A 35.1 -m length of copper wire at 20.0^degree C has a radius of 0.23 mm. If a p

Question

A 35.1 -m length of copper wire at 20.0^degree C has a radius of 0.23 mm. If a potential difference of 7.0 V is applied across the length of the wire, determine the current in the wire. (Use the values in this table.) (b) If the wire is heated to 36.0^degree C while the 7.0-V potential difference is maintained, what is the resulting current in the wire? Resistivity's and Temperature Coefficients of Resistivity for Various Materials (at 20^degree C) A nickel-chromium alloy commonly used in heating elements.

Explanation / Answer

Given

   length of the copper wire of radius 0.23mm is l= 35.1 m
  
   potential difference V = 7.0 V

   current in the wire is I = ?

from ohm's law V = I*R

here R is resistance of the wire , but we know the relation between resistance and resistivity as

   rho = R*A/l ==> R = rho*L/A

A is area of cross section A pi*r^2 = pi*(0.23*10^-3)^2 m^2 = 1.6619*10^-7 m^2

   R = 1.7*10^-8*35.1*10^-3/(1.6619*10^-7) ohm = 0.00359 ohm

so the current is I = V/R = 7/0.00359 A = 1949.86072 A

b) if temperature increases from 20 0C to 36 0C the resistivity also changes as

   rho_T = rho_0(1+alpha(DT))

from data alpha= 3.9*10^-3 /0C

   rho_36 = 1.7*10^-8(1+3.9*10^-3(36-20)) ohm-m

       = 1.80608*10^-8 ohm m

now the resistance is R_T = rho_T*L/A

           = 1.80608*10^-8 *35.1*10^-3/(1.6619*10^-7) ohm

           = 0.00381 ohm

now the current at temp 36 0C is I = V/R_T

               = 7/0.00381 A
                 
              = 1837.27034 A

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