Two conducting shells of radius $a$ and $b$ are connected by a conducting wire as shown in the figure. The larger shell is grounded. The capacitance of the system is:

In the circuit shown,initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1=10 \mu F$,$C_2=30 \mu F$,and $C_3=C_4=80 \mu F$.
Which of the statement$(s)$ is/are correct?
$(1)$ The key $S_1$ is kept closed for a long time such that capacitors are fully charged. Now key $S_2$ is closed. At this time,the instantaneous current across the $30 \Omega$ resistor (between points $P$ and $Q$) will be $0.2 A$.
$(2)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage difference between points $P$ and $Q$ will be $10 V$.
$(3)$ At time $t=0$,the key $S_1$ is closed,the instantaneous current in the closed circuit will be $25 mA$.
$(4)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage across the capacitor $C_1$ will be $4 V$.

$A$ circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed,the total amount of charge that flows from $Y$ to $X$ is

The radii of two metallic spheres $P$ and $Q$ are $r_1$ and $r_2$ respectively. They are given the same charge. If $r_1 > r_2$,then on connecting them with a thin wire,the charge will flow

$A$ $1\,\mu F$ capacitor is connected in the circuit shown below. The $EMF$ of the cell is $3\,V$ and its internal resistance is $0.5\,\Omega$. The resistors $R_1$ and $R_2$ have values $4\,\Omega$ and $1\,\Omega$ respectively. The charge on the capacitor in steady state is.......$\mu C$.

In the given circuit, if point $C$ is connected to the earth and a potential of $+2000 \, V$ is applied to point $A$, the potential at point $B$ is.....$V$.