Figure given below shows two identical parallel plate capacitors connected to a battery with switch $S$ closed. The switch is now opened and the free space between the plate of capacitors is filled with a dielectric of dielectric constant $3$. What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric
A$3:1$
B$5:1$
C$3:5$
D$5:3$
IIT 1983, Diffcult
Download our app for free and get started
C$3:5$
c (c) Initially potential difference across both the capacitor is same hence energy of the system is
${U_1} = \frac{1}{2}C{V^2} + \frac{1}{2}C{V^2} = C{V^2}$$……(i)$
In the second case when key $K$ is opened and dielectric medium is filled between the plates, capacitance of both the capacitors becomes $3C$, while potential difference across $A$ is $V$ and potential difference across $B$ is $\frac{V}{3}$ hence energy of the system now is
${U_2} = \frac{1}{2}\,(3C){V^2} + \frac{1}{2}\,(3C)\,{\left( {\frac{V}{3}} \right)^2}$$ = \frac{{10}}{6}\,C{V^2}$$……(ii)$
So, $\frac{{{U_1}}}{{{U_2}}} = \frac{3}{5}$
Download our app
and 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.*
A 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
Two capacitors of capacitances $1\ \mu F$ and $3\ \mu F$ are charged to the same voltages $5\,V$. They are connected in parallel with oppositely charged plates connected together. Then:
The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively
A capacitor is made of a tlat plate of area $A$ and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $\mathrm{d}$, the capacitance of the arrangement is:
Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the dielectric constant of a material, which when fully filled between the plates produces same capacitance?
An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air cored parallel capacitor charged to a potential $V$. The two capacitors share charges and the common potential is $V$. The dielectric constant $K$ is