A parallel plate capacitor with air as the di | vedclass

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

Question

(A) The original capacitance of the air-filled parallel plate capacitor is $C = \frac{\varepsilon_0 A}{d}$.When a dielectric slab of constant $K$ is i

Vedclass · Accepted Answer

$(K+3) \frac{C}{4}$

Vedclass · Answer

(A) The original capacitance of the air-filled parallel plate capacitor is $C = \frac{\varepsilon_0 A}{d}$.When a dielectric slab of constant $K$ is introduced to fill one-fourth of the area,the capacitor can be considered as two capacitors in parallel.One capacitor has air as the dielectric with area $\frac{3A}{4}$ and plate separation $d$. Its capacitance is $C_1 = \frac{\varepsilon_0 (3A/4)}{d} = \frac{3}{4} \frac{\varepsilon_0 A}{d} = \frac{3C}{4}$.The other capacitor has a dielectric $K$ with area $\frac{A}{4}$ and plate separation $d$. Its capacitance is $C_2 = \frac{K \varepsilon_0 (A/4)}{d} = \frac{K}{4} \frac{\varepsilon_0 A}{d} = \frac{KC}{4}$.Since these two capacitors are in parallel,the equivalent capacitance is $C_{net} = C_1 + C_2$.$C_{net} = \frac{3C}{4} + \frac{KC}{4} = \frac{C}{4}(K+3)$.

$A$ parallel plate capacitor with air as the dielectric has capacitance $C$. $A$ slab of dielectric constant $K$ and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

Similar Questions

$A$ parallel plate capacitor with air between plates has a capacitance of $8\,\mu F$. What will be the capacitance if the distance between the plates is reduced by half,and the space between them is filled with a substance of dielectric constant $6$?

Consider a parallel plate capacitor of $10\,\mu F$ with air filled in the gap between the plates. Now,one half of the space between the plates is filled with a dielectric of dielectric constant $K = 4$,as shown in the figure. The capacity of the capacitor changes to.......$\mu F$.

In the figure,a capacitor is filled with dielectrics. The resultant capacitance is

Assertion : If the distance between parallel plates of a capacitor is halved and the dielectric constant is increased to three times its original value,then the capacitance becomes $6$ times.
Reason : The capacity of a capacitor does not depend upon the nature of the material between the plates.

Vedclass Test Series

Exam Paper Generator

Online Exam Module