• Two electric bulbs have tungsten filaments of the same thickness. If one of them gives 60 W and the other gives 100 W, then 60 W lamp filament has a longer length.
• This is because the power output of an electric bulb is directly proportional to the temperature of the filament, which depends on the resistance of the filament.
• The resistance of the filament is proportional to its length and inversely proportional to the power output of the bulb.

The power output of an electric bulb is given by the formula P = V²/R

The resistance of a conductor is given by the formula R = ρL/A,

where

ρ is the resistivity of the conductor
L is the length of the conductor
A is its cross-sectional area.

Assuming that both bulbs have tungsten filaments of the same thickness, their cross-sectional areas (A) are equal.

Rearranging the resistance formula, we get L = RA/ρ.

Substituting this expression for L into the formula for power, we get P = V²ρ/A²L.

Rearranging this formula, we get L = V²ρ/AP.

Since the voltage (V), resistivity (ρ), and cross-sectional area (A) of both bulbs are assumed to be the same, we can simplify this expression to L ∝ 1/P.

Therefore, the length of the filament is inversely proportional to the power output of the bulb.

Hence, the filament of the bulb with lower power (60 W) will have a longer length compared to the filament of the bulb with higher power (100 W).