A parallel plate capacitor has plates with area $A$ and separation $d$ . A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d $ is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced is
A parallel plate capacitor has plates with area $A$ and separation $d$ . A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d $ is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced is
- A
$K$
- B
$\frac {1}{K}$
- C
$\frac {A}{d^2K}$
- D
$\frac {d^2K}{A}$
Similar Questions
In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.
Heat flow
Electrostatics
$T( r )$
$V( r )$
$j ( r )$
$E ( r )$
We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is
In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.
| Heat flow | Electrostatics |
| $T( r )$ | $V( r )$ |
| $j ( r )$ | $E ( r )$ |
We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is
- [KVPY 2018]
Two identical point charges are placed at a separation of $ l.$ $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?
Two identical point charges are placed at a separation of $ l.$ $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?
A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$
A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$
A charged object is launched inside a time varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$ , its position vector $\vec r$, velocity $\vec v$ and acceleration $\vec a$ are measured. A student watches the video at a later time but mistakenly plays the tape in the reverse direction. What is the position, velocity, and acceleration of the object, at moment $A$ observed by the student respectively?
A charged object is launched inside a time varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$ , its position vector $\vec r$, velocity $\vec v$ and acceleration $\vec a$ are measured. A student watches the video at a later time but mistakenly plays the tape in the reverse direction. What is the position, velocity, and acceleration of the object, at moment $A$ observed by the student respectively?
Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is
Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is