A copper wire having area of cross section `0.4mm^(2)` and a length of 10 cm is initially at `75^(@)C` and is thermally insulated from the surroundings. If a current of `10A` is set up in this wire. ltbr. (a) Find the time in which the wire will strat melting. ignore variation of resistance with temperature.
(b) If length of wire is doubled, find time.
Given for copper : density =`10^(4) kg//m^(3)`, specific heat = `9xx10^(-2) kcal kg^(-1)(.^@C)^(-1)`, melting point =`1075^(@)C`, resispectively `=1.6xx10^(-8)Omega * m`.

Explanation

(a) Resistace of wire `R = (rhol)/(A)`
Heat required to melt the copper wire
`H = i^2 Rt` ..(i)
also `H = msDelta theta` ..(ii)
`i^(2)Rt = ms Delta theta`
`i^2 (rhol)/(A)t = (dAl)s Delta theta`
`t = (dA^(2)s Delta theta)/(i^2rho)`
`=(10^4xx(0.4xx10^(-6))^(2)(9xx10^(-2))xx4.2xx10^3xx(1075-75))/((10)^(2)xx1.6xx10^(-8))`
`=378 sec`
(b) `t` is independent of length of wire. Time of melting remains same.