A 500 -W heating coil designed to operate from 110 $\mathrm{V}$ is made of Nichrome wire 0.500 $\mathrm{mm}$ in diameter. (a) Assuming the resistivity of the Nichrome remains constant at its $20.0^{\circ} \mathrm{C}$ value, find the length of wire used. (b) What If? Now consider the variation of resistivity with temperature. What power is delivered to the coil of part (a) when it is warmed to $1200^{\circ} \mathrm{C} ?$