Q$2.$

a$.$ Use superposition theorem to find the value of $\backslash ((\backslash$mathbf$\{$I$\})\backslash )$ and $\backslash (\backslash$mathbf$\{($ v $)\}\backslash )$ as shown in figure $3.$

$(16$ marks$)$

Figure $3$

b$.$ A $8$ nF parallel$-$plate capacitor has an area $20$ in $2$ and separation of plates of $8$ mm $.$ Find the relative permittivity of the dielectric medium used. What separation would be required to obtain the same capacitance if the dielectric material between the plates is changed to waxed paper with dielectric constant of $2,$ and having the same area of plates as given above?

$(9$ marks$)$