Energy of a Capacitor

Q. I have a capacitor who’s potential difference between the plates is maintained at 5V using a battery. If the capacitance is 5 F and a dielectric of relative permittivity 3 is placed between the plates such that it fully fills the space, What is the change in energy?

1. Increases by $6.24\times {10}^{-4}J$
2. Decreases by $6.24\times {10}^{-4}J$
3. Increases by $9.36\times {10}^{-4}J$
4. Decreases by $9.36\times {10}^{-4}J$

Q. The Electric Field between the capacitor plates is a constant 5N/C. If the region between the plates has vacuum, what is the energy density for the capacitor?

1. $10{\epsilon }_{0}J/m^3$
2. $12.5{\epsilon }_{0}J/m^3$
3. $15{\epsilon }_{0}J/m^3$
4. $Noneofthese$

Q. A capacitor of capacitance $10\mu F$ is connected to a battery providing a potential difference of 10 V across the capacitor. The energy stored inside the capacitor is?

1. $100\mu J$
2. $1mJ$
3. $5mJ$
4. $500\mu J$

Q. The area of the plates of a capacitor is $10c{m}^2$ each and the separation between them is 10 mm. The surface charge density of each facing side is $100\mu C/c{m}^2$. The energy stored inside the capacitor is?

1. $4.6\times {10}^{5}J$
2. $5.6\times {10}^{5}J$
3. $3.6\times {10}^{5}J$
4. None of these

Q. A uniformly charged conducting sphere of radius 9 m has a surface charge density of $10C/m^2$. What is the energy stored inside the sphere (i.e. from 0-R)?

1. 9MJ
2. 90MJ
3. 0J
4. 900KJ

Q. A parallel plate air capacitor is connected to a battery. If plates of the capacitor are pulled further apart, then which of the following statements are correct?

1. Strength of electric field inside the capacitor remain unchanged, if battery is disconnected before pulling the plate.
2. Potential energy in the capacitor decreases if the battery is disconnected before pulling plates apart.
3. Potential energy in the capacitor decreases if the battery remains connected during pulling plates apart.
4. During the process, work is done by an external force applied to pull the plates whether battery is disconnected or it remain connected.

Q. The work done in placing a charge of $8\times {10}^{-18}$ coulomb on a condenser of capacity 100 micro-Farad is:
[AIEEE-2003]

1. $16\times {10}^{-32}joule$
2. $3.1\times {10}^{-26}joule$
3. $4\times {10}^{-10}joule$
4. $32\times {10}^{-32}joule$

Q. When we say that a capacitor with at a certain potential and charges on the plates has a certain amount of energy, what do we mean?

1. The charges on the capacitor radiate energy.
2. A capacitor with a potential difference across its plates has kinetic energy.
3. None of these.
4. An external agent like a battery does work which is stored as the potential energy of the charges on the capacitor.

Q.

The capacity of a condenser is 4x10^-6 farad and its potential is100 volts. The energy released on discharging it fully will be

1. 0.025 Joule

2. 0.02 Joule

3. 0.04 Joule

4. 0.05 Joule

Q. Change Q on a capacitor varies with voltage V as shown in the figure, where Q is taken along the X-axis and V along the Y-axis. The area of triangle OAB represents

1. Capacitance

2. Capacitive reactance

3. Magnetic field between the plates

4. Energy stored in the capacitor