# How quick does a regular household bulb lights up after being switched on? [closed]

In this video the narrator mentions a study in which if a light bulb lights up quicker than 40ms it would seem as though it lit up before it was even switched on.

How quick does a regular household bulb lights up after being switched on? Is it anywhere near ~80ms?

• Even though I like the question (+1), IMHO it is not about physics. Consider migration to engineering.SE Feb 28, 2016 at 17:57
• @AccidentalFourierTransform: I think it could make a good Fermi estimation problem: what's the mass of the filament, what's a plausible start-up transient and so on. I'd guess 10 cycles, so about 1/5s for a domestic light.
– user107153
Feb 28, 2016 at 18:32
• I'm voting to close this question as off-topic because it's not about physics. Feb 29, 2016 at 11:16

When a resistor is connected to a source of e.m.f. a current will begin to flow. This flow of current causes the resistor to heat, which results in a temperature increase, which, in turn, causes the resistance to increase. If the resistance increases less current is drawn from the supply, which implies that the temperature of the resistor drops. Eventually an equilibrium situation is reached and the temperature reaches a steady state value.

Ignoring switch dynamics you would have to take into account the dependence on resistance with temperature, the Stefan Boltzmann law and the thermal capacity of the material. I think the time scale is set by the parameter $\frac{mc}{A \epsilon \sigma T_e^3} = \frac{mc T_e}{A \epsilon \sigma T_e^4}$, where $m$ is the mass of the filament, $c$ its specific thermal capacity, $A$ the surface area of the filament, $\epsilon$ its emissitivity, $\sigma$ the Stefan Boltzmann constant and $T_e$ the equilibrium temperature. I never did put numbers to this, but suspect that it will turn out $\approx ms$ (this estimate ignores the variation of resistance with temperature).

• One thing we know is that the thermal cycling is small over a cycle of mains (or incandescent bulbs would not last long). Mains (in Europe) is 50Hz so there's little change in temperature over times around 0.01s. I would therefore guess (again) a warm-up time of about 0.2s
– user107153
Feb 28, 2016 at 19:59
• @AccidentalFourierTransform It should be that $c$ is the specific heat capacity (unit $J kg^{-1} K^{-1}$), so that $mc$ is the heat capacity, as well I think the denominator should be $T_e^3$. Think this has the correct units: Units of the numerator, $mcT_e$, are $J$ and the units of the denominator, $A \epsilon \sigma T_e^4$ are $W$.
– jim
Feb 28, 2016 at 20:07
• I think if you include resistivity it introduces a factor of about $\frac{1}{4}$ to the black body estimate.
– jim
Mar 6, 2016 at 15:41

The filament in an incandescent bulb produces light by getting hot enough to produce black-body radiation in the visible spectrum. When the filament is cold, the resistance of the filament is only about 1/15 as much as when the filament is hot. Since both the current through the filament and the amount of light produced by the filament depend crucially on the filament's temperature, how long the filament takes to get hot enough for the current to decrease to close to its normal value is a good proxy for how long it takes the filament to get hot enough to produce close to its normal amount of light. According to the graph of the inrush current on this page, it only takes about 10 or 20 milliseconds for the filament of a 100W bulb to get hot, which is only about one cycle of the mains frequency. Higher wattage bulbs take longer.