If a capacitor of capacitance $100 \mu \mathrm{~F}$ is charged at a steady rate of $100 \mu \mathrm{C} \mathrm{s}^{-1}$, then the time taken to produce a potential difference of 100 V between the capacitor plates is

A parallel plate capacitor of plate area $10 \mathrm{~cm}^2$ and plate separation 3 mm is charged to a potential difference 12 V and then the battery is disconnected. A slab of dielectric constant 3 is then inserted between the plates. The work done on the system in the process of inserting the slab is $\alpha \varepsilon_0$. The value of $\alpha$ is (take $\varepsilon_0$ as the permittivity of free space)

The equivalent capacitance between points $A$ and $B$ is

The following figure shows a 9 V battery and 3 uncharged capacitors of capacitances $C_1=C_2=C_3=1 \mu \mathrm{~F}$. The switch is thrown to the right side until capacitor $C_1$ is fully charged, then the switch is thrown to the left. The final charge on capacitor $C_2$ is