A parallel plate air capacitor has capacitanc | vedclass

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

Question

(C) Let the area of the plates be $A$ and the distance between them be $d$. The capacitance of the air capacitor is $C_p = \frac{\epsilon_0 A}{d}$.Whe

Vedclass · Accepted Answer

$\frac{K_1+K_2}{2 K_1 K_2}$

Vedclass · Answer

(C) Let the area of the plates be $A$ and the distance between them be $d$. The capacitance of the air capacitor is $C_p = \frac{\epsilon_0 A}{d}$.When the space is filled with two parallel layers of dielectric materials of thickness $d/2$ each,the capacitor acts as two capacitors $C_1$ and $C_2$ in series.$C_1 = \frac{K_1 \epsilon_0 A}{d/2} = \frac{2 K_1 \epsilon_0 A}{d} = 2 K_1 C_p$.$C_2 = \frac{K_2 \epsilon_0 A}{d/2} = \frac{2 K_2 \epsilon_0 A}{d} = 2 K_2 C_p$.Since they are in series,the equivalent capacitance $C_K$ is given by $\frac{1}{C_K} = \frac{1}{C_1} + \frac{1}{C_2}$.$\frac{1}{C_K} = \frac{1}{2 K_1 C_p} + \frac{1}{2 K_2 C_p} = \frac{1}{2 C_p} \left( \frac{1}{K_1} + \frac{1}{K_2} \right) = \frac{1}{2 C_p} \left( \frac{K_1 + K_2}{K_1 K_2} \right)$.Therefore,$C_K = \frac{2 C_p K_1 K_2}{K_1 + K_2}$.The ratio $\frac{C_p}{C_K} = \frac{C_p}{\frac{2 C_p K_1 K_2}{K_1 + K_2}} = \frac{K_1 + K_2}{2 K_1 K_2}$.

$A$ parallel plate air capacitor has capacitance $C_p$. It is equally filled with parallel layers of materials of dielectric constants $K_1$ and $K_2$. Now its capacity becomes $C_K$. The ratio $C_P$ to $C_K$ is

Similar Questions

The distance between the plates of a parallel plate capacitor is $8\,mm$ and the potential difference $(P.D.)$ is $120\,V$. If a $6\,mm$ thick slab of dielectric constant $K = 6$ is introduced between its plates,then:

The area of the plates of a parallel plate capacitor is $A$ and the distance between the plates is $10\,mm$. There are two dielectric sheets in it,one of dielectric constant $10$ and thickness $6\,mm$ and the other of dielectric constant $5$ and thickness $4\,mm$. The capacity of the capacitor is

$A$ charged conductor produces an electric field of intensity $10^3 \ V/m$ just outside its surface in vacuum. Then,it produces an electric field of intensity $E$ just outside its surface,when it is placed in a medium of dielectric constant $4$. The value of $E$ will be (in $V/m$)

$A$ capacitor of capacitance $C = 10 \ \mu F$ is connected to a $12 \ V$ battery. When a dielectric slab of dielectric constant $K = 5$ is inserted between its plates,how much additional charge (in $\mu C$) will flow from the battery to the capacitor?

Two identical parallel plate air capacitors are connected in series to a battery of emf $V$. If one of the capacitors is completely filled with a dielectric material of constant $K$,then the potential difference across the other capacitor will become:

Vedclass Test Series

Exam Paper Generator

Online Exam Module