Question

Coefficient of recessivity of wire problem: Given how much resistance increases when raised at certain temperature, What is temperature coefficient of recessivity ? Make up a problem with made up values and solve show all equations used to solve a problem like this show all equations

Answer 1

as we know that the resistance of the conductors increases as the temperature increases

because the the number of collisions increases.

let the resistance of the copper wire at a reference temperature is R0, as the change in temperature is DT

then the resistance can also increase to R is given by

   the ratio of change in resistance to original resistance is proportional to change in temperature

  
       DR/R0 = alpha*DT

  
where alpha is called , temperature coeffficient of resistance

      
for copper alpha is = 0.004041 / 0C

Let the copper wire is at a resistance R = 20 ohm when the temperatue is at 20 0C, when the temperature is raised to 40 0C, the resistance of the wire is ?

   from the formula

   R = R0(1+alpha(DT))
   R = 20 (1+0.004041 (40-20)) ohm

   R = 21.6164 ohm

so the resistance of the wire has been increased to 21.6164 ohm from 20 ohm