What will be the capacity of a parallel-plate | vedclass

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

Question

(A) Let the area of each plate be $A$ and the distance between them be $d$. The capacity of the capacitor in air is $C = \frac{\varepsilon_0 A}{d}$.Wh

Vedclass · Accepted Answer

$\frac{2\varepsilon_r C}{1 + \varepsilon_r}$

Vedclass · Answer

(A) Let the area of each plate be $A$ and the distance between them be $d$. The capacity of the capacitor in air is $C = \frac{\varepsilon_0 A}{d}$.When the space between the plates is filled with a dielectric of constant $\varepsilon_r$ up to half the distance $d/2$,the capacitor can be considered as two capacitors in series.One capacitor has air as the dielectric with thickness $d_1 = d/2$,so its capacity is $C_1 = \frac{\varepsilon_0 A}{d/2} = 2C$.The other capacitor has a dielectric material with thickness $d_2 = d/2$,so its capacity is $C_2 = \frac{\varepsilon_r \varepsilon_0 A}{d/2} = 2\varepsilon_r C$.Since they are in series,the equivalent capacity $C_{eq}$ is given by $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$.$\frac{1}{C_{eq}} = \frac{1}{2C} + \frac{1}{2\varepsilon_r C} = \frac{1}{2C} \left(1 + \frac{1}{\varepsilon_r}\right) = \frac{1}{2C} \left(\frac{\varepsilon_r + 1}{\varepsilon_r}\right)$.Therefore,$C_{eq} = \frac{2\varepsilon_r C}{\varepsilon_r + 1}$.

What will be the capacity of a parallel-plate capacitor when the half of the parallel space between the plates is filled by a material of dielectric constant $\varepsilon_r$? Assume that the capacity of the capacitor in air is $C$.

Similar Questions

$A$ parallel plate capacitor has capacitance $C$. If it is equally filled with parallel layers of materials of dielectric constants $K_1$ and $K_2$,its capacity becomes $C_1$. The ratio of $C_1$ to $C$ is

In a parallel plate air capacitor of plate separation $d$,a dielectric slab of thickness $t$ is introduced between the plates $(t < d)$. The capacitance becomes one-third of the original value. The dielectric constant of the slab will be

The capacity of an air-filled parallel plate capacitor is $C_0$. One-half of the space between the plates is filled with a dielectric of constant $K$ as shown in the figure. The new capacity becomes $C_n$. The ratio of $C_n$ to $C_0$ is:

$A$ capacitor stores $60\,\mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric,an additional charge of $120\,\mu C$ flows through the battery. The dielectric constant of the dielectric inserted is

Vedclass Test Series

Exam Paper Generator

Online Exam Module