A parallel plate capacitor with plate area A | vedclass

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

Question

(D) The capacitance of a parallel plate capacitor with a dielectric slab of thickness $x$ and dielectric constant $K$ is given by:$C = \frac{\epsilon_

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) The capacitance of a parallel plate capacitor with a dielectric slab of thickness $x$ and dielectric constant $K$ is given by:$C = \frac{\epsilon_0 A}{d - x + \frac{x}{K}}$Given $K = 4$,the formula becomes:$C = \frac{\epsilon_0 A}{d - x + \frac{x}{4}} = \frac{\epsilon_0 A}{d - \frac{3x}{4}}$For $x = \frac{d}{3}$:$C_1 = \frac{\epsilon_0 A}{d - \frac{3}{4}(\frac{d}{3})} = \frac{\epsilon_0 A}{d - \frac{d}{4}} = \frac{\epsilon_0 A}{\frac{3d}{4}} = \frac{4}{3} \frac{\epsilon_0 A}{d}$Given $C_1 = 2 \mu F$,we have $\frac{4}{3} \frac{\epsilon_0 A}{d} = 2 \mu F \implies \frac{\epsilon_0 A}{d} = \frac{6}{4} = 1.5 \mu F$.For $x = \frac{2d}{3}$:$C_2 = \frac{\epsilon_0 A}{d - \frac{3}{4}(\frac{2d}{3})} = \frac{\epsilon_0 A}{d - \frac{d}{2}} = \frac{\epsilon_0 A}{\frac{d}{2}} = 2 \frac{\epsilon_0 A}{d}$Substituting $\frac{\epsilon_0 A}{d} = 1.5 \mu F$:$C_2 = 2 	imes 1.5 \mu F = 3 \mu F$.

Similar Questions

Two parallel plate capacitors are connected in series and then connected to a $100 \ V$ battery. $A$ dielectric slab of dielectric constant $K = 4.0$ is inserted between the plates of the second capacitor. What will be the potential difference across each capacitor respectively?

Two capacitors,each having capacitance $40\,\mu F$,are connected in series. The space between the plates of one of the capacitors is filled with a dielectric material of dielectric constant $K$ such that the equivalent capacitance of the system becomes $24\,\mu F$. The value of $K$ is:

When a dielectric material is introduced between the plates of a charged condenser,what happens to the electric field between the plates?

$A$ parallel plate capacitor has two layers of dielectrics as shown in the figure. This capacitor is connected across a battery. The ratio of the potential difference across the dielectric layers $(V_1/V_2)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module