor = V d = V d A k ε 0 A k ε 0 = V C A k ε 0 ∵ k A ε 0 d = C 10 6 = 500 × 15 × 10 - 12 10 - 4 × k × 8.85 × 10 - 12 k = 15 × 500 8.85 × 10 - 4 × 10 6 = 75 8.85 k = 8.47 ≈ 8.5

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