Problem $4$

The unit melting energy for a certain sheet metal is $9\mathrm{.}04\frac{J}{m}{m}^3.$ The thickness of each of the two sheets to be spot welded is $3\mathrm{.}75$ mm $.$ To achieve required strength, it is desired to form a weld nugget that is $5\mathrm{.}65$ mm in diameter and $3\mathrm{.}6$ mm thick. The weld duration will be set at $0\mathrm{.}45$ sec $.$ If the electrical resistance between the surfaces is $140$ micro ohms, and only one third of the electrical energy generated will be used to form the weld nugget $($the rest being dissipated$),$ determine the minimum current level required in this operation.