Two electric bulbs have tungsten filament of the same thickness. If one of them gives 60 W and the other gives 100 W, then
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,
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).