Question

A given copper wire has a resistance of 5.16 ? at 20.0

Answer 1

The resistance of a material at any temperature ''t'' can be given as ::

R_t = R_o ( 1 + (t-t_o) )           
Rt = resistance at final temperature ''t'

R_o = resistance at initial temperature ''t_o'

= Temperature Coefficient of resistance

Lets assume the final temperature at ''t'' .

initial temperature for each copper and wire = t_o = 20

Temperature Coefficient of resistance = _c = 3.9 x 10^-3

Temperature Coefficient of resistance = _t = 4.5 x 10^-3

Resistance of copper at initial temperature ''t_o=20 '' = R_oc = 5.16 ohm

Resistance of tungsten at initial temperature ''t_o=20 '' = R_ot = 4.73 ohm

the final Resistance of Copper and tungsten at temperature ''t'' are equal so we write

R_tc = R_tt

R_oc ( 1 + _c (t-t_o) )   = R_ot ( 1 + _t (t-t_o) )  

5.16 ( 1 + (3.9 x 10^-3)(t- 20)) = 4.73 ( 1 + (4.5 x 10^-3)(t- 20))

t = 390.4 c