The resistance of the bulb filament is `100Omega` at a temperature of `100^(@)C` . If its temperature co-efficient of resistance be 0.005 per `5 ""^(@)C`, its resistance will becomes `200 Omega` at a temperature

Options

A. `300^(@)C`
B. `400^(@)C`
C. `500^(@)C`
D. `1,200^(@)C`

Answer

D

Explanation

We can write temperature dependence of resistance as follows:
Temperature coefficient is written on per `5^(@)C` basis so that actual `alpha = 0.001` per `""^(@)C`
`R= R_(0) [1 + alpha t]`
`100 = R_(0) [1 + 100 xx 0.001]`
`rArr R_(0) = (100//1.1) Omega`
Let t be the temperature at which the resistance becomes `200Omega`.
`200 = R_(0) [1 + t xx (0.001)] = (100//1.1) [1 + t xx (0.025)]`
`rArr 1 + t xx (0.001) = 2.2`
`rArr t= 1,200 ""^(@)C`
Hence, option (d) is correct