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JEE Main202621 January 2026Morning ShiftPhysicsCapacitanceActual

A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates. A sheet having thickness ( 1 3 )^ rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

Options

  1. A4 K C 3 K-1
  2. B3 C K² (2 K+1)²
  3. C3 K C 2 K+1
  4. DC K 2+K

Correct answer

C. 3 K C 2 K+1

Step-by-step solution

Original capacitance: C = ₀ A d After inserting dielectric of thickness d 3 , system becomes two capacitors in series. Vacuum region: C₁ = ₀ A 2d/3 = 3C 2 Dielectric region: C₂ = K ₀ A d/3 = 3KC Equivalent capacitance: 1 C_ new = 1 C₁ + 1 C₂ = 2 3C + 1 3KC = 2K+1 3KC C_ new = 3KC 2K+1

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