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AP EAMCET201920 Apr 2019Morning ShiftPhysicsCapacitanceActual

A capacitor is made of a flat plate of area (A ) and a second plate of stair-like structure as shown in the figure. The area of each stair is ( A 3 ) and the height is (d ). The capacitance of the arrangement is

Options

  1. A( ₀ A 3 d )
  2. B( 6 ₀ A 11 d )
  3. C( 3 ₀ A d )
  4. D( 11 ₀ A 18 d )

Correct answer

D. ( 11 ₀ A 18 d )

Step-by-step solution

According to the question, Given, area of each stair (= A 3 ) and height of each stair (=d ) ( ) Capacitance of parallel plate capacitor is given as (C= ₀ A d ) First capacitance of capacitor, (C₁= ₀ A 3 d ) second capacitance of capacitor, (C₂= ₀ A 3(2 d) = ₀ A 6 d ) and third capacitance of capacitor, (C₃= ₀ A 3(3 d) = ₀ A 9 d ) Equivalent capacitance of capacitor, ( gathered C_ e q =C₁+C₂+C₃ C_ e q = ₀ A 3 d + ₀ A 6 d + ₀ A 9 d C_ e q = (6 ₀+3 ₀+2 ₀ ) A 18 d = 11 ₀ A 18 d gathered ) Hence, the capacitance of the

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