Why current rating of a fuse wire does not depend on its length? If legth is increased, resistance is increased and heat produced is directly proportional to the resistance. So why current rating is still independent of its length? Please give answer assuming that there is no heat loss
 A: A wire will melt if it exceeds a certain temperature.  If resistive heating is happening in the wire, its temperature will increase until the rate of heat loss (via conduction to the air, largely) balances the rate of heat generation, or until it melts, whichever comes first.  The rate of heat loss is proportional to the difference in temperature between the air and the wire, and to the surface area of the wire.
Now, if we double the length of the wire, the surface area of the wire is also proportional to the length, and the rate of heat transfer is proportional to the surface area.  This means that a wire that is twice as long will generate heat at twice the rate.  But at a given temperature of the wire, the rate at which the heat is lost will still balance out the rate at which heat is generated, since both numbers are twice as large when we double the length of the wire.  The net effect is that the equilibrium temperature will be the same.
(All of this assumes that the wire is not coiled up or enclosed, which would reduce the rate of cooling and lead to a higher equilibrium temperature.)
