```--------------------------------------------------------------
General Electric lamp life vs. voltage data.

The exponents in the table below and the characteristic curves
(not shown) show the effects of operating incandescent lamps
at other than rated voltage.  These characteristics are
averages of many lamps, and can be reduced to equations which
help predict lamp performance under varying conditions Values
given apply to lamps operated at efficiencies near normal, and
are accurate enough for calculations in this voltage range
normally encountered.  For operating voltages that differ from
design voltage by much more than 10%, the exponents become
progressively less reliable.  In the case of excessive
"undervoltage" burning, the theoretical life of lamps
calculated by the exponential relationship of life and voltage
is seldom realized because handling, cleaning, vibration, etc.
introduce breakage factors that reduce lamp life.

TABLE OF TYPICAL EXPONENTS
(Exponents for specific lamp types may differ significantly)
Gas-filled    Vacuum            Gas-filled    Vacuum
a     3.86          3.85        y     6.25          6.05
b     7.1           7.0         z     7.36          8.36
d    13.1          13.5         f     0.544         0.550
u    24.1          23.3         g     1.84          1.93
k     3.38          3.51        j     3.40          3.33
h     1.84          1.82        t     0.541         0.580
s     2.19          2.22        n     1.54          1.58

CAPITALS   REPRESENT   NORMAL   RATED   VALUES

a                         b
life         /  LUMENS  \         /  LUMENS/WATT  \
------   =   |  --------  |   =   |  -------------  |
LIFE         \  lumens  /         \  lumens/watt  /

d                     u
/  VOLTS  \         /  AMPERES  \
=   |  -------  |   =   |  ---------  |
\  volts  /         \  amperes  /

k                         h
lumens        /  volts  \         /  lumens/watt  \
------   =   |  -------  |   =   |  -------------  |
LUMENS        \  VOLTS  /         \  LUMENS/WATT  /

s                  y                 z
/ watts \       / amperes \         /  ohms \
=   |  -----  |  =  |  -------  |   =   |  ------ |
\ WATTS /       \ AMPERES /         \  OHMS /

f                   g
LUMENS/WATT         /  LUMENS  \         /  VOLTS  \
-------------  =   |  --------  |   =   |  -------  |
lumens/watt         \  lumens  /         \  VOLTS  /

j
/ amperes \
=  |  -------  |
\ AMPERES /

t
amperes         /  volts  \
---------   =   |  -------  |
AMPERES         \  VOLTS  /

n
watts          /  volts  \
-------    =   |  -------  |
WATTS          \  VOLTS  /

Assume that a gas-filled 120-volt lamp with l000-hour rated
life is to be operated at 130 volts. Its life Is calculated
from the equations:

13.1
life           /   120    \
------    =    |  --------  |    =    0.350
1000           \   130    /

Thus, average life in this service will be about 350 hours.
Changes in light output, wattage, and other characteristics
can be calculated by similar means.

Note Lumens is a measure of light output,  Lumens/watt
or Lumens per watt is a measure of lamp efficiency.

--------------------------------------------------------------
```
Note:

The above chart was one of many useful pieces of info contained in a thin pamphlet printed by General Electric simply titled Incandescent Lamps and on the outside cover I found this reference number TP-110R2 (5/84) it's probably out of print by now, but if you are lucky enough to find it, or a later reprint of it, snag it, and hang on to it. Incandescent lamps are a well established technology that are unlikely to undergo very much change in the coming years.

Finally:

Knowing the rated voltage, and wattage, of say a 120 volt, 100 watt light bulb, you can work out the resistance 144 ohms. From the chart above, using the operating, vs. design voltages of 0.75 volts to 120 volts ratio, which is the case if you measure the resistance of a 100 watt bulb with your trusty Micronta Multimeter on the Rx1 setting. This calculation can give you the theoretical current ratio of a gas filled lamp, using the second equation from the bottom of the chart. From there you can work the problem backward to get the Cold Filament resistance.

I get 14.0175 ohms, and as I've mentioned before when you actually measure a 100 watt 120 volt light bulb's Cold Filament resistance it stubbornly reads 10.0 ohms, so what's going on here?

The statement at the outset "For operating voltages that differ from design voltage by much more than 10%, the exponents become progressively less reliable." clearly warns you not to take these exponents too seriously when working with operating, vs. design voltage ratios wider than 0.9 to 1.0 and in my extreme example of 0.75 to 120 I demonstrate the limits of these calculations.

back to lesson 014

The large print Giveth, and the small print Taketh away