A piece of copper wire has a resistance of `25 Omega` at `10^(@)C`. What is the maximum operating temperature, if the resistance of the wire is to be increased by 20 % ? (Assume `alpha` at `10^(@)C=0.0041// .^(@)C^(-1)`).

Options

A. `60.38^(@)C`
B. `58.78^(@)C`
C. `40.73^(@)C`
D. `20.23^(@)C`

Answer

B

Explanation

`R_(1)=50 Omega, t_(1)=10^(@)C, alpha_(1)=0.0041^(@)C`
`R_(2)=50+0.2xx50=60 Omega`
`t_(2)` = the unknown temperature at which R will be `60 Omega`.
Since, `" " R_(t_(2))=R_(t_(1))[1+alpha_(t_(1))(t_(2)-t_(1))]`
Here, `" " R_(2)=R_(1)[1+alpha_(t_(1))(t_(2)-t_(1))]`
`" " 60=50[1+0.0041xx(t_(2)-10)]`
`rArr " " t_(2)-10=((60)/(50)-1)xx(1)/(0.0041)`
or `" " t_(2)=58.78 .^(@)C`