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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance2 Marks
Question
Net capacitance of three identical capacitors in series is $1\mu\text{F}.$ What will be their net capacitance if connected in parallel?
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
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Answer

$\frac{1}{\text{C}_\text{s}}=\frac{1}{\text{c}}+\frac{1}{\text{c}}+\frac{1}{\text{c}}$$\frac{1}{\text{C}_{s}} = \frac{3}{\text{C}}$
$\text{C}_{\text{s}} = \frac{\text{C} }{ 3 }$
$1= \frac{\text{C}} {3}$
$\therefore\text{C} = 3 \mu\text{F}$
$\text{C}_{p} = \text{C}_{1} + \text{C}_{2} + \text{C}_{3} = 9 \mu \text{F}$
$\frac{\text{E}_{S}}{\text{E}_{P}} = \frac{\frac{1}{2}\text{C}_{s}\text{V}^{2}}{\frac{1}{2}\text{C}_{P}\text{V}^{2}}$
$ = \frac{1}{9}.$

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