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Question

# An infinite number of identical capacitors, each of capacitance 1μF are connected as shown in the figure. Then the equivalent capacitance between A and B is :

A
1μF
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B
2μF
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C
12μF
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D
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Solution

## The correct option is B 2μFFirstly calculating the equivalent capacitance of capacitors which are in series,1Ceq=1C1+1C2+...+1CnFor C1=C2=.....=Cn, we get Ceq=CnThus for first row, we get CA=CFor 2nd row, we get CB=C2For third row we get CC=C4 and so on.Looking at the diagram all the capacitors are in parallel, now ultimate equivalent capacitanceCfinal=CA+CB+CC+...+C∞⇒Cfinal=C+C2+C4+C8+...+C∞ which represents a geometric progression⇒Cfinal=C1−12=2C=2μF

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