Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, `100W, 60W and 40W` bulbs have filament resistances `R_(100), R_(60) and R_(40)`, respectively, the relation between these resistances is

Options

A. `(1)/(R_(100))=(1)/(R_(40))+(1)/(R_(60))`
B. `R_(100)=R_(40)+R_(60)`
C. `R_(100) gt R_(60) gt R_(40)`
D. `(1)/(R_(100)) gt (1)/(R_(60)) gt (1)/(R_(40))`

Answer

D

Explanation

Power `= VI= V . (V)/(R )=(V^(2))/(R )`
Thus `P prop (1)/(R ) or R prop (1)/(P)`
`because P_(100) gt P_(60) gt P_(40)`
`therefore (1)/(R_(100)) gt (1)/(R_(60)) gt (1)/(R_(40))`