CBSE 2023 · Region 1 · Set 2 · Q30 · 3 marks
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?
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)
$\displaystyle C_{eq} = C_{1} + C_{2}$
$\displaystyle = 200\ \mu F$
$\displaystyle Q = CV$
$\displaystyle = 100 \times 10^{-6} \times 12$
$\displaystyle = 12 \times 10^{-4}\,C$
$\displaystyle U = \dfrac{Q^{2}}{2C_{eq}} = \dfrac{(12 \times 10^{-4})^{2}}{2 \times 200 \times 10^{-6}}$
$\displaystyle = \dfrac{144}{4} \times 10^{-4}$
$\displaystyle = 36 \times 10^{-4}\,J = 3.6\ \text{m J}$
Electrostatic Potential and CapacitanceEnergy Stored in a CapacitorApplyshort_answermedium
Practice Electrostatic Potential and Capacitance →All Electrostatic Potential and Capacitance questions
More from Electrostatic Potential and Capacitance
- (i) A parallel plate capacitor with plate area A and plate separation d has a capacitance C 0. A slab of…2025 · asked 3×
- (i) In the figure, OA and OB show the variation of electric potential V at a point due to two point charges Q…2026 · asked 3×
- Two metal spheres of radii r 1 and r 2( r 1) having charges q 1 and q 2 respectively kept in air, are brought…2026 · asked 3×
- (i) Explain the following statements giving reason: (I) An equipotential surface through a point is normal to…2026 · asked 3×
- A parallel plate capacitor has two parallel plates which are separated by an insulating medium like air,…2025 · asked 3×
- (i) Derive an expression for potential energy of an electric dipole p in an external uniform electric field…2024 · asked 3×
- Dielectrics play an important role in design of capacitors. The molecules of a dielectric may be polar or…2024 · asked 3×
- The figure shows four pairs of parallel identical conducting plates, separated by the same distance 2.0 cm…2024 · asked 3×
CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.