Physics-
General
Easy

Question

The capacity of a parallel plate condenser is 10 mu F without dielectric. Dielectric of constant 2 is used to fill half the distance between the plates, the new capacitance in mu F is

  1. 10    
  2. 20    
  3. 15    
  4. 13.33    

The correct answer is: 13.33


    C equals fraction numerator A epsilon subscript 0 end subscript over denominator d end fraction equals 10 mu F
    C subscript 1 end subscript equals fraction numerator A epsilon subscript 0 end subscript over denominator d minus t plus fraction numerator t over denominator k end fraction end fraction equals fraction numerator A epsilon subscript 0 end subscript over denominator d minus fraction numerator d over denominator 2 end fraction plus fraction numerator d over denominator 2 k end fraction end fraction equals fraction numerator A epsilon subscript 0 end subscript over denominator fraction numerator d over denominator 2 end fraction open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses end fraction equals fraction numerator 4 over denominator 3 end fraction. fraction numerator A epsilon subscript 0 end subscript over denominator d end fraction
    therefore C subscript 1 end subscript equals fraction numerator 4 over denominator 3 end fraction cross times 10 equals 13.33 mu F

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