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Question

# A number of capacitors, each of equal capacitance C, are arranged as shown in the figure. The equivalent capacitance between A and B is

A
n2C
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B
(2n+1)C
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C
(n1)n2C
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D
(n+1)n2C
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Solution

## The correct option is D (n+1)n2CAs the capacitors are connected in parallel in all the respectives branches . The equivalent capacitance in respective brances can be given by C,2C,3C,4C........nC Further all the branches are also connected in parallel thus, the equivalent capacitance of the whole circuit can be given by Ceq=C+2C+3C+4C...........+nC This is nothing but the sum of first n natural numbers ∴Ceq=n(n+1)2C

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