Physics Electrostatic Potential and Capacitance

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $\lambda$  where C/V = $\lambda$  

Consider the combination of 2 capacitors C₁ and C₂, with C₂ > C₁, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series, Calculate the ratio of capacitors, $\frac{C_2}{C_1}.$

Two identical conducting spheres with negligible volume have 2.1 nC and 0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5m. The electrostatic force acting between the spheres is …………….* 10^-9N.

$\left[Given:4\pi {\epsilon }_0=\frac{1}{9*10^9}SIunit\right]$

Two small spheres each of mass 10mg are suspended from a point by threads 0.5m long. They are equally charged and repel each other to a distance of 0.20m. The charge on each of the sphere is $\frac{a}{21}*10^{-8}C.$  The value of 'a' will be……. [Given g = 10 ms^-2]

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:

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:

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

If $c$  is the velocity of light in free space, the correct statements about photon among the following are:

A. The energy of a photon is  $E=hv$ .

B. The velocity of a photon is c.

C. The momentum of a photon,  $p=\frac{hv}{c}$ .

D. In a photon-electron collision, both total energy and total momentum are conserved.

E. Photon possesses positive charge.

Choose the correct answer from the options given below:

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: