Filament lamp current at switch-on

A metal filament has a positive temperature coefficient, so its resistance is much lower when cold. At the instant of switching on, the filament is at 20°C, so the current is far larger than the normal running current.

Hot resistance (at 2000°C)

Rated power and voltage give the running resistance:

R_hot = V²/P = 240²/60 = 960 Ω

Cold resistance (at 20°C)

The question does not state the reference temperature for α, so take α = 0.0045 per °C at 20°C:

R_t = R₂₀ [1 + α(t − 20)]

960 = R₂₀ [1 + 0.0045 × (2000 − 20)] 960 = R₂₀ × 9.91

R₂₀ = 960/9.91 = 96.87 Ω

Switch-on current

I = V/R₂₀ = 240/96.87 = 2.48 A

The running current is 60/240 = 0.25 A, so the switch-on surge is about 10 times larger.

Answer: Current at the instant of switching on ≈ 2.48 A

(If α = 0.0045 is taken at 0°C instead, R₂₀ = 960 × 1.09/10 = 104.6 Ω and I ≈ 2.29 A.)