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Physics · 2023 · 3 marks
CBSE 2023 · Region 1 · Set 2 · Q30
A 100 μ F capacitor is charged by a 12 V battery. (a) How much electrostatic energy is stored by the capacitor? (b) The capacitor is disconnected…
A $\displaystyle 100 \mu \mathrm{~F}$ capacitor is charged by a $\displaystyle 12$ V battery.
(a)
How much electrostatic energy is stored by the capacitor?
(b)
The capacitor is disconnected from the battery and connected in parallel to another uncharged $\displaystyle 100 \mu \mathrm{~F}$ capacitor. What is the electrostatic energy stored by the system?
Marking-scheme solution
$\displaystyle C = 100\ \mu F = 100 \times 10^{-6}\,F,\quad V = 12\,V$
(a)
$\displaystyle U = \dfrac{1}{2}CV^{2}$
$\displaystyle = \dfrac{1}{2} \times 100 \times 10^{-6} \times (12)^{2}$
$\displaystyle = \dfrac{1}{2} \times 10^{-4} \times 144$
$\displaystyle = 72 \times 10^{-4}\,J = 7.2\ \text{m J}$
(b)
$\displaystyle C_{eq} = C_{1} + C_{2}$
$\displaystyle = 200\ \mu F$
$\displaystyle Q = CV$
$\displaystyle = 100 \times 10^{-6} \times 12$
$\displaystyle = 12 \times 10^{-4}\,C$
$\displaystyle U = \dfrac{Q^{2}}{2C_{eq}} = \dfrac{(12 \times 10^{-4})^{2}}{2 \times 200 \times 10^{-6}}$
$\displaystyle = \dfrac{144}{4} \times 10^{-4}$
$\displaystyle = 36 \times 10^{-4}\,J = 3.6\ \text{m J}$
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