A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V =12\, V$ between its plates. The charging battery is now disconnected and a porcelin plate with $k =7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of $..........pJ$. (Assume no friction)
JEE MAIN 2021, Medium
Download our app for free and get started
$U _{ i }=\frac{1}{2} \times 14 \times 12 \times 12 pJ \quad\left(\because U =\frac{1}{2} CV ^{2}\right)$
$=1008 pJ$
$U _{ f }=\frac{1008}{7} pJ =144 pJ \quad\left(\because C _{ m }= k C _{0}\right)$
Mechanical energy $=\Delta U$
$=1008-144$
$=864 pJ$
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
- 1A 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, isView Solution
- 2A uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{{3{V_0}}}{2},\;\frac{{5{V_0}}}{4},\;\frac{{3{V_0}}}{4}$ and $\frac{{{V_0}}}{4}$ have rasius $R_1,R_2,R_3$ and $R_4$ respectively. ThenView Solution
- 3A point charge $Q$ is placed in uniform electric field $\vec E = E_1 \hat i + E_2\hat j$ at position $(a, b)$. Find work done in moving it to position $(c, d)$View Solution
- 4Four capacitors of capacitance $10\,mF$ and a battery of $200\,V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed .....$\mu C$View Solution
- 5A spherical conductor of radius $2\,m$ is charged to a potential of $120\,V.$ It is now placed inside another hollow spherical conductor of radius $6\,m.$ Calculate the potential to which the bigger sphere would be raised......$V$View Solution
- 6A thin metallic partition of negligible thickness is inserted between two shaded metallic plates as shown. The remaining ends are then packed with insulating plates to form a container like structure.$2$ taps shown are opened at $t = 0$ and finally closed at $t = 5s$. Find capacitance of system between $A$ and $B$ after closing taps. (Assume liquid to be non conducting) Volumetric flow rates and dieletric constants of liquid are given.View Solution
- 7For a uniformly charged thin spherical shell, the electric potential $(V)$ radially away from the center $(O)$ of shell can be graphically represented asView Solution
- 8The area of the plates of a parallel plate condenser is $A$ and the distance between the plates is $10\,mm$. There are two dielectric sheets in it, one of dielectric constant $10$ and thickness $6\,mm$ and the other of dielectric constant $5$ and thickness $4\,mm$. The capacity of the condenser isView Solution
- 9Two capacitors having capacitance $C _{1}$ and $C _{2}$ respectively are connected as shown in figure. Initially, capacitor $C _{1}$ is charged to a potential difference $V$ volt by a battery. The battery is then removed and the charged capacitor $C_{1}$ is now connected to uncharged capacitor $C _{2}$ by closing the switch $S$. The amount of charge on the capacitor $C _{2}$, after equilibrium isView Solution
- 10View SolutionA parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then