A parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, volt$ battery. Then the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ and the plates are maintained in connection with the battery, is
Medium
Download our app for free and get started
${\rm{C}} = \mathop {\frac{{{ \in _0}{\rm{A}}}}{{\rm{d}}}}\limits_{({\rm{here}}\,\,{\rm{d}} - 1{\rm{mm}})} \quad {{\rm{C}}_{{\rm{Final}}}} = \frac{{{ \in _0}{\rm{A}}}}{{10{\rm{d}}}} = \frac{{\rm{C}}}{{10}}$
$\mathrm{Loss}=\mathrm{E}_{\mathrm{initial}}-\mathrm{E}_{\mathrm{final}}$
$\quad=\frac{1}{2} \mathrm{V}^{2}\left(\mathrm{C}-\frac{\mathrm{C}}{10}\right)$
$=12.5 \mathrm{\,ergs}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1In the $RC$ circuit shown, switch is closed at $t = 0$ . Graphs showing variation of potential $(V_R)$ across resistor and potential $(V_C)$ across capacitor are given. Time constant of circuit is approximately equal to.....$ms$View Solution
- 2Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance $C$, a potential $V$, and a charge $q$, then the capacitance of the bigger drop will beView Solution
- 3In figure a system of four capacitors connected across a $10\, V$ battery is shown. Charge that will flow from switch $S$ when it is closed isView Solution
- 4An electric charge $10^{-3}\ \mu C$ is placed at the origin $(0, 0)$ of $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt 2 ,\sqrt 2 )$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be......$V$View Solution
- 5In the figure shown the electric potential energy of the system is: ( $q$ is at the centre of the conducting neutral spherical shell of inner radius $a$ and outer radius $b$ )View Solution
- 6Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.View Solution
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \in_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \in_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \in_0 a}$.
- 7A parallel plate capacitor filled with a medium of dielectric constant $10$ , is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant $15$ . Then the energy of capacitor will ......................View Solution
- 8Two capacitors of capacities ${C_1}$ and ${C_2}$ are charged to voltages ${V_1}$ and ${V_2}$ respectively. There will be no exchange of energy in connecting them in parallel, ifView Solution
- 9A parallel plate capacitor with a dielectric slab completely occupying the space between the plates is charged by a battery and then disconnected. The slab is pulled out with a constant speed. Which of the following curves represent qualitatively the variation of the capacitance $C$ of the system with time?View Solution
- 10View SolutionDielectric constant for metal is