Capacitance question bank (Physics)

A parallel plate capacitor is having separation between plates $0.885$ mm. It has a capacitance of $1\,\mu$F when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\,\Omega$m and resistance $17.7\times 10^{14}\,\Omega$. Relative permittivity of the insulating material is $\alpha\times 10^7$. The value of $\alpha$ is ________. (Take permittivity of free space $=8.85\times 10^{-12}$ F/m)

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 $\alpha \times 10^{-7}$ J. The value of $\alpha$ is __________. (combined capacitance of spheres is $200$ pF)