Due to cold weather, a 1   m water pipe of cross-sectional area 1   cm 2 is filled with ice at -…

Due to cold weather, a $1 \mathrm{m}$ water pipe of cross-sectional area $1{ \mathrm{cm}}^2$ is filled with ice at $-10 °\mathrm{C}.$ Resistive heating is used to melt the ice. Current of $0.5 \mathrm{A}$ is passed through $4 \mathrm{k\Omega }$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?

(Given latent heat of fusion for water/ice$=3.33\times {10}^5 \mathrm{J}{ \mathrm{kg}}^{-1},$ specific heat of ice $=2\times {10}^3 \mathrm{J}{ \mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$ and density of ice $={10}^3 \mathrm{kg} {\mathrm{m}}^{-3} )$