Physics-
General
Easy

Question

In the following circuit, the resultant capacitance between A and B is 1 mu F. Then value of C is

  1. fraction numerator 32 over denominator 11 end fraction mu F    
  2. fraction numerator 11 over denominator 32 end fraction mu F    
  3. fraction numerator 23 over denominator 32 end fraction mu F    
  4. fraction numerator 32 over denominator 23 end fraction mu F    

The correct answer is: fraction numerator 32 over denominator 23 end fraction mu F


    12 mF and 6mF are in series and again are in parallel with 4mF.
    Therefore, resultant of these three will be
    equals fraction numerator 12 cross times 6 over denominator 12 plus 6 end fraction plus 4 equals 4 plus 4 equals 8 mu F
    This equivalent system is in series with 1 mF.
    Its equivalent capacitance equals fraction numerator 8 cross times 1 over denominator 8 plus 1 end fraction equals fraction numerator 8 over denominator 9 end fraction mu F ....(i)
    Equivalent of 8mF, 2mF and 2mF
    equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction mu F .....(ii)
    (i) and (ii) are in parallel and are in series with C
    \ fraction numerator 8 over denominator 9 end fraction plus fraction numerator 8 over denominator 3 end fraction equals fraction numerator 32 over denominator 9 end fraction and C subscript e q end subscript equals 1 equals fraction numerator fraction numerator 32 over denominator 9 end fraction cross times C over denominator fraction numerator 32 over denominator 9 end fraction plus C end fractionÞ C equals fraction numerator 32 over denominator 23 end fraction mu F

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