Current Electricity 5 Question 17

17. A copper wire having cross-sectional area of 0.5mm2 and a length of 0.1m is initially at 25C and is thermally insulated from the surrounding. If a current of 1.0A is set up in this wire, (a) find the time in which the wire will start melting. The change of resistance with the temperature of the wire may be neglected. (b) What will this time be, if the length of the wire is doubled?

(1979)

Melting point of copper =1075C, Specific resistance of copper =1.6×108Ωm, Density of copper =9×103kg/m3, Specific heat of copper =9×102cal/kgC

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Solution:

  1. (a) I2Rt=mSΔθ=m(SΔθ)

I2ρ1lAt=Alρ2(SΔθ)

 Here, ρ1= specific resistance  and ρ2= density t=A2ρ2(SΔθ)I2ρ1

Substituting the values, we have

t=(0.5×106)2(9×103)(9×102×4.18×1050)(1.0)2(1.6×108)=55.5s

(b) From Eq. (i) we can see that time is independent of length of wire.



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