In a parallel plate capacitor the separation between the plates is $3\,mm$ with air between them. Now a $1\,mm$ thick layer of a material of dielectric constant $2$ is introduced between the plates due to which the capacity increases. In order to bring its capacity to the original value the separation between the plates must be made......$mm$
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Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant ' $k$ '. The charge on each capacitor is q. Find the extension in the spring at equilibrium
A charge $( - q)$ and another charge $( + Q)$ are kept at two points $A$ and $B$ respectively. Keeping the charge $( + Q)$ fixed at $B$, the charge $( - q)$ at $A$ is moved to another point $C$ such that $ABC$ forms an equilateral triangle of side $l$. The net work done in moving the charge $( - q)$ is
The plates of parallel plate capacitor are charged upto $100\;V$. A $2\,mm$ thick plate is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by $1.6\;mm$. The dielectric constant of the plate is
Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is
A parallel plate air capacitor is charged to a potential difference of $V\, volts$. After disconnecting the charging battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result, the potential difference between the plates
A hollow metal sphere of radius $5\,\, cm$ is charged so that the potential on its surface is $10\,\, V$. The potential at the centre of the sphere is.....$V$
A charged capacitor is allowed to discharge through a resistor by closing the key at the instant $t =0$. At the instant $t = (ln \,4) $ $\mu s$, the reading of the ammeter falls half the initial value. The resistance of the ammeter is equal to
The area of each plate of a parallel plate capacitor is $20\,cm^2$ and separation between the plates is $2\,mm$. If dielectric strength of air is $3 \times 10^6\,V/m,$ the maximum possible value of emf of the battery, which can be connected across the plates of this capacitor and the corresponding charge on the plates is