Two charged spherical conductors of radius R_₁ and R_₂ are connected by a Wire. Then the ratio of surface charge densities of the sphere (σ₁/σ₂ is:

When a slab of insulating material 4 mm thick is introduced between the plates of a parallel plate capacitor of separation 4 mm. it is found that the distance between the plates has to be increased by 3.2 mm to restore the capacity to its original value. The dielectric constant of the material is ____________.
Fill in the blank the correct answer from the given below.

Two parallel plate capacitors of capacitances 2 μF and 3 μF are joined in series and the combination is connected to a battery of V volt. The values of potential across the two capacitors respectively are related as ____________.
Fill in the blank with the correct answer from the options given below.

A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates. Now an insulating slab of same area but thickness d/2 is inserted between the plates as shown in figure having dielectric constant K(=4). The ratio of new capacitance to its original capacitance will be,

The variation of electrostatic potential with radial distance r from the centre of a positively charged metallic thin shell of radius R is given by the graph

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

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is:

Given blow are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The potential (V) at any axial point, at 2m distance (r) from the center of the dipole of dipole moment vector magnitude,

Reason R: where r is the distance of any axial point, situated at 2 m from the center of the dipole.
In the light of the above statements, choose the correct answer from the options given below:

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:

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.