The diameter of each plate of an air capacito | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The capacitance of a spherical conductor of radius $R$ is given by $C_1 = 4\pi \varepsilon_0 R$. Given diameter $D = 20\,cm$,so radius $R = 10\,cm

Vedclass · Accepted Answer

$4 	imes 10^{-3}\,m$

Vedclass · Answer

(A) The capacitance of a spherical conductor of radius $R$ is given by $C_1 = 4\pi \varepsilon_0 R$. Given diameter $D = 20\,cm$,so radius $R = 10\,cm = 0.1\,m$. Thus,$C_1 = 4\pi \varepsilon_0 (0.1)$.The capacitance of a parallel plate capacitor is given by $C_2 = \frac{\varepsilon_0 A}{d}$,where $A = \pi r^2$ and $r$ is the radius of the plate. Given diameter of the plate is $4\,cm$,so $r = 2\,cm = 0.02\,m$. Thus,$A = \pi (0.02)^2 = 4\pi 	imes 10^{-4}\,m^2$.Equating the two capacitances,$C_1 = C_2$:$4\pi \varepsilon_0 (0.1) = \frac{\varepsilon_0 (4\pi 	imes 10^{-4})}{d}$$0.1 = \frac{4 	imes 10^{-4}}{d}$$d = \frac{4 	imes 10^{-4}}{0.1} = 4 	imes 10^{-3}\,m$.

The diameter of each plate of an air capacitor is $4\,cm$. To make the capacity of this parallel plate capacitor equal to that of a sphere of diameter $20\,cm$,the distance between the plates will be:

Similar Questions

One plate of a parallel plate capacitor is smaller than the other. What can be said about the charge on the smaller plate?

The capacitance of a parallel plate capacitor is $12\,\mu F$. If the distance between the plates is doubled and the area is halved,then the new capacitance will be.........$\mu F$.

Three plates $A, B$ and $C$ each of area $0.1 \ m^2$ are separated by $0.885 \ mm$ from each other as shown in the figure. A $10 \ V$ battery is used to charge the system. The energy stored in the system is

Four identical plates each of area $a$ are separated by a distance $d$. The connection is shown below. What is the capacitance between $P$ and $Q$?

$A$ parallel plate air capacitor has capacity $C$ and separation between the plates is $d$. $A$ potential difference $V$ is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module