A $230-$W heating coil designed to operate from $110$ V is made of Nichrome wire $0\mathrm{.}640$ 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