Wednesday, September 30, 2009

The truth about leaving light bulbs on

A common piece of urban folklore: Its better to leave a light on than to turn it off and turn it on a half hour later. The theory is that the bulb takes more energy on startup than it takes while in regular operation.
Time to debunk this foolish folklore with some math and specifications.( for incandescent bulbs)
Cold resistance of a tungsten incandescent bulb is usually around 1/10 or 1/15 the hot resistance of the bulb.( depending on the bulb). The startup time for the bulb to get from cold resistance to hot resistance is at maximum 1/5 of a second.
So when the bulb is starting up and turning on , it has cold resistance. After the the bulb is all turned on, it now has the higher resistance.
And we all know that with great power comes great current squared times resistance, or power = current* resistance. So Power = Current^2 * Resistance.

Lets take a common incandescent bulb with the following specs:
100W power consumption
120 volt source
Hot Resistance of 150 ohms
Cold resistance of 10 ohms
Startup Time(cold to hot) of .20 seconds

So that means that during that startup time , you will spend 3.16 amps(100 = i^2 * 10) for .2 seconds . Whereas with the hot resistance you will spend 0.81 amps(100 = i^2 * 150).
So lets see: upon startup you are spending around 4 times(3.16/.81=3.9) as much energy as you would spend , but only for 1/5 of a second.

Lets solve to see how many seconds of hot current draw equals cold current draw.
3.16 amps * .2 seconds = .81 amps * X seconds
X seconds = .78 seconds

Conclusion:
It takes less than one second to compensate for that startup current "surge"! Urban myth is busted!

Keith said...

Neat, but Mythbusters did it.

But since I know that you didn't know that at the time of writing this - good job! Impressive.

Anonymous said...

saying . It refered to Fkuorescent tubes when they first came on the scene in the 50's or so.

The start up current was massive so it was better to leave them turned on

Anonymous said...

Eric,

The urban myth is not really concerned about the differences in power consumption cost. It is more derived from the cost of bulb replacement, time to replace and gas to go get the bulbs you forgot to stock up on.

Bulbs blowing is directly related to the inrush of current during power up. Each and everyone doing molecular damage per flick of the switch.