Energy Stored in a Capacitor

The total electrostatic energy stored in both the capacitors (in $\mathrm{\mu J}$) is

The heat generated through $2 \mathrm{\Omega }$ and $8 \mathrm{\Omega }$ resistances separately, when a condenser of $200 \mu \mathrm{F}$ capacity charged to $200 \mathrm{V}$ is discharged one by one, will be

An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of 10V. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance 0.5 mH. The current at a time when the potential difference across the capacitor is 5V is:

On increasing the plate separation of a charged capacitor,  the energy

A charging device consists of eight identical, ideal cells in a proper series connection and a capacitor is charged using this device. Charging process is done by two ways : In first case, capacitor is connected across the whole device (eight cells) in a single step. In second case charging is done in steps which means, first capacitor is connected across a single cell, then across two cells, .........., then across eight cells. If loss of heat in first case is $E_1$ and in second case is $E_2,$ then find $\frac{E_1}{E_2}$

A capacitor has initial charge $q=C E$ with polarity as shown in figure. This capacitor is connected in a circuit with a cell of emf $E$ and resistance $R$ as shown. At $t=0$, the key $k$ is closed. The heat dissipated across $R$ after long time, is $xC{E}^2$. The value of $x$ is:

A capacitor of capacitance $10\mu \mathrm{F}$ is charged up to a potential difference of $2 \mathrm{V}$ and then the cell is removed. Now it is connected to a cell of emf $4 \mathrm{V}$ and is charged fully. In both cases the polarities of the two cells are in the same directions. Total heat produced in the charging process by $4 \mathrm{V}$ cell is : (in $\mathrm{\mu J}$)

A parallel-plate capacitor of capacitance $100 \mathrm{\mu F}$ is connected to a power supply of $200 \mathrm{V}.$ A dielectric slab of dielectric constant $5$ is now inserted into the gap between the plates. Find the change in the electrostatic energy (in $\mathrm{J}$) of the electric field in the capacitor.

Three identical large metal plates of area $A$ are at distances $2d$ and $d$($d\ll$ length of plates) from each other (refer figure). Metal plate $A$ is uncharged, while metal plates $B$ and $C$ have respective charges $+q$ and $-q.$ Metal plates $A$ and $C$ are connected by switch $K$ through a wire. The heat produced after closing the switch $K$ is $\frac{q^2 d}{P{\epsilon }_0 A}.$ Find $P\mathit{.}$

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:

A capacitor of capacitance $2\mu \mathrm{F}$ is charged to a potential $V$ as shown in figure. The percentage loss in stored energy, when switch is turned to position $2$ is

The value of ratio between the energy stored in $5 \mathrm{\mu F}$ capacitor to the $4 \mathrm{\mu F}$ capacitor in the given figure is:

A $60 \mathrm{pF}$ capacitor is fully charged by a $20 \mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $60 \mathrm{pF}$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $nJ$)______.

Two capacitors with capacitance values $C_1=2000\pm 10 \mathrm{pF}$ and $C_2=3000\pm 15 \mathrm{pF}$ are connected in series. The voltage applied across this combination is $V=5.00\pm 0.02 \mathrm{V}.$ The percentage error in the calculation of the energy stored in this combination of capacitors is $\alpha$. Write the value of $\left[\alpha \right],$where $\left[ \right]$ is the greatest integer function.

The capacitor of capacitance $C$ in the circuit shown is fully charged initially, Resistance is $R$.

After the switch $S$ is closed, the time taken to reduce the stored energy in the capacitor to half its initial value is: 

The maximum charge stored on a metal sphere of radius $15 \mathrm{cm}$ may be $7.5 \mathrm{\mu C}$. The potential energy of the sphere in this case is

The capacity of a capacitor is $4\times {10}^{-6} \mathrm{F}$ and its potential is $100 \mathrm{V}$. The energy released on discharging it fully will be

Two concentric conducting shells of radius $R$ and $2R$are shown in the figure below. The inner shell is charged with $Q$ and the outer shell is uncharged. The amount of energy dissipated when the shells are connected by a conducting wire is

Three plates $A$, $B$ and $C$, each of area $50 {\mathrm{cm}}^2$, have separation $3 \mathrm{mm}$ between $A$ and $B$ and $3 \mathrm{mm}$ between $B$ and $C$. The energy stored when the plates are fully charged is

A parallel plate capacitor having a plate separation of $2 \mathrm{mm}$ is charged by connecting it to a $300 \mathrm{V}$ supply. The energy density is