A $400-$m long, $0\mathrm{.}15$ mm radius copper wire is coated with a thin insulating material. An engineer decides to use it for designing a temperature sensor for the range of $10$C to $20$C$.$ A $1\mathrm{.}5-$V battery is used to bias the sensor$.$

Determine the resistance of the sensor and corresponding current at the two extremes of the sensor$.$

Determine the maximum power that the sensor will dissipate.

Assume that the conductivity of copper is $5\mathrm{.}8107$ S$/$m at $20$C and its temperature coefficient is $0\mathrm{.}0039/($C$).$