Electrical math

[CWMurf]

When overdriving a lamp is there a factor of reactance which effects the E*I formula? Running a 50w lamp at 12v draws 4.16w. Does sourcing the same lamp with 18v cause 74.9w and draw the same 4.16w?

Thanks for the clarification.

Murf

 

[herman]

When overdriving a lamp is there a factor of reactance which effects the E*I formula? Running a 50w lamp at 12v draws 4.16w. Does sourcing the same lamp with 18v cause 74.9w and draw the same 4.16w?

Thanks for the clarification.

Murf

Welcome to the board.
It's been a while since I did power formulas but here goes.
Assuming this is steady state DC the one constant (more or less) is filament resistance- Rf.
To find that we need, we have to modify the power formula
P=E(2)/Rf or Rf= E(2)/P= 144V/50W= 2.88 ohms is our steady state resistance
(be darned if I know how to make an exponent ... E(2) is voltage squared)

So if we up the voltage to 18V the new values will be :
P= e(2)/Rf= 324V/2.88 ohms = 112.5 watts
I= P/E = 112.5w/18V= 6.25A is going to be our new filament current....but not for long I would bet

Depending on the temperature coefficient of the filament the final current and actual operating resisitance will vary but this should be close.

That what you needed?

 

[MikeFerrara]

When overdriving a lamp is there a factor of reactance which effects the E*I formula? Running a 50w lamp at 12v draws 4.16w. Does sourcing the same lamp with 18v cause 74.9w and draw the same 4.16w?

Thanks for the clarification.

Murf

I think the answer to your question is that as voltage is increased the current also increase and so does the disapated power. There isn't really a constant here but the resistance of the bulb comes closest to being constant. The problem with overdriving a bulb (guessing as to the reason for your question) is that, while you'll get more light, you'll also get more heat and potentially shorten the life of the bulb. The life of the bulb is not always liniarly related to the current. It may result in a less than predictable "mean time to failure" (an unreliable light).

Personally I haven't bothered to check on the claims that some manufacturers over drive bulbs or that even if they do if it's enough to make any difference in bulb life or reliability.

 

[Charlie99]

Some rules of thumb for tungsten filament bulbs such as halogen lamps:

Power is proportional to V^1.6 (if it were a constant resistance, it would be V^2, but the resistance of the filament goes up signficantly as it get hotter)

So at 18V it would draw about 96 watts.

The light output goes up as V^3.4, so at 18V the light output would be about 4 times the output at 12V.

The big drawback, though, is life, which is inversely proportional to V^16. More likely than not, 18V would heat the filament to the point of immediate failure, making the approximation invalid, but if it were, the life expectancy would be reduced by a factor of 650.

In the more normal range of small tweaks on voltage, some reasonable approximations is that 5% voltage change will be 20% change in light, and a doubling or halving of life. The power difference from 5% change in voltage is about 8%, rather than the 10% that would occur in a fixed value resistance.

 

[CWMurf]

Thanks for all the great information. It has been awhile since I worked these types of formulas and they are getting more complex than I remembered.

As for the filament resistence, I was under the impression that as temperature increased resistance decreased. Do I remember that backward?

As for filament life, I don't know yet to what extent overdriving will reduce the life but I have powered up a 50w bulb dry for a few minutes without losing the filament so I'm sure failure won't be instant. I'm also asuming that H2O cooling will help some with the heat buildup in the the lamp. I have read others' posts stating that they have gotten about 70 hours out of a 50w halogen run at about 18v.

 

[Don Burke]

Thanks for all the great information. It has been awhile since I worked these types of formulas and they are getting more complex than I remembered.

As for the filament resistence, I was under the impression that as temperature increased resistance decreased. Do I remember that backward?

As for filament life, I don't know yet to what extent overdriving will reduce the life but I have powered up a 50w bulb dry for a few minutes without losing the filament so I'm sure failure won't be instant. I'm also asuming that H2O cooling will help some with the heat buildup in the the lamp. I have read others' posts stating that they have gotten about 70 hours out of a 50w halogen run at about 18v.

Filament resistance increases with temperature. A light bulb makes a pretty good current limiter for a charging circuit in some applications.

The penalty for overdriving is pretty stiff. While the water will help, the temperature at the filament is the determining factor and the water can only help so much.

70 hours sounds like good luck.

 

[deepseafalcon]

When overdriving a lamp is there a factor of reactance which effects the E*I formula? Running a 50w lamp at 12v draws 4.16w. Does sourcing the same lamp with 18v cause 74.9w and draw the same 4.16w?

Thanks for the clarification.

Murf

you might be interested in that
http://www.pcmus.com/Dive-Photos/Dive-Light-DIY-SCUBA.htm
it answers your questions, and then some

d-s-f