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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance5 Marks
Question
Three capacitors having capacitances $20\mu\text{F},\ 30\mu\text{F}$ and $40\mu\text{F}$ are connected in series with a 12V battery. Find the charge on each of the capacitors. How much work has been done by the battery in charging the capacitors?
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Answer


$\therefore$ The equivalent capacity
$\text{C}=\frac{\text{C}_1\text{C}_2\text{C}_3}{\text{C}_2\text{C}_3+\text{C}_1\text{C}_3+\text{C}_1\text{C}_2}$
$=\frac{20\times30\times40}{30\times40+20\times40+20\times30}=\frac{24000}{2600}=9.23\mu\text{F}$
Let Equivalent charge at the capacitor = q
$\text{C}=\frac{\text{q}}{\text{V}}$
$\Rightarrow\text{q}=\text{C}\times\text{V}=9.23\times12=110\mu\text{C}$ on each.
As this is a series combination, the charge on each capacitor is same as the equivalent charge which is $110\mu\text{C}.$
Let the work done by the battery = W
$\therefore\text{V}=\frac{\text{W}}{\text{q}}$
$\Rightarrow\text{W}=\text{Vq}=110\times12\times10^{-6}$
$=1.33\times10^{-3}\text{J.}$

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