$64$ identical mercury drops,each charged to a potential of $10\, V$,are combined to form a single larger drop. The potential of the new larger drop is........$V$.

In the given capacitive network,the resultant capacitance between points $A$ and $B$ is: (in $\mu F$)

Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10 \mu F$ are individually charged by a $100 \, V$ $D.C.$ source. Capacitor $C_1$ is kept connected to the source and a dielectric slab is inserted between its plates. Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards,the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be $......... \, V$. (Assuming dielectric constant $K = 10$)

If $V_{A}-V_{B}=7 \text{ V}$,then find the stored energy in $C_1$.

While working on a physics project at a school physics lab,you require a $4 \,\mu F$ capacitor in a circuit across a potential difference of $1 \,kV$. Unfortunately,$4 \,\mu F$ capacitors are out of stock in your lab,but $2 \,\mu F$ capacitors which can withstand a potential difference of $400 \,V$ are available in plenty. If you decide to use the $2 \,\mu F$ capacitors in place of the $4 \,\mu F$ capacitor,what is the minimum number of capacitors required?

Two capacitors of $3 \mu F$ and $6 \mu F$ are connected in series and a potential difference of $900 \ V$ is applied across the combination. They are then disconnected and reconnected in parallel. The potential difference across the combination is