Energy Stored in a Capacitor and Energy Stored in Electric Field

An uncharged capacitor of capacitance $100 \mathrm{\mu F}$ is connected to a battery of emf$20 \mathrm{V}$ at $t=0$ through a resistance of $10 \mathrm{\Omega }$, then:

(i) The maximum rate at which energy is stored in the capacitor

(a) $10 \mathrm{J} {\mathrm{s}}^{-1}$

(b)  $20 \mathrm{J} {\mathrm{s}}^{-1}$

(c) $40 \mathrm{J} {\mathrm{s}}^{-1}$

(d) $5 \mathrm{J} {\mathrm{s}}^{-1}$

(ii) Time at which the rate has this maximum value

(a) $\left(4\ln 2\right) \mathrm{ms}$

(b) $\left(2\ln 2\right) \mathrm{ms}$

(c) $\left(\ln 2\right) \mathrm{ms}$

(d) $\left(3\ln 2\right) \mathrm{ms}$

A $600 \mathrm{pF}$ capacitor is charged by $200 \mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $600 \mathrm{pF}$ capacitor. Electrostatic energy lost in the process is _____ $\mathrm{\mu J}$.

In the circuit shown, the energy stored in the capacitor is $n \mathrm{\mu J}$. The value of $n$ is _____.

A parallel plate capacitor of capacitance $2 \mathrm{F}$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $\frac{E_2}{E_1}$ is

Find the energy stored in the capacitor in the given circuit.

Condenser is a device used to store

A parallel plate capacitor of capacitance $8 \mu \mathrm{F}$ is connected to a $20 \mathrm{V}$ battery and is allowed to charge completely. The battery is then disconnected and a dielectric material of dielectric constant $8$ is introduced between the plates of the capacitor. The energy dissipated in this process is

A $10 \mu \mathrm{F}$ capacitor is charged by $200 \mathrm{V}$. The heat lost in charging it is

If capacitance is increased by $2$ times what will be the energy? Give the answer for vice versa case also?

Calculate the equivalent capacity of the system as shown in the figure. What is the energy stored in the system if voltage applied is $500 \mathrm{V}$.

The capacitance of system is $C$. If key is closed, the total energy loss is equal to:

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

The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant $K$ is inserted to fill the whole space between the plates with voltage with voltage source remaining connected to the capacitor. Then

A capacitor of capacitance $5 \mathrm{\mu F}$ is connected to a source of constant emf of $200 \mathrm{V}$ for a long time, then the switch was shifted to contact $1$ from contact $2$ . The amount of heat generated in the $500 \mathrm{\Omega }$ resistance is $H$. Find value of $16H$ (in $\mathrm{J}$).

In the given circuit, find the heat generated if switch $S$ is closed.

Two capacitors one of capacity $C$ and the other of capacity $\frac{C}{2}$, are connected to a $V$ volt battery, as shown. Work done by the battery in charging of this combination will be:

In the circuit shown switch is placed in position-$1$ till the capacitor is charged to half of the maximum possible charge in this situation.

Now the switch $S$ is placed in position-$2$. The maximum energy lost by the circuit after $S$ is placed in position-$2$ is $\frac{x}{8}C{E}^2$. Find $x$.

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

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 $P\mathit{.}$