Lamp Current vs Voltage

[Joseph]

I am trying to determine the relationship between voltage and current for a light bulb, in my case, a heat lamp. I think I have the approximate formula determined by examining a couple of graphs of current vs. voltage for two different bulbs.<p>Can anyone confirm that the current increases approximately in proportion to the sqrt of the voltage increase? For example, if the voltage is doubled, the current goes up 1.4 times. Thanks.

[Enzo]

Hard to say. What is happening is that the filament resistance changes with temperature. The cold resistance is lower than the hot. As you play with the voltage, you are also then changing how hot the thing is.<p>An experiment: measure the resistance of the cold filament with the bulb out of circuit. Then measure the voltage across and current through the bulb when running at rated voltage and fully warm. Use Ohm's law to infer the resistance. That should demonstrate the concept.<p>I doubt there is any listing of such data.

[Dean Huster]

It is a fun little experiment to do. When I was teaching, the auto mechanics instructor was having trouble teaching Ohm's Law to his students. He was using a light bulb, measuring the resistance, making the calculation and then wasn't able to figure out why the measurements were all jabberwocky.<p>I can't imagine any lamp manufacturer having this data tabulated or plotted out with the possible exception of some of the lamps that were used in the feedback loop of Wein bridge oscillators, such as the Hewlett-Packard 200CD (a 6S6 lamp maybe?).<p>Dean

[Joseph]

Based on the graph

and my intuition, I suspect the relationship to be rather universal and independent of the light bulb used. If anyone has a variable lab power supply which can measure voltage and current independently, I think it would be interesting to try to test the idea.<p>[ September 27, 2004: Message edited by: Joseph ]</p>

[rshayes]

Some of the old ap notes for incandescent bulbs give general approximations for the effect of voltage changes.<p>Life is approximately the inverse 12 power of voltage.<p>Current is approximately the .55 power of voltage.<p>Light output is approximately the 3.5 power of voltage.<p>The current will increase slightly faster than the square root of voltage, since the square root is represented as the .5 power.<p>These approximations do not apply to long life lamps (over 5000 hours) or to halogen lamps.<p>The HP oscillators used a pear shaped lamp with a screw base. These were often used in industrial indicators, since they could illuminate an indicator that was about 1 inch in diameter. I think that the Hewlwtt Packard instruments used the 120 volt, 7 watt bulb. There was also a 120 volt, 3 watt bulb, but I think this was less common.<p>The operating point for the bulb in the oscillator circuit was probably around 10 volts. If the bulb was rated for 1000 hours life at 120 volts, the estimated life at 10 volts would be about 10^16 hours, which is ridiculous. This is about 10^12 years, more than the estimated age of the earth by quite a bit. Most of the failures in the HP oscillators were probably due to shock or vibration.

[Joseph]

Stephen, thanks for that cool information. I seem to be intrigued by the nonlinear characteristics of incandescent lamps.

[Chris Smith]

Non linear describes it best, just like Semi conductors can be non linear. The only real rating is at fullpower, and then it becomes some what stable, IF the surrounding temps dont change drastically.

[Joseph]

True about semiconductors, they can be fun too.<p>Here is what I came up with for my project so far for two 120v heat lamps operating in series so that each drops 60v:

• current through each is 1.42a
• Power through each is 85w.

I am not making sense out of the life formula, it just seems too long an increase for even a small drop in voltage. Since the life is 2000 hours at 120v, At 60 volts, the life would still be infinite for all intents and purposes, which seems wrong to me.<p>[ September 28, 2004: Message edited by: Joseph ]</p>

[Joseph]

BTW, the lamps are rated 250w at 120 volts. Sorta like Enzo was saying, I used that figure to calculate the current at 120v.<p>[ September 28, 2004: Message edited by: Joseph ]</p>

[Will]

Joseph,
The resistivity of the filaments is a function of the filament temperature - but, as is already established - it's not a linear function. I curve fitted both lamp currents in erms of voltage and, for the 3 volt lamp the equation was i = v/(a*v + b) where a was 1.3809 and b was 5.3425 that correlated all results to within 4.0 % - for the 6 volt lamp the equation was i = a + v*b where a = 0.2067 and b = 0.105 - they correlated to within 1.0 % - could not find a correation between power and resistance but the ratio of resistance to current came relatively close for the 3 volt (6.667, 5.893,5.587,5.405,5.454, and 5.325 and that for the 6 volt came to 3.226, 3.367 and 3.331
I'm not sure that any of that means anything but you can play with it.

[Edd]

As per your statement:
<<<Here is what I came up with for my project so far for two 120v heat lamps operating in series so that each drops 60v:
current through each is 1.42a
Power through each is 85w.
I am not making sense out of the life formula, it just seems too long an increase for even a small drop in voltage. Since the life is 2000 hours at 120v, At 60 volts, the life would still be infinite for all intents and purposes, which seems wrong to me.>>><p>Made me think of back in ’86 when an aunt had increased her dress shop in size and the new area incorporated a raised display window. There were 6 spare recessed light fittings left over from another area so I opted to space out them to top light the model area below in the showcase. Considering the difficulty to crawl up to that area for lamp replacement, I thought of no better solution than to take each adjacent pair of lamps and connect them in series for reduced voltage operation. Six 130 volt rated flood light lamps then provided the illumination complement. Connection into a junction box that was in the shopping centers fascia attic completed the power interfacing. That supply line provided for fill in walkway lighting on the sidewalks for the strip center, with dusk to dawn photocell activation.
The end result, to date, is that those dimmed (dammned?...!!!) lamps have been running ~ 9 hrs a day for 18+ years with no failures.
FIO…at that reduced lighting level there was still white lighting provided…not a reduction and spectral shift towards yellow , as one would get at yet a lower voltage supply level.<p>73's de Edd
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<p>[ September 28, 2004: Message edited by: Edd Whatley ]</p>

[Dean Huster]

Stephen, the 6S6 that I had mentioned is just such a pear-shaped lamp, although I don't remember if it was the 6S6. The 6S6 is/was available in several versions:<p>6S6/120V 120.0V 6 watts
6S6/130V 130.0V 6 watts
6S6/145V 145.0V 6 watts
6S6/155V 155.0V 6 watts
6S6/30V 30.0V 6 watts
6S6DC/120V 120.0V 6 watts
6S6DC/130V 130.0V 6 watts
6S6DC/30V 30.0V 6 watts<p>The 3S6 had only one option:<p>3S6/120V 120.0V 3 watts<p>Even in a pitch-black room, it was rare that you'd even see a glow from one of these lamps as an element in the oscillator circuit since it was there for the delta-resistance vs. the light output. I don't know how many students I've had that've built a Wein bridge oscillator using an incandescent lamp who, even after being told about the lamp's function, would tear down and rebuild the circuit many times because the lamp doesn't light up.<p>In all my years in metrology as a test equipment repair/calibration technician, I've never had to replace one of those lamps for any kind of failure, vibration or whatever.<p>Joseph, I'm certain that all tungsten lamps will exhibit similar curves with a shift of data depending upon the filament wattage, voltage, etc. Try it with a carbon filament lamp if you can find one.<p>Dean

[rshayes]

I found a partial copy of a HP205 manual. It has a serial number and a 1950 date noted on it, and the original seems to have been mimeographed. The schematic simply identifies the bulb as a 3 watt bulb. I suspect that this was later designated as the 3S6. There is an adjustment for the DC bias on the bulb. It was biased to about 20 volts, plus whatever AC voltage developed across it.<p>These 110 volt lamps seem to be a special case. They are not listed in the GE miniature lamp catalog that I have from the late 60's. They apparently weren't considered a miniature lamp. The original identification may have been simply the voltage and wattage, like normal illuminating light bulbs.

[toejam]

just to add, if you want a bulb to last a LOT longer and can accept a little less output put a diode in series with one.I wonder what a full wave bridge would do?

[Joseph]

Another time I used to my advantage the property of metal conductors like copper having a positive temperature coefficient of resistance was when one of my cars had some ground-down starter flywheel teeth. The problem would cause further grinding 5-10% of the time the key switch was engaged. What I did was to interpose an extra Ford-type solenoid between the original starter wire and the starter. I placed a length of 24 gauge solid copper wire in parallel with the Ford-type solenoid.<p>When I would turn the ignition switch, the 24 gauge wire would gently jolt the starter gear out and mesh it with the flywheel teeth, turning it about 0.5-1.0 inch. Then I would press a switch to engage the external solenoid to spin the starter and flywheel. I got around about a $350 repair bill on an old car that way.<p>toejam, I think a single diode cuts the voltage in half because half of each AC cycle is truncated. A full bridge would only reduce the voltage, compared to unrectified, by the diode voltage drop--very little. <p>Dean, when I googled a phrase containing such key words as light bulb, current vs. voltage, and graph, I saw how popular exploring the positive temperature coefficient of lamp filaments is now in schools. On a different note, I suspect that a night light bulb may work well in place of a 656 in many applications. Many even have brass screw ends which would make soldering wire connections easier.<p>Hmm, since carbon is not a metal, it would be interesting to check its temperature coefficient of resistance. The "on" as in "silicon" may provide a hint. I bet its resistance is relatively stable with temperature changes since it has been the most commonly used material in manufacturing resistors. Then it would tend to not be the best material for filaments since tungsten's positive tempco. provides some overload protection. I won't be too surprised now if some specialty bulbs come out with carbon nanotube filaments though.<p>Will, I find it interesting that your equations use different approaches. I must admit that I am not much of a mathematician. In the second equation, the b term somewhat correlates with the reciprocal of the filament resistance, while in the first, the key term, a, does not have an inverted relationship because the entire right side of the equation contains the reciprocal instead.<p>Edd, One of my former employers connected two incandescent bulbs in series as a hall/night light. That trick undoubtedly influenced my thinking. Though my heat lamps-in-series setup won't have an infinite lifespan, I don't think I would ever experience them burning out. Eighteen years is far from being an eon or even an epoch, but is a long time in relation to a person's lifespan.<p>I even tried a test of connecting all 4 heat lamps in series. Then I estimate that the power from each dropped to the 30w figure the .55 exponent, from the formula Stephen provided, predicts.<p>[ September 29, 2004: Message edited by: Joseph ]</p>