JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer The equivalent capacity of the network, (with all capacitors having the same capacitance C)  

    A)  \[\infty \]                                  

    B)  zero

    C)  \[C[\sqrt{3}-1)/2]\]

    D)  \[C[\sqrt{3}+1)/2]\]

    Correct Answer: C

    Solution :

     \[\frac{1}{{{C}_{\infty }}}=\frac{1}{{{C}_{\infty }}+C}+\frac{2}{C}=\frac{3C+2{{C}_{\alpha }}}{{{C}_{\alpha }}({{C}_{\alpha }}+C)}\]\[2{{C}_{\infty }}^{2}+2C{{C}_{\infty }}-{{C}^{2}}=0\to {{C}_{\infty }}=C\left( \frac{-1+\sqrt{3}}{2} \right)\]

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