Consider a FET with a two$-$dimensional channel. Suppose we scale down the linear dimensions of the channel by a factor $,$ so that the channel length, L$,$ for example, becomes L$/$$.($a$)$ At fixed source$-$drain voltage V $,$ show that the source$$drain field scales like $.($b$)$ Show that the timescale associated with a carrier crossing the device scales like $1/$$2$ if V is fixed. $($c$)$ Show that the power dissipated scales like $1/$$2$ for constant electric field but remains unchanged for constant V $.$