Two uncharged thin concentric spherical conducting shells '$A$' and '$B$' of radii $R$ and $3R$ are connected through a resistance '$r$' and switch '$S$' initially opened as shown in the figure. A positive point charge '$Q$' is fixed at a distance $2R$ from the centre of the shells. At $t=0$, the switch ' $S$ ' is closed till the steady state is reached. Then choose the correct options(s)

  

A parallel plate capacitor with plate area '$A$' and distance of separation '$d$' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:

$\epsilon \left(x\right)={\epsilon }_0+kx$, for $\left(0<x\le \frac{d}{2}\right)$

$\epsilon \left(x\right)={\epsilon }_0+k\left(d-x\right)$, for $\left(\frac{d}{2}\le x\le d\right)$

Four identical rectangular plates with length, $l=2 \mathrm{cm}$ and breadth, $b=\frac{3}{2} \mathrm{cm}$ are arranged as shown in figure. The equivalent capacitance between $A$ and $C$ is $\frac{x{\epsilon }_0}{ d}.$ The value of $x$ is _______.

(Round off to the Nearest Integer)

Find the total capacitance and total charge on the capacitors

Which of the following devices does not allow d.c to pass through?

The dimensional formula of capacitance is _______.

Take $Q$ as the dimension formula of charge.

What are the charges stored in the $1 \mu F$ and $2 \mu F$ capacitors in the circuit below, once the currents become steady?

An electron enters a parallel plate capacitor with horizontal speed $\mu$ and is found to deflect by angle $\theta$ on leaving the capacitor as shown. It is found that $\tan \theta =0.4$ and gravity is negligible.

If the initial horizontal speed is doubled, then $\tan \theta$ will be: