$A$ fully charged capacitor of capacity $C$ is discharged through a small resistance wire embedded in a solid block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the initial potential difference across the capacitor is

Find the potential difference between $A$ and $B$ in the given circuit in the steady state. (in $V$)

$A$ capacitor $C_1 = 1\,\mu F$ can withstand a maximum voltage of $V_1 = 6\,kV$,and a capacitor $C_2 = 3\,\mu F$ can withstand a maximum voltage of $V_2 = 4\,kV$. If these two capacitors are connected in series,what is the maximum voltage (in $kV$) that can be applied to the combination?

$A$ capacitor of unknown capacity is connected across a battery of $V$ volt. The charge stored in it is $Q$ coulomb. When the potential across the capacitor is reduced by $V_1$ volt,the charge stored in it becomes $Q_1$ coulomb. The potential $V$ is

$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \; \mu C$ and $-2 \; \mu C$ (with no external field) placed at $(-9 \; cm, 0, 0)$ and $(9 \; cm, 0, 0)$ respectively.
$(b)$ How much work is required to separate the two charges infinitely away from each other?
$(c)$ Suppose that the same system of charges is now placed in an external electric field $E = A(1/r^2)$; $A = 9 \times 10^5 \; C \cdot m^{-2}$. What would the electrostatic energy of the configuration be?

Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10\; \mu F$. When these capacitors are individually connected to a voltage source of $1\; V,$ the energy stored in the capacitor $C_{2}$ is $4$ times that of $C_{1}$. If these capacitors are connected in series,their effective capacitance will be (in $; \mu F$)