A$580-$W heating coil designed to operate from $110$ V is made of Nichrome wire$0\mathrm{.}570$mm in diameter. $($Assume$=1\mathrm{.}5010-6$m$,$ and$=4\mathrm{.}00010-4($C$)1$for Nichrome.$)$

$($a$)$ Assuming the resistivity of the Nichrome remains constant at its $20\mathrm{.}0$C value, find the length of wire used.

$$m

$($b$)$ Now consider the variation of resistivity with temperature. What power is delivered to the coil of part $($a$)$ when it is warmed to$1200$C$?$

$$W