The resistance of the filament of a lamp increases with the increase in temperature. A lamp rated `100 W` and `220 V` is connected across `220 V` power supply. If the voltage drops by `10%`, then the power of the lamp will be

Options

A. `90 W`
B. `81 W`
C. between `90 W and 100 W`
D. between `81 W and 90 W`

Answer

D

Explanation

Let the resistance of the lamp filament be `R`. Then `100 = (220)^(2)// R`. When the voltage drops, expected power is `P = (220 xx 0.9 )^(2) //R'` will be less than `R`, because now the rise in temperature will be less. Therefore, `P` is more than `( 220 xx 0.9)^(2) // R = 81 W`. But it will not be `90%` of the earlier vallue, because fall in temperature is smalll. Hence, option (d) is correct.