Physics Electrostatic Potential and Capacitance

In a vernier callipers, $\left(N+1\right)$ divisions of vernier scale coincide with $N$  divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

A composite parallel plate capacitor is made up to two different dielectric materials with different thickness (t₁ and t₂) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The  voltage of the conducing foil is ___________V.

Given below 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 2 m distance ( $r$ ) from the centre of the dipole of dipole moment vector $\dot{P}$ of magnitude, $4*10^{-6}Cm$ , is $\pm 9*10^3 V$ .

(Take $\frac{1}{4\pi {ϵ}_0}=9*10^9$ SI units)

Reason R :  $V=\pm \frac{2P}{4\pi {?}_0{r}^2}$ , where $r$  is the distance of any axial point, situated at 2 m from the centre of the dipole.

In the light of the above statements, choose the correct answer from the options given below:

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

A certain charge Q is divided into parts q and (Q – q). How should the charges Q and q be divided so that q and (Q – q) placed at a certain distance apart experience maximum electrostatic repulsion?

A capacitor is connected to a 20 V battery through a resistance of 10 $\Omega .$  It is found that the potential difference across the capacitor rises to 2V in 1 $\mu s.$  The capacitance of the capacitor is________   $\mu F.$

Given  $In\left(\frac{10}{9}\right)=0.105$

Two metallic plates form parallel plate capacitor. The distance between the plates is 'd'.  A metal sheet of thickness $\frac{d}{2}$  and of area equal to area of each plate is introduced between the plates. What will be ratio of the new capacitance to the original capacitance of the capacitor?

Figure shows a rod AB, which is bent in a 120° circular arc of radius R. A charge (-Q) is uniformly distributed over rod AB. What is the electric field $\overrightarrow{E}$  at the centre of curvature O?

Three capacitors C₁ = $2\mu F,C_2=12\mu F$  and C₃ = $12\mu F$  are connected as shown in figure. Find the ratio of the charges on capacitors C₁, C₂ and C₃ respectively:

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be…………V.