A capacitor is made of a flat plate of area A | vedclass

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

Question

(A) The arrangement can be viewed as three capacitors connected in parallel,each having an area of $\frac{A}{3}$ but different plate separations.For t

Vedclass · Accepted Answer

$\frac{11 \varepsilon_0 A}{18 d}$

Vedclass · Answer

(A) The arrangement can be viewed as three capacitors connected in parallel,each having an area of $\frac{A}{3}$ but different plate separations.For the first capacitor,the separation is $d$. Its capacitance is $C_1 = \frac{\varepsilon_0 (A/3)}{d} = \frac{\varepsilon_0 A}{3d}$.For the second capacitor,the separation is $2d$. Its capacitance is $C_2 = \frac{\varepsilon_0 (A/3)}{2d} = \frac{\varepsilon_0 A}{6d}$.For the third capacitor,the separation is $3d$. Its capacitance is $C_3 = \frac{\varepsilon_0 (A/3)}{3d} = \frac{\varepsilon_0 A}{9d}$.Since they are in parallel,the equivalent capacitance is $C_{eq} = C_1 + C_2 + C_3$.$C_{eq} = \frac{\varepsilon_0 A}{3d} + \frac{\varepsilon_0 A}{6d} + \frac{\varepsilon_0 A}{9d} = \frac{\varepsilon_0 A}{d} \left( \frac{1}{3} + \frac{1}{6} + \frac{1}{9} \right)$.Taking the least common multiple of $3, 6, 9$,which is $18$:$C_{eq} = \frac{\varepsilon_0 A}{d} \left( \frac{6 + 3 + 2}{18} \right) = \frac{11 \varepsilon_0 A}{18 d}$.

$A$ capacitor is made of a flat plate of area $A$ and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height of each step is $d$,the capacitance of the arrangement is:

Similar Questions

The area of each plate of a parallel plate capacitor is $100 \, cm^2$ and the distance between the plates is $1 \, mm$. It is filled with mica of dielectric constant $6$. The radius of the equivalent capacity of the sphere will be.......$m$.

$A$ parallel plate capacitor is made of two plates with a diameter of $4 \ cm$. What should be the distance between the two plates so that its capacitance is equal to the capacitance of a sphere with a diameter of $20 \ cm$?

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ with a potential difference $V$ between the plates is

$A$ capacitor is made of a flat plate of area $A$ and a second plate of stair-like structure as shown in the figure. The area of each stair is $\frac{A}{3}$ and the height is $d$. The capacitance of the arrangement is

Does the capacitance of a parallel plate capacitor depend on the potential difference $(V)$ between its plates?

Vedclass Test Series

Exam Paper Generator

Online Exam Module