Download App

Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance2 Marks
Question
Two capacitors of equal capacitance are connected to a battery as shown. Switch $S$ is initially in closed state. Now the switch $S$ is opened and a material of dielectric constant $\epsilon_r=3$ is filled between the plates of the capacitor. Find the ratio of the values of electrical energy stored in the capacitors before and after placing the dielectric material. Image
✓

Answer

Initially, when the switch $S$ is closed, both the capacitors will be at the same potential $V$ because they are connected in parallel,
i.e., $U_i =\frac{1}{2} C_1 V^2+\frac{1}{2} C_2 V^2$
$ =\frac{1}{2}\left(C_1+C_2\right) V^2=CV^2 $
$(i)$ When dielectric material is placed between the plates of the capacitor by keeping the switch $S$ open, then the capacitance of each capacitor will become $\epsilon_r$ times. And since capacitor $A$ is still connected to the battery.
Therefore, the value of potential difference on it will be equal to the value $V$ of the initial potential difference, whereas the new value of potential difference on capacitor $B$ will become $V ^{\prime}$
$=\frac{ V }{\epsilon_r}$ and the charge will remain constant. Therefore in this situation the electric energy of the system will be :
$U _f=\frac{1}{2} C ^{\prime} V ^2+\frac{1}{2} C ^{\prime} V ^{\prime 2}$
$=\frac{1}{2} \epsilon_r CV ^2+\frac{1}{2} \epsilon_r C \left(\frac{ V }{\epsilon_r}\right)^2$
$\because V ^{\prime}=\frac{ V }{\epsilon_r}$ and $C ^{\prime}=\epsilon_r C$
$=\frac{1}{2} CV ^2\left(\epsilon_r+\frac{1}{\epsilon_r}\right)=\frac{1}{2} CV ^3\left(3+\frac{1}{3}\right)$
$=$$\frac{1}{2} CV ^2\left(\frac{10}{3}\right)$
Image
On dividing eq.$(ii)$ by eq. $(i),$
Therefore, $ \frac{U_f}{U_i}=\frac{\frac{10}{6} CV^2}{CV^2} $ or $ \frac{U_f}{U_i}$
$=1.66$
$\because \epsilon_r=3$ Ans.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Electrostatic Potential and Capacitance→Electrostatic Potential and Capacitance — all question types→Physics STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Explain paramagnetism and paramagnetic substances.
→
Work function of sodium is 2.3eV. Does sodium show photoelectric emission for light of wavelength $6800\mathring{\text{A}}?$
→
A long narrow horizontal slit is placed $1\ mm$ above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen $1.0m$ away from the slit. Find the fringe$-$width if the light used has a wavelength of $700\ nm.$
→
Write the characteristics of electric field lines.
→
Give the sign convection for electric or magnetic field leaving and entering the plane of the paper.
→
A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.
→
The total energy of electron is negative. What do you mean by this fact? It is positive then what is the indication?
→
A hollow spherical body of inner and outer radii $6\ cm$ and $8\ cm$ respectively floats half submerged in water. Find the density of the material of the sphere.
→
Find the equivalent resistance of the network shown in figure. between the points a and b.
→
The current in a discharging LR circuit is given by $\text{i}=\text{i}_0\text{e}^{\frac{-\text{t}}{\tau}}$ where $\tau$ is the time constant of the circuit. Calculate the rms current for the period $\text{t}=0$ to $\text{t}=\tau.$
→