Four metallic plates A, B, C and D of the sam | vedclass

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

Question

(C) Let the capacitance of each pair of plates without a dielectric be $C = \frac{\epsilon_0 A}{d}$.There are three capacitors formed by the plates: $

Vedclass · Accepted Answer

$\frac{4}{5} C$

Vedclass · Answer

(C) Let the capacitance of each pair of plates without a dielectric be $C = \frac{\epsilon_0 A}{d}$.There are three capacitors formed by the plates: $C_1$ between $A$ and $B$,$C_2$ between $B$ and $C$,and $C_3$ between $C$ and $D$.$C_1 = C$ (air between $A$ and $B$).$C_2 = K C = 2C$ (dielectric $K=2$ between $B$ and $C$).$C_3 = K C = 2C$ (dielectric $K=2$ between $C$ and $D$).Plates $B$ and $D$ are connected together. Thus,$C_2$ and $C_3$ are in parallel between points $B$ and $C$. The equivalent capacitance of this parallel combination is $C_{23} = C_2 + C_3 = 2C + 2C = 4C$.Now,$C_1$ is in series with the combination $C_{23}$ between points $A$ and $C$. However,looking at the circuit,$A$ is connected to one plate of $C_1$,and the other plate $B$ is connected to $C_2$ and $C_3$. Since $B$ and $D$ are connected,the effective capacitance between $A$ and $C$ is the series combination of $C_1$ and $C_{23}$.$C_{eq} = \frac{C_1 	imes C_{23}}{C_1 + C_{23}} = \frac{C 	imes 4C}{C + 4C} = \frac{4C^2}{5C} = \frac{4}{5} C$.

Similar Questions

$A$ parallel plate capacitor with oil between the plates (dielectric constant of oil $K = 2$) has a capacitance $C$. If the oil is removed,then the capacitance of the capacitor becomes:

Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the dielectric constant of a material,which when fully filled between the plates produces the same capacitance?

$A$ capacitor is kept connected to the battery and a dielectric slab is inserted between the plates. During this process

The capacitance of a parallel plate capacitor with air as medium is $6\, \mu F$. With the introduction of a dielectric medium,the capacitance becomes $30\, \mu F$. The permittivity of the medium is..........$C^{2} N^{-1} m^{-2}$.
$(\varepsilon_{0} = 8.85 \times 10^{-12} C^{2} N^{-1} m^{-2})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module