Physics-
General
Easy

Question

A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

  1. open parentheses K plus 3 close parentheses fraction numerator C over denominator 4 end fraction    
  2. left parenthesis K plus left parenthesis b right parenthesis blank fraction numerator C over denominator 4 end fraction    
  3. left parenthesis K plus left parenthesis a right parenthesis blank fraction numerator C over denominator 4 end fraction    
  4. fraction numerator K C over denominator 4 end fraction    

The correct answer is: open parentheses K plus 3 close parentheses fraction numerator C over denominator 4 end fraction


    The capacitor with air as the dielectric has capacitance
    C subscript 1 end subscript equals fraction numerator epsilon subscript 0 end subscript over denominator d end fraction open parentheses fraction numerator 3 A over denominator 4 end fraction close parentheses equals fraction numerator 3 epsilon subscript 0 end subscript A over denominator 4 d end fraction
    Similarly, the capacitor with K as the dielectric constant has capacitance C subscript 2 end subscript equals fraction numerator epsilon subscript 0 end subscript K over denominator d end fraction open parentheses fraction numerator A over denominator 4 end fraction close parentheses equals fraction numerator epsilon subscript 0 end subscript A K over denominator 4 d end fraction
    Since, C subscript 1 end subscript a n d blank C subscript 2 end subscript are in parallel
    C subscript n e t end subscript equals C subscript 1 end subscript plus C subscript 2 end subscript
    equals fraction numerator 3 epsilon subscript 0 end subscript A over denominator 4 d end fraction plus fraction numerator epsilon subscript 0 end subscript A K over denominator 4 d end fraction
    equals fraction numerator epsilon subscript 0 end subscript A over denominator d end fraction open square brackets fraction numerator 3 over denominator 4 end fraction plus fraction numerator K over denominator 4 end fraction close square brackets
    equals fraction numerator C over denominator 4 end fraction left parenthesis K plus 3 right parenthesis

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