The arc - voltage characteristics of a $$DC$$ power source has a linear power source characteristic of $$V=20+40L,$$ where $$V$$ is the arc voltage in volts and $$L$$ is the arc length in $$cm.$$ The static volt-ampere characteristic of the power source is approximated by a straight line with open circuit voltage $$=80V$$ and short circuit current is $$600Amps,$$ determine the optimum arc length for maximum power

Two different pairs of sheets of same material are welded by resistance-spot welding. In one pair, the average radius $$(r)$$ of each spherical bridge is $$0.2$$ $$mm$$ and the number of bridges per $$c{m^2}\,\,\left( n \right)$$ is $$25.$$ In another pair, the number of bridges per $$c{m^2}$$ is $$50$$ with the same $$'r'$$ of bridge. The contact resistance $${R_c}$$ per unit area is given by $${R_c} = 0.85$$ $$\left( {\rho /n\pi r} \right)$$ where $$'\,\rho \,'$$ is the resistivity of metal. If the voltage applied is $$5$$ volts and the resistivity of metal is $$2 \times {10^{ - 5}}$$ ohm-cm. The rate of heat generated per $$c{m^2}$$ in each case

For butt welding $$40mm$$ thick steel plates, when the expected quantity of such jobs is $$5000$$ per month over a period of $$10$$ years, choose the best suitable welding process out of the following available alternatives.

In butt welding operation on plates, the heat input necessary is given by

$$Q = 8\,K\,{T_c}\,t\,\,\,\left[ {0.2 + {{Vb} \over {4\alpha }}} \right]$$
Where $$K=$$ thermal conductivity,
$${T_c} = $$ temp increases from room temp up to $$MP,$$
$$t=$$ thickness of plate,
$$V=$$ welding speed,
$$b=$$ width of weld,
$$\alpha = thermal diffusivity

Two alloy steel plates as shown in fig are to be welded using a power source rated at $$5$$ $$kVA$$ having a duty cycle of $$75\% .$$ Using the given data, determine the maximum welding speed for the job given in $$mm/s$$

Data : $$K = 45\,W/{m^0}C,\,\,{T_c} = {1450^ \circ }C,$$ and
$$\alpha = 1.2 \times {10^{ - 5}}\,\,{m^2}/s.$$