--------------------------------------------------------------
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

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Copyright 2000 Jim Phillips

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