Question

To what value would you have to raise the temperature of a copper wire (originally at 20 ∘C) to increase its resistance by 17 % ?

Answer 1

The temperature is
`T_2=  63.59 ^oC`

Step-by-step explanation:

Generally the equation that represents the variation of resistance with respect to temperature is mathematically represented as

`R = R_i (1 +  \alpha *  \Delta  T  )`

=>
`R = R_i (1 +  \alpha *  [T_2 -  T_1] )`

Here
`T_1` is the original temperature with value
`T_1 = 20^oC`

`R_i` is the initial resistance of the copper

R is the resistance at temperature
`\Delta  T`

`\alpha` is the temperature coefficient of resistivity with a value

`\alpha =3.9 *10^(-3) \  ^oC^(-1)`

From the question we are told that

`R =  17\% \  of  R_i + R_i`

So

`R =  0.17R_i + R_i`

`R =  1.17R_i`

Hence

`1.17 R_i = R_i (1 + 3.9 *10^(-3)  *  [T_2 -  20] )`

`1.17  =  (1 + 3.9 *10^(-3)  *  [T_2 -  20] )`

=>
`0.17 = 3.9 *10^(-3)  *  [T_2 -  20] )`

=>
`[T_2 -  20]  = 43.5897`

=>
`T_2=  63.59 ^oC`