Question

A tungsten lightbulb filament is designed to dissipate 120 W at a 120-V potential difference. If the lit filament is at 2050 K , what's its resistance when off? This question has been asked numerous times on this site by several people and the answer given is always incorrect and downvoted.

Answer 1

we know that

Watts = Volts x Amps

we can write

I = W/V

I = 120/120

I = 1 A

given If the lit filament is at 2050 K

now filament resistance when lit lets say R

R= V/I

= 120/1

R= 120 ohm

now resistance when filament is off = Ro

R = Ro[1+(T_on-T_off) ]

= 4.5 x10^-3 ohm/c for tungsten

Toff = room temp = 273 + 20 = 293 K

Ton = 2050 K ( given)

now

R = Ro[1+(T_on-T_off) ]

120 = Ro [ 1+ (4.5 x10^-3)(2050-293)]

Ro = 13.47 ohm