To establish an instantaneous current of $2\,A$ through a $1\,\mu F$ capacitor,the potential difference across the capacitor plates should be changed at the rate of:

Calculate the electrostatic potential energy of the system of charges shown in the figure (in $ergs$).

$A$ series combination of $N_1$ capacitors (each of capacity $C_1$) is charged to a potential difference $3V$. Another parallel combination of $N_2$ capacitors (each of capacity $C_2$) is charged to a potential difference $V$. The total energy stored in both combinations is the same. The value of $C_1$ in terms of $C_2$ is:

When two identical capacitors are charged individually to different potentials and then connected in parallel,after disconnecting from the source . . . . . .

$A$ 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 escape speed of an electron launched from the surface of a glass sphere of diameter $1 \ cm$ that has been charged to $10 \ nC$ is $x \times 10^7 \ m/s$. The value of $x$ is: