Energy of a Capacitor

Q. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

1. increases by a factor of 2.
2. increases by a factor of 4.
3. decreases by a factor of 2.
4. remains the same.

Q. In a series $LR$ circuit, power of $400\text{W}$ is dissipated from a source of $250\text{V},50\text{Hz}.$ The power factor of the circuit. is $0.8$. In order to bring the power factor to unity, a capacitor of value $C$ is added in series to the $L$ and $R$. Taking the value $C$ as $\left(\frac{n}{3\pi }\right)\mu \text{F},$ then value of $n$ is ________.

Q. A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position $2$, the percentage of its stored energy dissipated is

1. $75\%$
2. $80\%$
3. $0\%$
4. $20\%$

Q.

A certain household has consumed $250units$ of energy during a month. How much energy is this in joules?

Q. Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius $10\text{cm}$ surrounding the total charge is $25{\text{N-m}}^2/\text{C}$. The flux over a concentric sphere of radius $20\text{cm}$ will be

1. $25{\text{N-m}}^2/\text{C}$
2. $50{\text{N-m}}^2/\text{C}$
3. $75{\text{N-m}}^2/\text{C}$
4. $100{\text{N-m}}^2/\text{C}$

Q. A capacitor of $20\mu F$ charged to $500\text{V}$, is connected in parallel to another capacitor of $10\mu F$ charged to $200\text{V}$, Find the common potential?

1. $200\text{V}$
2. $400\text{V}$
3. $600\text{V}$
4. $800\text{V}$

Q. Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.

1. 9 : 16
2. 5 : 9
3. 2 : 3
4. 3 : 5

Q. Two condensers, one of capacity $C$ and other of capacity $\frac{C}{2}$ are connected to a $V$ - volt battery as shown in the figure. The work done in charging both the condensers fully is

1. $\frac{3}{4}C{V}^2$
2. $\frac{1}{4}C{V}^2$
3. $2C{V}^2$
4. $\frac{1}{2}C{V}^2$

Q. A neutral conducting sphere of radius $R$ contains two spherical cavities of radii $a$ and $b$ that contains point charges $q_a$ and $q_b$ placed at the center of each cavity as shown in the figure below . Find the electric field inside the cavity of radius $a$ at a distance $r$ from the center of cavity.

1. $\frac{q_a}{4\pi {\epsilon }_0{r}^2}$
2. $\frac{q_a+q_b}{4\pi {\epsilon }_0{r}^2}$
3. $\frac{q_a-q_b}{4\pi {\epsilon }_0{r}^2}$
4. Zero

Q. The charge on the $4\mu \text{F}$ capacitor in the given circuit is ____ (in $\mu \text{C})$.

1. $12$
2. $24$
3. $36$
4. $32$

Q. If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

1. $E^2$
2. $E$
3. $E^3$
4. $1/E^2$

Q.

Two springs of spring constants 1500 N/mand 3000 N/mrespectively are stretched with the same force. The ratio of potential energies will be

1. 4 : 1

2. 1 : 4

3. 2 : 1

4. 1 : 2

Q.

A $6\mu F$ capacitor is charged from $10V$ to $20V$. An increase in energy will be?

Q. Three capacitors \(C_1 = 2 \mu \text F, ~C_2 = 6 \mu\text F ~\text{and}~ C_3 = 12 \mu\text F\) are connected as shown in figure. Find the ratio of the charges on capacitors \(C_1, ~C_2 ~\text{and}~ C_3\) respectively

Q.

How does an inductor work?

Q. A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

Q.

A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

Q. Two identical parallel plate capacitors are connected in series to a battery of $100\text{V}$. A dielectric slab of dielectric constant $4$ is inserted between the plates of the second capacitor to fill the space between its plates, completely. The potential difference across the capacitors will now be, respectively.

1. $50\text{V},50\text{V}$
2. $80\text{V},20\text{V}$
3. $20\text{V},80\text{V}$
4. $75\text{V},25\text{V}$

Q.

A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.

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.

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If $\sigma$ is the surface tension of soap solution, the energy spent in doing so is

1. $3\pi \sigma r^2$

2. $6\pi \sigma r^2$

3. $12\pi \sigma r^2$

4. $24\pi \sigma r^2$

Q. A piece of cloud having area $25\times {10}^6{m}^2$ and electric potential of ${10}^5$ volts. If the height of cloud is 0.75 km, then energy of electric field between earth and cloud will be

1. 250 J
2. 750 J
3. 1225 J
4. 1475 J

Q.

Where does the energy of a capacitor reside?

Q. A capacitor stores energy within a dielectric between the conducting plates in the form of .

1. a magnetic field
2. positive voltage
3. an electric field

Q. A hollow charged metal sphere has radius r. If the potential difference between its surface and a point { at a distance 3 rfrom the centre is V, then the electric field intensity at distance 3r from the centre is

Q. Find the equivalent capacitance between $A$ and $B$ in the circuit shown in the figure. Given $C=5\mu \text{F}$

1. $25\mu \text{C}$
2. $10\mu \text{C}$
3. $7.5\mu \text{C}$
4. $7\mu \text{C}$

Q. In finding the electric field using Gauss law, the formula $|\overrightarrow{E}|=\frac{q_{enc}}{{\epsilon }_0|A|}$ is applicable. In the formula ${\epsilon }_0$ is permittivity of free space, $A$ is the area of Gaussian surface and $q_{enc}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation ?

1. Only when the Gaussian surface is an equipotential surface.
2. Only when a Gaussian surface is an equipotential surface and $|\overrightarrow{E}|$ is constant on the surface.
3. Only when $|\overrightarrow{E}|=$ constant on the surface.
4. For any choice of Gaussian surface.

Q. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of energy stored in the capacitor and work done by the battery will be?

1. $\frac{1}{4}$
2. $1$
3. $\frac{2}{1}$
4. $\frac{1}{2}$

Q. An ellipsoidal cavity is carved within a perfect conductor. A charge $+q$ is placed at the centre of the cavity. The points $A$ and $B$ are on the cavity surface as shown in the figure. Then

1. electric field near $A$ in the cavity $=$ electric field near $B$ in the cavity
2. charge density near $A$ on the conductor surface $=$ charge density near $B$ on the conductor surface
3. potential at $A=$ potential at $B$
4. total electric field flux through the surface of the cavity is $\frac{q}{{ϵ}_o}$

Q.

Why is capacitance constant?