In the given system,the area of each plate is | vedclass

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

Question

(B) Let the potential of the positive terminal of the battery be $V$ and the negative terminal be $0$.Plates $1, 3,$ and $5$ are connected to the posi

Vedclass · Accepted Answer

$\frac{{{\varepsilon _0}AV}}{d},\frac{{ - 2{\varepsilon _0}AV}}{d}$

Vedclass · Answer

(B) Let the potential of the positive terminal of the battery be $V$ and the negative terminal be $0$.Plates $1, 3,$ and $5$ are connected to the positive terminal,so their potential is $V$.Plates $2$ and $4$ are connected to the negative terminal,so their potential is $0$.This arrangement forms capacitors between adjacent plates.Capacitor $C_1$ is formed by plates $1$ and $2$,$C_2$ by plates $2$ and $3$,$C_3$ by plates $3$ and $4$,and $C_4$ by plates $4$ and $5$.Each capacitor has capacitance $C = \frac{{{\varepsilon _0}A}}{d}$.Plate $1$ has only one face forming a capacitor with plate $2$. The charge on plate $1$ is $Q_1 = C 	imes (V - 0) = \frac{{{\varepsilon _0}AV}}{d}$.Plate $4$ has two faces: one forming a capacitor with plate $3$ and another with plate $5$. Both plates $3$ and $5$ are at potential $V$,while plate $4$ is at potential $0$.The charge on plate $4$ is $Q_4 = C 	imes (0 - V) + C 	imes (0 - V) = -\frac{{{\varepsilon _0}AV}}{d} - \frac{{{\varepsilon _0}AV}}{d} = -\frac{{2{\varepsilon _0}AV}}{d}$.

In the given system,the area of each plate is $A$ and the distance between two consecutive plates is $d$. What is the charge on plates $1$ and $4$?

Similar Questions

How will the voltage $(V)$ between the two plates of a parallel plate capacitor depend on the distance $(d)$ between the plates,if the charge on the capacitor remains the same?

$A$ parallel plate capacitor has rectangular plates of area $400 \, cm^2$ separated by a distance of $2 \, mm$ with air as the medium. If a potential difference of $200 \, V$ is applied across the capacitor,what is the charge on the plates?

What is a parallel plate capacitor? Obtain the formula for the capacitance of such a parallel plate capacitor and state the factors on which the value of capacitance depends.

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module