Three identical capacitors are first connected in series and then in parallel. The ratio of effective capacitances in the two cases is

9 : 1

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3 : 1

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1 : 3

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1 : 9

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Solution

The correct option is D $1 : 9$
Let the capacitance of each capacitor be $C$ .
Effective capacitance in series connection $\frac{1}{C_{s}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C}$
$∴$ $C_{s} = \frac{C}{3}$
Effective capacitance in parallel connection $C_{p} = C + C + C$
$∴$ $C_{p} = 3 C$
Thus ratio of effective capacitance $\frac{C_{s}}{C_{p}} = \frac{C / 3}{3 C}$
$⟹$ $C_{s} : C_{p} = 1 : 9$

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Three identical capacitors are first connected in series and then in parallel. The ratio of effective capacitances in the two cases is

The correct option is D 1:9Let the capacitance of each capacitor be C.Effective capacitance in series connection 1Cs=1C+1C+1C∴ Cs=C3Effective capacitance in parallel connection Cp=C+C+C∴ Cp=3CThus ratio of effective capacitance CsCp=C/33C⟹ Cs:Cp=1:9