Question

To what temperature must you raise a silver wire (c = 0.0038), originally at 20.0°C, to double its resistance, neglecting any changes in dimensions? (You can assume that resistivity varies with temperature linearly)

Answer 1

`T=283^(\circ)C`

Step-by-step explanation:

Given a material with temperature coefficient of resistance c, the equation that relates the resistance
`R_0` at temperature
`T_0` and the resistance
`R` at temperature
`T` is

`(R-R_0)/(R_0)=c(T-T_0)`

We want to double our resistance, so
`R=2R_0`, thus having:

`(2R_0-R_0)/(R_0)=(R_0)/(R_0)=1=c(T-T_0)`

For this T must be:

`1=cT-cT_0`

`T=(1+cT_0)/(c)`

which for our values means (with
`T=20^(\circ)C=293^(\circ)K`, remember to write temperature in S.I., and that for silver
`c=0.0038^(\circ)K^(-1)`):

`T=(1+(0.0038^(\circ)K^(-1))(293^(\circ)K))/((0.0038^(\circ)K^(-1)))=556^(\circ)K=283^(\circ)C`