Electrostatic P...

In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $${S}_{1}$$ is closed, $${S}_{2}$$ kept open. ($$q$$ is charge on the capacitor and $$\tau=RC$$ is capacitive time constant). Which of the following statement is correct?

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A parallel plate capacitor having plates of area $$S$$ and plate separation $$d$$, has capacitance $${C}_{1}$$ in air. When two dielectrics of different relative permittivities ($${ \epsilon }_{ 1 }=1$$ and $${ \epsilon }_{ 2 }=4$$) are introduced between the two plates as shown in the figure, the capacitance become $${C}_{2}$$. The ratio $$\dfrac { { C }_{ 2 } }{ { C }_{ 1 } }$$ is 

The gravitational field strength $$\vec {E}$$ and gravitational potential $$V$$ are related as $$\vec {E} = -\left (\dfrac {\partial V}{\partial x} \hat {i} + \dfrac {\partial V}{\partial y} \hat {j} + \dfrac {\partial V}{\partial z}\hat {k}\right )$$
In the figure, transversal lines represent equipotential surfaces. A particle of mass $$m$$ is released from rest at the origin. The gravitational unit of potential, $$1\overline {V} = 1\ cm^{2}/ s^{2}$$.
X-component of the velocity of the particle at the point $$(4cm, 4cm)$$ is

Figure shows four identical metal plate each of area $$A$$. The plates are kept at equal distance $$d$$ successively. A source of emf $$12V$$ is connected between $$x$$ and $$B$$. Potential difference between $$x$$ and $$y$$ is

The diagram shows a small bead of mass $$m$$ carrying charge $$q$$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plan. In the same plane a charge $$+Q$$ has also been fixed as shown. The potential at the point $$P$$ due to $$+Q$$ is $$V$$. The velocity with which the bead should projected from the point $$P$$ so that it can complete a circle should be greater than

The equivalent capacitance across $$A$$ and $$B$$ in the adjoining circuit is:

The capacity of a parallel plate capacitor formed by the plates of same are A is 0.02$$\mu F$$ with air as dielectric. Now one plate is replaced by a plate of area 2A and dielectric (K = 2) is introduced between the plates, the capacity is :

$$4\ \mu F$$ and $$6\ \mu F$$ capacitors are joined in series and $$500\ v$$ are applied between the outer plates of the system. What is the charge on each plate ?

Which of the following statements are true?