light bulbs

[Allan Adler]

I have some naive questions about light bulbs that maybe someone here
knows how to answer.

(1) What is the theoretical voltage-current relationship for a light bulb?
I realize this depends on aspects of its construction, including the
material the filament is made of.
(2) The resistance of a light bulb apparently increases with voltage but
not linearly. What is the theoretical voltage-resistance relationship
of a light bulb?
(3) What mechanisms explain the relationship among voltage, current and
resistance of a light bulb and how do I compute them? For example,
how do the temperature and the work function of the filament and
the resulting electron cloud around the filament behave and how do
I compute their effect, if any, on current and resistance.

These questions derive from my continuing attempts to read Kloeffler's
book, Electron Tubes. I realized that the problems I was having with it
were all my own fault, caused by plunging into the chapter I was interested
in instead of reading the book carefully from the beginning. Often I can
get away with it, but Kloeffler's book is written a lot more carefully than
I realized and even the parts that I considered too trivial to read contain
some information that is necessary for understanding the conventions of rest
of the book. So, now I'm starting to appreciate the book. In particular,
it is nice to see that he starts with light bulbs to illustrate his
graphic techniques. I'll refer to a light bulb as a "unode". But he has
no theoretical discussion of the characteristics of unodes and I would like
to fill that lacuna.

Ignorantly,
Allan Adler
ara@zurich.ai.mit.edu

****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************

 

[Boris Mohar]

On 10 Oct 2003 10:28:47 -0400, Allan Adler <ara@nestle.ai.mit.edu> wrote:

I have some naive questions about light bulbs that maybe someone here
knows how to answer.

(1) What is the theoretical voltage-current relationship for a light bulb?
I realize this depends on aspects of its construction, including the
material the filament is made of.
(2) The resistance of a light bulb apparently increases with voltage but
not linearly. What is the theoretical voltage-resistance relationship
of a light bulb?
(3) What mechanisms explain the relationship among voltage, current and
resistance of a light bulb and how do I compute them? For example,
how do the temperature and the work function of the filament and
the resulting electron cloud around the filament behave and how do
I compute their effect, if any, on current and resistance.

These questions derive from my continuing attempts to read Kloeffler's
book, Electron Tubes. I realized that the problems I was having with it
were all my own fault, caused by plunging into the chapter I was interested
in instead of reading the book carefully from the beginning. Often I can
get away with it, but Kloeffler's book is written a lot more carefully than
I realized and even the parts that I considered too trivial to read contain
some information that is necessary for understanding the conventions of rest
of the book. So, now I'm starting to appreciate the book. In particular,
it is nice to see that he starts with light bulbs to illustrate his
graphic techniques. I'll refer to a light bulb as a "unode". But he has
no theoretical discussion of the characteristics of unodes and I would like
to fill that lacuna.

Ignorantly,
Allan Adler
ara@zurich.ai.mit.edu

****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************

--

Boris Mohar

 

[Peter Bennett]

On 10 Oct 2003 10:28:47 -0400, Allan Adler <ara@nestle.ai.mit.edu>
wrote:

I have some naive questions about light bulbs that maybe someone here
knows how to answer.

(1) What is the theoretical voltage-current relationship for a light bulb?
I realize this depends on aspects of its construction, including the
material the filament is made of.
(2) The resistance of a light bulb apparently increases with voltage but
not linearly. What is the theoretical voltage-resistance relationship
of a light bulb?

The resistivity of tungsten (the material normally used for lamp
filaments), as for most metals, increases with temperatures. This
change in resistance is a property of the material, and not something
that the light bulb designers specifically designed.

I suspect that tungsten is used for lamp filaments because it has a
very high melting point, and a fairly high resistivity. This means
that the filament can be heated white-hot without fear of it melting,
and you don't need a long wire, or very thin wire, to make a useful
lamp.

(3) What mechanisms explain the relationship among voltage, current and
resistance of a light bulb and how do I compute them?

Ohm's Law.

For example,
how do the temperature and the work function of the filament and
the resulting electron cloud around the filament behave and how do
I compute their effect, if any, on current and resistance.

As I recall, the filament or cathode in a vacuum tube is specially
treated to make it emit useful quantities of electrons. The filament
of a light bulb will not be so treated, because it doesn't need an
electron cloud around it.

These questions derive from my continuing attempts to read Kloeffler's
book, Electron Tubes. I realized that the problems I was having with it
were all my own fault, caused by plunging into the chapter I was interested
in instead of reading the book carefully from the beginning. Often I can
get away with it, but Kloeffler's book is written a lot more carefully than
I realized and even the parts that I considered too trivial to read contain
some information that is necessary for understanding the conventions of rest
of the book. So, now I'm starting to appreciate the book. In particular,
it is nice to see that he starts with light bulbs to illustrate his
graphic techniques. I'll refer to a light bulb as a "unode". But he has
no theoretical discussion of the characteristics of unodes and I would like
to fill that lacuna.

A light bulb is not a "unode" (whatever that may be). A light bulb
has very little in common with a vacuum tube.

--
Peter Bennett, VE7CEI
new newsgroup users info : http://vancouver-webpages.com/nnq
GPS and NMEA info: http://vancouver-webpages.com/peter
Vancouver Power Squadron: http://vancouver.powersquadron.ca

 

[JeffM]

A light bulb is not a "unode" (whatever that may be).
A light bulb has very little in common with a vacuum tube.

At various points in the evolution of incandescant lights,
the envelopes have been evacuated
rather than filled with (relatively) inert gas.

For historical perspective,
the Edison Effect was discovered by Thomas Alva
when he was messing around with light bulbs.

This was long before John Ambrose Fleming & Lee deForest put it to use.

 

[JeffM]

A light bulb is not a "unode" (whatever that may be).
A light bulb has very little in common with a vacuum tube.

At various points in the evolution of incandescant lights,
the envelopes have been evacuated
rather than filled with (relatively) inert gas.

For historical perspective,
the Edison Effect was discovered by Thomas Alva
when he was messing around with light bulbs.

This was long before John Ambrose Fleming & Lee deForest put it to use.

 

[Harry Conover]

Peter Bennett <peterbb@interchange.ubc.ca> wrote in message news:<sp9hov0g97fpitibhpqaq1vfnkcnaigghc@news.supernews.com>...

A light bulb is not a "unode" (whatever that may be). A light bulb
has very little in common with a vacuum tube.

Indeed. For that matter, a light bulb does not even enclose a vacuum.

Harry C.

 

[Don Klipstein]

In <7ce4e226.0310121547.2495482c@posting.google.com>, Harry Conover wrote:

Peter Bennett <peterbb@interchange.ubc.ca> wrote

A light bulb is not a "unode" (whatever that may be). A light bulb
has very little in common with a vacuum tube.

Indeed. For that matter, a light bulb does not even enclose a vacuum.

Some do. Roghly on an average, it is bgetter to use a vacuum than to
use the usual argon-nitrogen mixture if the wattage is less than 10 watts
per centimeter of apparent filament length (or maybe length plus diameter,
with these dimensions being the aparent-"visible" overall dimensions).
With near or over 10 watts per centimeter, light bulbs usually get a gas
fill.

Some examples among 120V ones in the USA:

Tubular refrigerator bulbs of 25 and 40 watts have a vacuum, and the (not
especially easy to find) 60 watt one has a gas fill.

"A19" "regular" bulbs with the coiled-coil filament about 2-2.5 cm long
normally get a gas fill from 25 watts on up. 120V bulbs with the
multi-supported C-shaped filament 40 watts and up get a gas fill. 120V
bulbs 15 watts and less generally have a vacuum.

The reasoning: A gas fill reduces filament evaporation by having gas
atoms "bounce" evaporated tungsten atoms back onto the filament. This
permits the filament to operate at a higher temperature for a given life
expectancy. (Note that gas filled ones have a trend of producing whiter
light than vacuum ones.) The higher temperature makes the filament's
radiation more in the visible and less in the infrared (although still
much more infrared than visible).
The drawback of a gas fill is that it conducts heat from the filament -
and this means energy going in that is not radiated at all. Heat
conduction is nearly enough proportional to filament visibly apparent
length but surprisingly independent of visible apparent diameter, since a
wider filament has a thicker "boundary layer" of gas around it and the
thicker boundary layer has a lower temperature gradient to nearly cancel
the greater circumference. Thinner filaments in a gas fill have almost as
much heat conducted from them (per unit length) as thicker ones, which
makes gas heat conduction a higher percentage of input power with the
thinner filaments. This is why filaments with more wattage per
centimeter of apparent length do better with a gas fill and ones with
lower wattage per centimeter of apparent length do better with a vacuum.

- Don Klipstein (don@misty.com, http://www.misty.com/~don/index.html)

 

[Allan Adler]

Thanks to don@manx.misty.com (Don Klipstein) for all the interesting
information about light bulbs. Is there a book you can recommend that
has all this design information?

Here is another question, on a lower level: the schematic for my EICO 460
oscilloscope calls for a #47 lamp somewhere. What is a #47 lamp and where
would one read its specs? The specs themselves are not a vital concern for
understanding the workings of the scope but I am curious to know where one
looks up stuff like that.

Regarding my original question, which pertained to how one can give a complete
accounting of various processes taking place in the bulb (how the resistance
of the filament depends on voltage, how much heat is generated, the structure
of the electron cloud and how its presence affects the energy inventory, etc.),
I haven't gotten any answers or any references but I have made some progress
on my own. First, I found that Tolman's Principles of Statistical
Thermodynamics has a discussion of "conduction electrons", which discussion
I've now read and am trying to digest. It is also discussed in van Vleck's
book on electric and magnetic susceptibilities, which I've since also read
briefly. There is also a book of Samsonov on his "configurational model of
matter" which applies the model to electrical conduction and thermionic
emission, among other things. So, hopefully I'll learn a little more about
what is going on that way. That doesn't mean I'll get the "inventory" I was
asking for, but it might help.

At any rate, thermodynamically, we can think of the electrons as a kind of
gas (obeying Fermi-Dirac statistics), some of which manages to get outside
the filament when the velocity is sufficiently high, and which otherwise
manages somehow to maintain an electric current. Athough this is nominally
about electrons, voltage, current, heat and clouds, maybe I should be asking
about this on a newsgroup devoted to thermodynamics.

Ignorantly,
Allan Adler
ara@zurich.ai.mit.edu

****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************

 

[Harry Conover]

Allan Adler <ara@nestle.ai.mit.edu> wrote in message news:<y93n0c5qj8l.fsf@nestle.ai.mit.edu>...

Here is another question, on a lower level: the schematic for my EICO 460
oscilloscope calls for a #47 lamp somewhere. What is a #47 lamp and where
would one read its specs? The specs themselves are not a vital concern for
understanding the workings of the scope but I am curious to know where one
looks up stuff like that.

This URL may help:

http://www.gbronline.com/radioguy/lamps.htm

Unfortunately, the above covers only the older classic type pilot
lamps and completely omit more recent types (of which there are
hundreds).

Both the Newark Electronic and Allied catalogs list virtually every
type of pilot lamp that is manufactured, including some
specifications. Their is also a table of pilot lamps and
characteristics in older editions of the ARRL Radio Amateur's Handbook
(along with extensive listings of vacuum tubes, crts, etc. Beyond
these sources, you may need to consult manufacturer's literature.

Harry C.

 

[John Fields]

On 13 Oct 2003 10:56:26 -0400, Allan Adler <ara@nestle.ai.mit.edu>
wrote:

Here is another question, on a lower level: the schematic for my EICO 460
oscilloscope calls for a #47 lamp somewhere. What is a #47 lamp and where
would one read its specs?

---
http://ecom.mysylvania.com/sylvaniab2c/b2c/z_login.do;jsessionid=ID4001DB0.9685618116077311End


--
John Fields

 

[Don Klipstein]

In article <y93n0c5qj8l.fsf@nestle.ai.mit.edu>, Allan Adler wrote:

Thanks to don@manx.misty.com (Don Klipstein) for all the interesting
information about light bulbs. Is there a book you can recommend that
has all this design information?

Here is another question, on a lower level: the schematic for my EICO 460
oscilloscope calls for a #47 lamp somewhere. What is a #47 lamp and where
would one read its specs?

#47: T3-1/4 bulb, miniature bayonet base, design voltage 6.3 volts,
drawing .15 amp at that voltage, .5 MSCD (approx. 6.3 lumens) light
output, design life expectancy 3,000 hours.
Variants include the 1847 (.38 MSCD or approx. 4.8 lumens, 5,000-plus
hours life expectancy), the 40 (same as 47 except screw base instead of
bayonet base), and the 755 (.33 MSCD or 4.1 lumens, 20,000 hour life
expecyancy at 6.3 volts).

Regarding my original question, which pertained to how one can give a
complete accounting of various processes taking place in the bulb

(how the resistanc of the filament depends on voltage,

Varies from one bulb to another and with voltage, but in most cases
within voltage ranges where the bulbs visibly glow and don't burn out
within a second the resistance is not too farr off from proportional to
the square root of voltage.

how much heat is generated,

Power in becomes heat. Where the light mostly fails to escape the room
that the lamp is in, power into the lamp becomes heat in the room. Light
(and infrared) that escapes the location becomes heat wherever the light
eventually goes.
It seems to me that roughly 40-65% of the power going into an
incandescent lamp is radiated, and the remainder becomes heat at the site
of the lamp.

the structure of the electron cloud

Sorry, I can't help much there.

and how its presence affects the energy inventory, etc.),

Energy stored in the electron cloud is small and reasonably constant
during lamp operation. By any accounting of energy breakdown in input and
output during continuous operation, energy storage in the electron cloud
should be insignificant.
I would not worry about electron clouds, thermionic emission nor the
like in any pie charts for input to (100% electric power) nor output from
an incandescent lamp.

- Don Klipstein (don@misty.com)

 

[Watson A.Name - "Watt Sun]

In article <slrnbok1ls.m88.don@manx.misty.com>, don@manx.misty.com
mentioned...

In <7ce4e226.0310121547.2495482c@posting.google.com>, Harry Conover wrote:
Peter Bennett <peterbb@interchange.ubc.ca> wrote

A light bulb is not a "unode" (whatever that may be). A light bulb
has very little in common with a vacuum tube.

Indeed. For that matter, a light bulb does not even enclose a vacuum.

Some do. Roghly on an average, it is bgetter to use a vacuum than to
use the usual argon-nitrogen mixture if the wattage is less than 10 watts
per centimeter of apparent filament length (or maybe length plus diameter,
with these dimensions being the aparent-"visible" overall dimensions).
With near or over 10 watts per centimeter, light bulbs usually get a gas
fill.

Some examples among 120V ones in the USA:

Tubular refrigerator bulbs of 25 and 40 watts have a vacuum, and the (not
especially easy to find) 60 watt one has a gas fill.

"A19" "regular" bulbs with the coiled-coil filament about 2-2.5 cm long
normally get a gas fill from 25 watts on up. 120V bulbs with the
multi-supported C-shaped filament 40 watts and up get a gas fill. 120V
bulbs 15 watts and less generally have a vacuum.

The reasoning: A gas fill reduces filament evaporation by having gas
atoms "bounce" evaporated tungsten atoms back onto the filament. This
permits the filament to operate at a higher temperature for a given life
expectancy. (Note that gas filled ones have a trend of producing whiter
light than vacuum ones.) The higher temperature makes the filament's
radiation more in the visible and less in the infrared (although still
much more infrared than visible).
The drawback of a gas fill is that it conducts heat from the filament -
and this means energy going in that is not radiated at all. Heat
conduction is nearly enough proportional to filament visibly apparent
length but surprisingly independent of visible apparent diameter, since a
wider filament has a thicker "boundary layer" of gas around it and the
thicker boundary layer has a lower temperature gradient to nearly cancel
the greater circumference. Thinner filaments in a gas fill have almost as
much heat conducted from them (per unit length) as thicker ones, which
makes gas heat conduction a higher percentage of input power with the
thinner filaments. This is why filaments with more wattage per
centimeter of apparent length do better with a gas fill and ones with
lower wattage per centimeter of apparent length do better with a vacuum.

Can you tell us how two light bulbs compare: the U.S. 120VAC light
bulb compared to the Euro 240VAC light bulb. I assume that the U.S.
filament is shorter and heavier than the Euro. So is it more
efficient?

I have an old Tensor lamp that uses the #91 (IIRC) light for autos.
Thing was always needing a lamp (maybe because I used it a lot!), but
they were readily available at the store. In that case, it didn't
seem as if the heavier filament was helping it last longer.

This weekend I bought a light bulb from the auto store. It's a
regular tubular light for a car dome light, but it has a blue coating
on it to make the radiated light blue. It draws more than .83A at
12V, so it eats up more than 10W, and gets hot (I'm surprised the blue
coating doesn't melt). Yet it puts out surprisingly little blue
light, in fact I'd say a dozen blue LEDs would easily outshine it.

- Don Klipstein (don@misty.com, http://www.misty.com/~don/index.html)

--
@@F@r@o@m@@O@r@a@n@g@e@@C@o@u@n@t@y@,@@C@a@l@,@@w@h@e@r@e@@
###Got a Question about ELECTRONICS? Check HERE First:###
http://users.pandora.be/educypedia/electronics/databank.htm
My email address is whitelisted. *All* email sent to it
goes directly to the trash unless you add NOSPAM in the
Subject: line with other stuff. alondra101 <at> hotmail.com
Don't be ripped off by the big book dealers. Go to the URL
that will give you a choice and save you money(up to half).
http://www.everybookstore.com You'll be glad you did!
Just when you thought you had all this figured out, the gov't
changed it: http://physics.nist.gov/cuu/Units/binary.html
@@t@h@e@@a@f@f@l@u@e@n@t@@m@e@e@t@@t@h@e@@E@f@f@l@u@e@n@t@@

 

[Watson A.Name - "Watt Sun]

In article <y93n0c5qj8l.fsf@nestle.ai.mit.edu>, ara@nestle.ai.mit.edu
mentioned...

Thanks to don@manx.misty.com (Don Klipstein) for all the interesting
information about light bulbs. Is there a book you can recommend that
has all this design information?

Here is another question, on a lower level: the schematic for my EICO 460
oscilloscope calls for a #47 lamp somewhere. What is a #47 lamp and where
would one read its specs? The specs themselves are not a vital concern for
understanding the workings of the scope but I am curious to know where one
looks up stuff like that.

The #47 lamp is an industry standard, the most common miniature light
bulb; it was used in just about every all american 5-tube radio in the
days of tube radios. It's 6.3VAC at 150 mA, which matched the current
of the filaments of a tube, so it could be run in series with the
tube. It should be easily found at any place that sells light bulbs,
maybe even Radio Snack. There should be an abbreviated list of the
various common miniature lamps available on the web. A search for it
should turn up something. Here's one that i got from google.
http://www.wps.com/archives/lamps.html The first one is a huge .JPG
that took forever to d/l, I wish the guy had saved it in a smaller
size. He doesn't realize that most of us are still using dialup.
Yeah, at work I have a 45 Mb connection to the rest of the world, but
not at home. If I wanna d/l the latest Mozilla or other huge file, I
do it at work. ;-)


--
@@F@r@o@m@@O@r@a@n@g@e@@C@o@u@n@t@y@,@@C@a@l@,@@w@h@e@r@e@@
###Got a Question about ELECTRONICS? Check HERE First:###
http://users.pandora.be/educypedia/electronics/databank.htm
My email address is whitelisted. *All* email sent to it
goes directly to the trash unless you add NOSPAM in the
Subject: line with other stuff. alondra101 <at> hotmail.com
Don't be ripped off by the big book dealers. Go to the URL
that will give you a choice and save you money(up to half).
http://www.everybookstore.com You'll be glad you did!
Just when you thought you had all this figured out, the gov't
changed it: http://physics.nist.gov/cuu/Units/binary.html
@@t@h@e@@a@f@f@l@u@e@n@t@@m@e@e@t@@t@h@e@@E@f@f@l@u@e@n@t@@

 

[Allan Adler]

Thanks to all for the abundant and diverse information on #47 lamps.

Regarding Don Klipstein's (don@misty.com) other replies to my questions,
I'll take them in turn.

(how the resistanc of the filament depends on voltage,
Varies from one bulb to another and with voltage, but in most cases
within voltage ranges where the bulbs visibly glow and don't burn out
within a second the resistance is not too farr off from proportional to
the square root of voltage.

Thanks, I'll check this against the graph in Kloeffler's book and get
back to this later. But how do you know this?

how much heat is generated,

Power in becomes heat. Where the light mostly fails to escape the room
that the lamp is in, power into the lamp becomes heat in the room. Light
(and infrared) that escapes the location becomes heat wherever the light
eventually goes.
It seems to me that roughly 40-65% of the power going into an
incandescent lamp is radiated, and the remainder becomes heat at the site
of the lamp.
[...]
Energy stored in the electron cloud is small and reasonably constant
during lamp operation. By any accounting of energy breakdown in input and
output during continuous operation, energy storage in the electron cloud
should be insignificant.
I would not worry about electron clouds, thermionic emission nor the
like in any pie charts for input to (100% electric power) nor output from
an incandescent lamp.

How do you compute the percentage that is radiated?

The electric field causes the electron to travel with a certain velocity
before it collides with something and gives up some or all of its kinetic
energy. Multiplying the electric field by the charge of the electron gives
what I guess is the maximum kinetic energy of the electron. When it collides
with something, that energy is converted to heat. That heat raises the
temperature of the filament, changing the resistance. The amount of heat
generated per second would be, I guess, the number of collisions per
second times the average kinetic energy of the electrons. The number of
collisions per second should be related to the mean free path of the
electron in the metal at the given voltage (which will vary through the
metal) and maybe also the number is proportional to the resistance.
If so, that might give a conceptual way to compute the study the relation
among voltage, heat generated and changes in resistance.

The electrons that are traveling fast enough have the possibility of
escaping into the electron cloud and not colliding with anything while
they are in it but maybe some energy is given up when they pass through
the surface of the filament. Mostly they fall back in and are replaced by
other electrons, so there is a certain percentage of the energy that is
stored in the electron cloud, namely maybe the number of electrons per second
that escape into the cloud minus the number per second that fall back in, all
multiplied by the work function of the metal.

I don't care if it is insignificant. I just want to know how one computes it
to prove that it is insignificant. I can speculate about methods for computing
stuff like that, but I don't know if the methods are right.

That's why I'm asking. The best answer would be to relevant literature,
preferably books that treat this kind of question. I've already mentioned
a few that I know about: (1) Tolman's Principles of Statistical Mechanics
(2) van Vleck's Electric and Magnetic Susceptibilities (3) Samsonov's
A configurational model of matter. The latter reference shows that one
can go even more deeply into it, by considering the actual electronic structure
of the atoms involved and seems quite fascinating in the scope of its
applications.

I'm going to cross-post this to sci.physics to see if they know more about
this kind of question there.


Ignorantly,
Allan Adler
ara@zurich.ai.mit.edu

****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************

 

[w_tom]

Examples to your question were posted in the newsgroup
misc.consumers.frugal-living on 8 Oct 2003 entitled "Watts
versus Lumens? Thoroughly confused". Notice the exponential
relationship for incandescent lamps. Every bulb technology
has a specific lumens per watt ratio when operated at its
standard conditions. For example, incandescent bulbs
typically have a 14 or maybe even as much as 18 lumens per
watt efficiency.

As voltage increases, light output increases typically by an
exponential factor of 3.5. However as voltage increases, the
life expectancy of an incandescent bulb tends to decrease by
an exponential factor of 13. If I remember correctly, a 120
VAC bulb will have life expectancy decreased by one half if
voltage is 126. A 120 volt light bulb running at 90 VAC will
output about 35% of normal light.

Allan Adler wrote:

Thanks to all for the abundant and diverse information on #47 lamps.

Regarding Don Klipstein's (don@misty.com) other replies to my
questions, I'll take them in turn.
...

 

[Paul Cardinale]

actual_current = rated_current * ((applied_voltage / rated_voltage) ^ 0.55)

 

[Allan Adler]

Apparently a lot of my questions about light bulbs and electron tubes are
answered at the following website and the literature it cites.

http://www.physics.csbsju.edu/thermionic.pdf

Ignorantly,
Allan Adler
ara@zurich.ai.mit.edu

****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************