Physics-
General
Easy

Question

Consider a parallel plate capacitor of 10 mu rightwards arrow over short leftwards arrow F (micro-farad) with air filled in the gap between the plates. Now one half of the space between the plates is filled with a dielectric of dielectric constant 4, as shown in the figure. The capacity of the capacitor changes to

  1. 25 mu F    
  2. 20 mu F    
  3. 40 mu F    
  4. 5 mu F    

The correct answer is: 25 mu F


    C subscript 1 end subscript equals fraction numerator epsilon subscript 0 end subscript open parentheses fraction numerator A over denominator 4 end fraction close parentheses over denominator d end fraction comma C subscript 2 end subscript equals fraction numerator K epsilon subscript 0 end subscript open parentheses fraction numerator A over denominator 2 end fraction close parentheses over denominator d end fraction comma C subscript 3 end subscript equals fraction numerator epsilon subscript 0 end subscript open parentheses fraction numerator A over denominator 4 end fraction close parentheses over denominator d end fraction

    C subscript e q end subscript equals C subscript 1 end subscript plus C subscript 2 end subscript plus C subscript 3 end subscript equals open parentheses fraction numerator K plus 1 over denominator 2 end fraction close parentheses fraction numerator epsilon subscript 0 end subscript A over denominator d end fraction equals open parentheses fraction numerator 4 plus 1 over denominator 2 end fraction close parentheses cross times 10 equals 25 mu F

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