labougie, Welcome to the forum!
While the question is reasonable, and simple enough.....the answer is not quite as straight-forward....."traditional" bulbs (ie incandescent ) have a relatively fixed impedance comprised primarily of resistance hence the power consumption from any given bulb is primarily dictated by ohm's law E=iR --> P = iE ==> P = E^2/R ....So the power increases as a function of the voltage squared....Light output on the other hand is essentially an inverse square...that is in a traditional light bulb, the "brightness" increments roughly as the square of the power.....All this is to say that the resulting relationship between voltage and output is fairly linear......In a traditional incandescent bulb......However, LEDs are NOT linear devices...they are semi-conductors.....In the case of an LED, semiconductor means that the relationship between voltage and output are highly non-linear....Take a "10W LED Chip" as an example......(as luck would have it I am currently working on a design using exactly those, so happen to have test data on them)....Following is an abbreviated list of experimental readings taken from an actual Chip:
Code:
@6.8V current = 55mA power = 374mW......there is the first sign of a dim glow in one or two of the chip's segments....light output is just barely above zero
@7.2V all of the segments of the LED are dimly lit
@8.0V current = 83mA (power = 664mW) the entire chip is lit and is relatively bright with a
@8.2V current = 102mA (power = 837mW) the LEDs are considerably brighter
@8.5V current = 154mA (power = 1.309W) and the chip is fairly bright....If you leave the voltage constant @ 8.5V for several minutes the current slowly climbs to 160mA (power = 1.36W!)
**Note: The climb in current occurs because the LED is getting warmer....the warmer it gets, the more current will flow at any given voltage (more on that later) ....
@9.0V current = 260mA (power = 2.34W) the LED is perhaps 30% of "full power brightness"
NOTE: holding the voltage @ 9V the current fairly quickly rises to the 270mA level as the LED heats up...
from 9V onward I will report both the initial current and then the current after some specified time period(s)
@9.0V current = 270mA (power = 2.43W) time = 1 minute
@9.5V current = 375mA (power = 3.56W) time = initial NOTE: the LED is roughly 70% of "full brightness" and VERY WARM to the touch on a moderately sized heat sink...
@9.5V current = 430mA (power = 4.09W) time = 1 minute
NOTE: At this point Forced Air Cooling is Introduced
@9.5V current = 390mA (power = 3.71W) time = 30 seconds after forced air cooling begun
NOTE: It is important to note that the "brightness" is not perceptively effected by the change in temperature...just the power consumption.
@10.0V current = 550mA (power = 5.5W) time = initial .. roughly 80% of full brightness
NOTE: removed the forced air cooling
@10.0V current = 575mA (power = 5.75W) time = 15 Seconds after forced air cooling removed
@10.0V current = 600mA (power = 6.00W) time = 1 minute NOTE: the heat sink is HOT to the touch and the current continues to rise
@10.0V current = 620mA (power = 6.20W) time = 3 minutes NOTE: approaching equilibrium
NOTE: replaced the forced air cooling,
@10.0V current = 550mA (power = 5.50W) NOTE: no noticeable decrease in light output
@10.5V current = 650mA (power = 6.83W)
@10.5V current = 700mA (power = 7.35W) time = 1 minute NOTE: forced air cooling still on.....brightness is roughly 90% of the brightness @ full rated power
@10.5V current = 725mA (power = 7.60W) time = 3 minutes
NOTE: Removed Forced Air Cooling
@10.5V current = 750mA (power = 7.88W) time = 15 Seconds
@10.5V current = 780mA (power = 8.20W) time = 1 minute
@10.5V current = 800mA (power = 8.40W) time = 3 minutes NOTE: Heat Sink VERY HOT
NOTE: Forced Air cooling resumed
@10.5V current = 725mA (power = 7.60W) time = 1 minute
@11.0V current = 920mA (power = 10.12W) ***Rated Power*** NOTE: only a very slight increase in brightness from the 10.5V / 725mA
I should point out that identical chips taken from the same batch have some variation in the Voltage/Current .... the extreme variation in current for the 10.0V point at similar temperatures was 85mA with the majority of the chips measuring 550mA +/- 20mA...the highest was 595mA and the lowest was 510mA...there were a total of 10 chips tested....
So, to answer your question directly, NO, you cannot expect a linear light output based on a "fixed voltage", NOR should you expect an LED rated @ 12V to actually be able to handle 12V....however, in the specific case cited above it turns out that 9.0V was actually roughly 30% of full brightness light output and that by 9.5V the brightness was ~70% of full brightness...since typical batteries are nominally rated (voltage @ some specific current) their Actual measured no-load voltage is typically higher than the reference voltage specified....for instance a 12V car battery might have a measured voltage of 12.8V even though its nominal rating is 12V...to charge a 12V car battery requires ~14V, so while you might think of your car having a 12V electrical system, the typical measured voltage of a car's voltage is 14.4V...all of which is to say that just because you have a battery with a nominal voltage of 9V does not mean that the measured voltage might not be 9.5V to 10V depending on they type of battery.....
In general Hi-Power LEDs need to be driven by specially designed Constant Current drivers...the amount of light output is primarily a function of current and temperature...the voltage is constantly adjusted....
Good Luck!
Fish