A $$DC$$ welding machine with a linear power source characteristic provides open circuit voltage of $$80V$$ and short circuit current of $$800A,$$ during welding with the machine , the measured are current is $$500A$$ corresponding to an arc length of $$5.0$$ $$mm$$ and the measured are current $$460A$$ corresponding to an arc length of $$7.0$$ $$mm.$$ The linear voltage $$(E)$$ & arc length $$(L)$$ characteristic of the welding arc can be given as (where $$E$$ is in Volts and $$L$$ is in $$mm$$)

Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint configuration by resistance spot welding at a welding current of $$10$$ $$KA$$ and welding time of $$10$$ milliseconds. A spherical fusion zone extending up to the full thickness of each sheet is formed. The properties of the metallic sheets are given below:
Ambient temp $$=293$$ $$K$$
Melting point temp $$=1793$$ $$K$$
Density $$ = 7000kg/{m^3}$$
Latent heat of fusion $$=300$$ $$kJ/kg$$
Specific heat $$=800$$ $$J/kgK$$

Assume:
(i) Contact resistance along sheet - sheet interface is $$500$$ micro-ohm and along
$$\,\,\,\,\,\,$$electrode-sheet interface is zero.:
(ii) No conductive heat loss through the bulk sheet material; and
(iii) The complete weld fusion zone is at the melting temperature, the melting
$$\,\,\,\,\,\,\,\,\,$$efficiency (in %) of the process is .........

In arc welding process, the voltage and current are $$25V$$ and $$300A$$ respectively. The arc heat transfer efficiency is $$0.85$$ and welding speed is $$8$$ $$mm/sec$$. The net heat input (in $$J/mm$$) is

Spot welding of two $$1$$ $$mm$$ thick sheets of steel (density $$ = 8000kg/{m^3}$$ ) is carried out successfully by passing a certain amount of current for $$0.1$$ second through the electrodes. The resultant weld nugget formed is $$5$$ $$mm$$ in diameter and $$1.5$$ $$mm$$ thick. If the latent heat of fusion of steel is $$1400$$ $$kJ/kg$$ and the effective resistance in the welding operation is $$200\mu \Omega ,$$ the current passing through the electrodes is approximately