The resistance of a bulb filamanet 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. `300^@C`
B. `400^@C`
C. `500^@C`
D. `200^@C`

Explanation

Let resistance of bulb filament be`R_0` at `0^@C`, then from expression
`R_theta=R_0[1+a Delta theta]`
We have `100=R_0[1+0.005 times 100] and 200=R_0[1+0.005 times x]`
Where, x is temperature in `^@C` at which resistance become `200Omega` Dividing the above two equations, we get :
`200/100=(1+0.005x)/(1+0.005 times 100) implies x=400^@C`