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JEE Main202310 Apr 2023Evening ShiftPhysicsCapacitanceActual

The distance between two plates of a capacitor is d and its capacitance is C 1 , when air is the medium between the plates. If a metal sheet of thickness 2 d 3 and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes C 2 . The ratio C 2 C 1 is

Options

  1. A3   :   1  
  2. B2   :   1  
  3. C4   :   1  
  4. D1   :   1  

Correct answer

A. 3   :   1  

Step-by-step solution

The formula of capacitance is C 1 = ε 0 A d The dielectric constant of metal sheet is K m e t a l = ∞ The new value of capacitance is C 2 = ε 0 A d - t + t K m e t a l = ε 0 A d - 2 d 3 + 0 = 3 C 1 Clearly, the ratio, C 2 C 1 = 3 C 1 C 1 = 3 : 1

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