Energy per unit volume for a capacitor having area A and separati… - Vidyadip

MCQ

Energy per unit volume for a capacitor having area $A$ and separation $d$ kept at potential difference $V$ is given by

A
$\frac{Q^{2}}{2 C}$
B
$\frac{1}{2} C V^{2}$
C
$\frac{1}{2 \varepsilon_{0}} \frac{V^{2}}{d^{2}} $
✓
$\frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}$

✓

Answer

Correct option: D.

$\frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}$

d
For a parallel plate capacitor: $\quad C =\frac{ A \varepsilon_{0}}{ d }$

Volume of capacitor $= Ad$

Energy stored in a capacitor $= E =\frac{1}{2} CV ^{2}$

Energy stored per unit volume $= E ^{\prime}=\frac{\frac{1}{2} CV ^{2}}{ Ad }$

$E ^{\prime}=\frac{1}{2} \frac{\frac{A \varepsilon_{0}}{ d } V ^{2}}{ Ad }=\frac{1}{2} \varepsilon_{0} \frac{ V ^{2}}{ d ^{2}}$

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

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

In the figure given, voltage of point $A$ is ............ $V$

For protecting a sensitive equipment from the external magnetic field, it should be

A current of $2\,A$ flows through a wire of crosssectional area $25.0\,mm ^2$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms ^{-1}$ (given, charge on electron $=1.6 \times 10^{-19}\,C$ )

A very high magnetic field is applied to a stationary charge. Then the charge experiences

If $\vec{u}$ is instantaneous velocity of particle and $\vec{v}$ is velocity of wave, then

A body of mass $2 \,kg$ is projected vertically upwards with a velocity of $2\,m\,{\sec ^{ - 1}}$. The K.E. of the body just before striking the ground is ............. $\mathrm{J}$

A source of sound of frequency $256 Hz$ is moving rapidly towards a wall with a velocity of $5m/s$. The speed of sound is $330 m/s.$ If the observer is between the wall and the source, then beats per second heard will be .... $Hz$

Measure of two quantities along with the precision of respective measuring instrument $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ The value of $AB$ will be

Which of the following has the mass closest in value to that of the positron

$(1\;a.m.u = 931\;MeV)$

A block slides down on incline of angle $30^o$ with an acceleration $\frac{g}{4}$. Find the coefficient of kinetic friction