MHT CET · Physics · Capacitance
Energy per unit volume for a capacitor having area \(A\) and separation \(d\) kept at potential difference \(V\) is given by
- A \(\frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}\)
- B \(\frac{1}{2 \varepsilon_{0}} \frac{V^{2}}{d^{2}}\)
- C \(\frac{1}{2} C V^{2}\)
- D \(\frac{Q^{2}}{2 C}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}\)
Step-by-step Solution
Detailed explanation
Energy density \(=\frac{1}{2} \varepsilon_{0} E^{2}\)
Since
\(E=\frac{V}{d}\)
Therefore energy \(=\frac{1}{2} \varepsilon_{0}\left(\frac{V^{2}}{d^{2}}\right)\)
Since
\(E=\frac{V}{d}\)
Therefore energy \(=\frac{1}{2} \varepsilon_{0}\left(\frac{V^{2}}{d^{2}}\right)\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The electrostatic potential inside a charged spherical ball is given by \(V=a r^2+\mathrm{b}\) where ' r ' is the distance from its centre and ' \(a\) ' and ' \(b\) ' are constants. The volume charge density of the ball is \(\left[\varepsilon_0=\right.\) permittivity of free space]MHT CET 2024 Hard
- In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is \(\lambda\) is ' \(I\) '. The intensity at a point where the path difference is \(\lambda / 6\) is \(\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right]\) \([\lambda=\) wavelength of light \(][\cos \pi=-1]\)MHT CET 2025 Medium
- When the electron orbiting in hydrogen atom goes from one orbit to another orbit (principal quantum number \(=n\) ), the de-Broglie wavelength \((\lambda)\) associated with it is related to n asMHT CET 2025 Medium
- Two discs having moment of inertia \(\mathrm{l}_{1}\) and \(\mathrm{I}_{2}\) are made from same material have
same mass. Their thickness and radii are \(\mathrm{t}_{1}, \mathrm{t}_{2}\) and \(\mathrm{R}_{1}, \mathrm{R}_{2}\) respectively. The relation
between moment of inertia of each disc about an axis passing through its centre
and perpendicular to its plane and its thickness isMHT CET 2020 Easy - In SHM restoring force is \(F=-k x\), where \(k\) is force constant, \(x\) is displacement and \(A\) is amplitude of motion, then total energy depends uponMHT CET 2007 Easy
- Three solid spheres each of mass ' \(M\) ' and radius ' \(R\) ' are arranged as shown in the figure. The moment of inertia of the system about YY' will be
MHT CET 2021 Medium
More PYQs from MHT CET
- Identify ' \(\mathrm{A}\) ' in the following reaction.
MHT CET 2023 Medium - In triangle ABC , the point P divides BC internally in the ratio \(3: 4\) and Q divides CA internally in the ratio \(5: 3\). If AP and BQ intersect in a point \(G\), then \(G\) divides \(A P\) internally in the ratioMHT CET 2025 Medium
- The area of the region lying in the first quadrant by \(y=4 x^2, x=0, y=2, y=4\) isMHT CET 2024 Easy
- In biprism experiment, 21 fringes are observed in a given region using light of wavelength \(480 Å\). If light of wavelength \(560 Å\) is used, the number of fringes in the same region will beMHT CET 2021 Medium
- If for some \(\alpha \in \mathbb{R}\), the lines \(\mathrm{L}_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}\) and \(\mathrm{L}_2: \frac{x+2}{\alpha}=\frac{y+1}{5-\alpha}=\frac{z+1}{1}\) are coplanar, then the line \(\mathrm{L}_2\) passes through the pointMHT CET 2024 Medium
- A wire having tension produces six beats per second when it vibrates with some tuning fork. When the tension changes to , it vibrates with the same fork with the number of beats remaining unchanged. The frequency of the fork will beMHT CET 2016 Easy