Answer :
Answer:
The temperature is [tex] T_2= 63.59 ^oC[/tex]
Explanation:
Generally the equation that represents the variation of resistance with respect to temperature is mathematically represented as
[tex]R = R_i (1 + \alpha * \Delta T )[/tex]
=> [tex]R = R_i (1 + \alpha * [T_2 - T_1] )[/tex]
Here [tex]T_1[/tex] is the original temperature with value [tex]T_1 = 20^oC[/tex]
[tex]R_i[/tex] is the initial resistance of the copper
R is the resistance at temperature [tex]\Delta T[/tex]
[tex]\alpha[/tex] is the temperature coefficient of resistivity with a value
[tex]\alpha =3.9 *10^{-3} \ ^oC^{-1}[/tex]
From the question we are told that
[tex]R = 17\% \ of R_i + R_i [/tex]
So
[tex]R = 0.17R_i + R_i [/tex]
[tex]R = 1.17R_i [/tex]
Hence
[tex]1.17 R_i = R_i (1 + 3.9 *10^{-3} * [T_2 - 20] )[/tex]
[tex]1.17 = (1 + 3.9 *10^{-3} * [T_2 - 20] )[/tex]
=> [tex] 0.17 = 3.9 *10^{-3} * [T_2 - 20] )[/tex]
=> [tex] [T_2 - 20] = 43.5897 [/tex]
=> [tex] T_2= 63.59 ^oC[/tex]