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?

In the circuit shown,the charge on the $5\, \mu F$ capacitor is $........\mu C$.

Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_r$. The cell electromotive force (emf) $V_0 = 8 \ V$. First,the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged,$S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium,the charge on $C_3$ is found to be $5 \mu C$. The value of $\varepsilon_r = . . . . $

The switch $S_w$ is shifted from position $1$ to position $2$ as shown in the figure. Heat generated in the circuit is

Two capacitors of $6 \, pF$ are connected in series and a potential difference of $5000 \, V$ is applied across the combination. If the combination is disconnected and then reconnected in parallel, what will be the potential difference between the plates?

Calculate the charge on the capacitor in the steady state. (in $\mu C$)