The resistance of a bulb filmanet is `100Omega` at a temperature of `100^@C`. If its temperature coefficient of resistance be 0.005 per `""^@C`, its resistance will become `200 Omega` at a temperature of

Options

A. `500^(@)C`
B. `300^(@)C`
C. `200^(@)C`
D. `400^(@)C`

Answer

B

Explanation

Given, `R_(1)100 Omega, R_(2)=200 Omega, T_(1)=100^(@)C` and `alpha = 0.005`
We know that, new resistance of bulb filament,
`R_(2)=R_(1)[1+alpha(T_(2)-T_(1))]`
`200=100(1+0.005(T_(2)-100)]`
`2=1+[0.005(T_(2)-100)]`
`rArr 0.005 (T_(2)-100)=1`
or `T_(2)-100=(1)/(0.005)`
or `T_(2)-100=(1000)/(5)`
or `T_(2)-100=200`
or `T_(2)=200+100=300^(@)C`.