The operating temperature of the filament of lamp is `2000^(@) C`. The temperature coefficient of the material of the filament is `0.005^(@) C^(-1)`. If the atmospheric temperature is `0^(@) C`, then the current in the `100 W - 200 V` lamp when it is switched on is nearest to

Options

A. `2.5 A`
B. `3.5 A`
C. `4.5 A`
D. `5.5 A`

Answer

D

Explanation

`R_(200) = ( 200 xx 200)/( 100) = 400 Omega`
So `400 = R_(0) [ 1 + 0.005 xx 2000]`
or `(R_(0)) = ( 400 )/(11) Omega ~~ 36 Omega`
Hence , current
`I = ( 200) /( R_(0)) = 5.5 A`