The resistance of a wire at room temperature `30^(@)C` is found to be `10Omega`. Now to increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is `0.002//""^(@)C`]

Options

A. `36^(@)C`
B. `83^(@)C`
C. `63^(@)C`
D. `33^(@)C`

Answer

B

Explanation

`R=R_(0)(1+alphat)`
`therefore R_(0)(1+30alpha)=10Omega`
and `R_(0)(1+alphat)=11Omega`
Therefore, `(11)/(10)=(1+alphat)/(1+30alpha)`
or `11+330alpha=10+10alphat`
or `11+330xx0.002=10+10xx0.002t`
or `11.66=0.02t+10`
or `0.02t=1.66`
or `t=83^(@)C`