D$11\mathrm{.}7.$ A steel pipe is constructed of a material for which r $=180$ and

$=4106$ S$/$m$.$ The two radii are $5$ and $7$ mm$,$ and the length is $75$ m$.$ If

the total current I $($t$)$ carried by the pipe is $8$ cos t A$,$ where $=1200$ rad$/$s$,$

find: $($a$)$ the skin depth; $($b$)$ the effective resistance; $($c$)$ the dc resistance; $($d$)$

the time$-$average power loss.