How do you compare incandescent light bulb brightness using mathematics/physics?

Question

I have two scenarios. The first is a 60 W bulb and a 100 W bulb that are both separately connected to a 120 V outlet. Which one is brighter using math/physics?

The second scenario is both bulbs are connected in series starting with 120 V then the 60 W then the 100 W then back to the 120 V source. Which one is brighter on this using physics and math?

Answer 1

1) No brainer, 100W bulb, duh

2) P = IV = V^2 / R, so R = V^2 / P

So the resistance of the bulb is inversely proportional to its power for a given voltage.

So the 60W bulb has more resistance than the 100W bulb

According to the voltage divider rule, the voltage across a resistor is

V = Vtotal (R / Rtotal)

V1 = Vtot (R1 / (R1+R2))
V2 = Vtot (R2 / (R1+R2))

Power = V^2 / R

Power1 = Vtot^2 R1 / (R1+R2)^2
Power2 = Vtot^2 R2 / (R1+R2)^2

So the power is proportional to the resistance, so the 60W bulb burns brighter in this scenario.

Answer 2

Good for you. I've been doing the same, as the incandescent bulbs blew out, but I'm about to simply purchase enough compact fluorescent bulbs so that the rest of my lighting is fluorescent. Well, other than the two lamps that have halogen bulbs. Contact your local government to check the recycling rules. Any environmental organization will also be able to answer this for you. However, how this can be done may vary from one jurisdiction to another, so the better place to go is to your local government. The waste here, in getting rid of the incandescent bulbs, is in the money that we all of us spent on them.

Answer 3

There are some empirical formulas that apply.

lumens/LUMENS = (watts/WATTS)^2.19

The exponent is 2.19 if the bulbs are gas-filled, or 2.22 if hey are under vacuum.

lumens = (60/100)2.19 * LUMENS

The output of the 60 watt bulb will be 0.32 as much as the 100 Watt bulb.


When they are connected in series, the power ratios are 37.5% for the 60W and 62.5% for the 100W.

lumens = (0.375/0.625)^2.19 * LUMENS

The 60W bulb will be 0.32 as bright as the 100W bulb.
This is exactly the same as when they were in parallel.
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