Capacitors, series and parallel combination, parallel plate capacitor with/without dielectric

The plates of a parallel plate capacitor are separated by \(d\). Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(\frac{3}{8}d\) and \(\frac{d}{2}\), respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25\,K_2\), the value of \(K_1\) is :

In the following circuit, the equivalent capacitance between terminal \(A\) and terminal \(B\) is :

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then

A. the charge stored in it, increases.

B. the energy stored in it, decreases.

C. its capacitance increases.

D. the ratio of charge to its potential remains the same.

E. the product of charge and voltage increases.

Choose the most appropriate answer from the options given below:

The equivalent capacitance of the system shown in the following circuit is :

The equivalent capacitance of the combination shown in the figure is :

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 :

(\(\epsilon_0 = 8.85\times10^{-12}\) C\(^2\) N\(^{-1}\) m\(^{-2}\))

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

A parallel-plate capacitor of area \(A\), plate separation \(d\) and capacitance \(C\) is filled with four dielectric materials having dielectric constants \(k_1,k_2,k_3\) and \(k_4\) as shown in the figure below. If a single dielectric material is to be used to have the same capacitance \(C\) in this capacitor, then its dielectric constant \(k\) is given by