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Question: Three capacitors of capacitances \(3\mu F,\mspace{6mu} 9\mu F\) and \(18\mu F\) are connected once i...

Three capacitors of capacitances 3μF, 6mu9μF3\mu F,\mspace{6mu} 9\mu F and 18μF18\mu F are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases (CsCp)\left( \frac{C_{s}}{C_{p}} \right) will be

A

1 : 15

B

15 : 1

C

1 : 1

D

1 : 3

Answer

1 : 15

Explanation

Solution

1Cs=13+19+118=12\frac{1}{C_{s}} = \frac{1}{3} + \frac{1}{9} + \frac{1}{18} = \frac{1}{2} ⇒ Cs=2μFC_{s} = 2\mu F

Cp=3+9+18=30μFC_{p} = 3 + 9 + 18 = 30\mu F ⇒ CsCp=230=115\frac{C_{s}}{C_{p}} = \frac{2}{30} = \frac{1}{15}