Brightness of bulbs depending on their watt level

[momowoo]

Homework Statement

Two 110-V light bulbs, one "25W" and the other "100W" are connected in series to a 110 V source. Then:
a. the current in the 100W bulb is greater than in the 25W bulb
b. the 25W bulb will be brighter
c. the current in the 100W bulb is greater than that in the 25W bulb
d. the voltage drop across both bulbs will be the same
e. the 100W bulb will be brighter

Homework Equations

P=IV=V^2/R=I^2*R

The Attempt at a Solution

I thought that the power would tell me which bulb is brighter, so I instantly saw 100W and assumed that bulb would be the brighter one. But the answer is b, which I totally don't understand. I'm guessing it might have to do with resistance, but every time I try to reason with the relevant equations, nothing makes sense to me.

 

[berkeman]

Yeah, it's not a great question, but I think the reasoning is this.

As you know, the current is the same through both, since they are in series, which eliminates a couple of the choices.

The Lower power bulb probably has a higher resistance (hence less current and power when correctly connected in a circuit), so equal voltage drops is out as an answer.

So you are left with which would be brighter when connected in series, which to me is not an obvious thing. Again, though, one has a higher resistance than the other, and the current is the same through both, so which would have the higher power dissipation (so put out the brighter dim light)?

 

[TSny]

I thought that the power would tell me which bulb is brighter, so I instantly saw 100W and assumed that bulb would be the brighter one. But the answer is b, which I totally don't understand.

A 100W bulb consumes 100W of electric power only if the potential difference across it is 110 V. When the two bulbs are connected in series across a 110 V source, does each bulb have a potential difference of 110 V?

I'm guessing it might have to do with resistance

Yes, good.

but every time I try to reason with the relevant equations, nothing makes sense to me.

If a bulb is rated at 100W when it has a potential difference of 110 V, can you find the resistance of the bulb?

 

[momowoo]

Resistance would be 110 ohms.

 

[phinds]

Resistance would be 110 ohms.

I suggest that you do a full analysis of this circuit, developing all voltages, currents, and power dissipation. The results are quite interesting.

 

[momowoo]

I'm unsure how to go about doing that. Do I use the bulb wattage as the power, or should I not because that isn't the true power they dissipate?

 

[phinds]

I'm unsure how to go about doing that. Do I use the bulb wattage as the power, or should I not because that isn't the true power they dissipate?

Analyze each bulb at full voltage to get the resistance and then do a circuit with those two resistances in series. Give us a picture when you've filled in all the values.

 

[momowoo]

https://drive.google.com/file/d/0B_PrsFZNgMynZWtvVXRFS3JHX0E/view?usp=sharing

 

[phinds]

https://drive.google.com/file/d/0B_PrsFZNgMynZWtvVXRFS3JHX0E/view?usp=sharing

I don't read sideways stuff. Makes my neck hurt.

 

[momowoo]

https://drive.google.com/file/d/0B_PrsFZNgMynZWtvVXRFS3JHX0E/view?usp=sharing

 

[phinds]

https://drive.google.com/file/d/0B_PrsFZNgMynZWtvVXRFS3JHX0E/view?usp=sharing

Excellent. Interesting to see the "100W" bulb only dissipating 4W, yes?

 

[momowoo]

Yes, very interesting haha. Thank you!