A sphere of capacitance 100 pF is charged to a potential of 100 V . Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

(combined capacitance of spheres is 200 pF )

Under steady state condition the potential difference across the capacitor in the circuit is $\_\_\_\_$ V.

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is $\_\_\_\_$ $\mu \mathrm{F}$.

(take $C_1=C_2=C_3=1 \mu \mathrm{~F}$ and $C_4=2 \mu \mathrm{~F}$.)

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is $\_\_\_\_$ .